Negative Doubles - Tthe Final Word (Hopefully!)

One would think that after 3 blog posts I would have nothing more to say about negative doubles. I have discovered that trying to put finality to any bridge discussion is like raking up leaves in a windstorm. I was playing south in Ocala on Thursday, paired with Barbara Burgess, a new partner for me, but one of the best in ODBC.

Barbara opened 1 diamond, her LHO bid 2 clubs and I held something like KJxx, Q10xx, Jx, Axx. “Aha”, I said, classic negative double showing both majors, so I pulled out the double card and slid it on the table. Partner now bid 3 hearts. I could not resist the urge to show off a bit, and since I had a squarish 4-4-3-2, I thought I would offer her a choice of games. The thought also occurred to me that Barbara may have started with something like Axx, AQx, xx, Kxxxx and her heart raise could have been a “least worst” choice. In any event, I bid 3NT and Barbara passed. She did have 4 hearts, but a very minimum hand and 3NT "sunk like a rock." Each of us were careful not to start a food fight on the 2nd board of the day, but as it turned out Barbara felt that I only needed one major to make my negative double and that my bid of 3NT said you have hit my short major, but I have a club stopper.

The issue is “does 1d/2c/x guarantee both majors or can that negative double be made with a single major?” I turned to World Champion Mike Lawrence to get his take on this. Mike in his excellent book Double! New Meanings for Old Bids (2002) says in the 1d/2c/x sequence opener’s expectation should be that the negative double shows 4-4 in the majors, but responder can make the call with 4-3 in the majors, or even 4-2 in the majors, if he can afford to escape to 2NT when opener bids his short major. Here are two hands that are not 4-4 in the majors, and yet are good enough, according to our World Champion, to make a negative double after a 1d/2c sequence. (i) JT73, Q8, A742, KJ3 and (ii) J3, AJ83, KJT4, 763. Karen Walker (Bridge Bulletin Columnist) on her web site shows this hand as being good enough for a negative double with 4-3 in the majors: KT63, 762, K72, AJ3. She says that the double shows an invitational hand with a club stopper. Since you started with a negative double rather than 2NT, partner will know that you hold a 4 card major. Well done Karen! Got a game next week?

I also looked in Max Hardy's treatise Standard Bridge Bidding for the 21st Century (2000). Max shows an example KJ86, AJ9, 64, T742. Max is not thrilled about the hand, but says that a negative double is the best of the numerous evil choices. I think it helps that the hand has 4 clubs and 2 heart honors.

I think the bottom line is "Do you have a solution if partner bids your short major suit?" If so, you can afford the luxury of making the negative double with only 2 or 3 cards in one of the majors. So, Barbara was correct that my rebid of 3NT should be interpreted as a warning that “I may be short in hearts.” So much for being clever! If I just bid 4 hearts we go from 0 to 12 match points!

You may be asking what does responder do with 1d/2c/ holding KJxx, Qxx, Axx, xxx. I am open for suggestions, and until I get a good one, I’m going to pass.

While I was studying the problem I glanced down at Mike Lawrence’s discussion of the sequence 1c/1d/x. I knew that showed 4-4 in the majors (no ifs, ands, ors or buts about it!) and this was reading just to restore some of my shattered confidence. I found the agreement I was looking for: the negative double shows both majors, but hold on —Holy Cow – Mike says it doesn’t have to be 4-4; it often can be 5-4 in the majors. Mike suggests that experience shows that there are hands where it is appropriate to double the 1c/1d sequence holding hands like these: AJ73, J8543, 543, 3. He says if you bid 1 heart and the next opponent bids 2 diamonds, you might loose the spade suit. Also with KJ973, Q543, 54, Q3, same idea and same reasoning. If you bid 1 spade opponent can raise diamonds and you may loose a potential heart fit. Even with as much as this: KJ73, AQ762, 32, 82, negative double as well. Mike says that he inquired among his fellow experts and found no rule of thumb, but that he believes you need a good 11 hcps before you try to bid out 5-4 major suit hands in the 1c/1d/ sequence.

Does this contradict the rule that you double when you have a 4 card suit and bid the suit if you have 5 cards in the suit? No, that rule applies only to auctions where your negative double is showing only a single major such as 1d/1h/x. It has no application to auctions that start out with a minor suit opening and a minor suit overcall.

People ask me where I get my ideas for blog posts. Almost all of them are prompted by things I see at the table week in and week out. Most often if you look, at the center of the controversy you will see my face buried in my hands!

Support Doubles Made Simple

It seems logical to discuss support doubles after finishing negative doubles. They are both actions that let you convey multiple pieces of information to partner with one bid, saving a level of bidding space. The other thing they have in common is that the advantage achieved by those two actions could not be enjoyed without the opponent’s assistance and cooperation. Thanks for the overcall! As opener, after 1d/p/1h, I often find myself internally cheering for RHO to make an overcall. Without an overcall, I am going to have trouble finding out if my partner holds 4 hearts or 5 hearts, since “pass” takes away my support double. If you are defending in that sequence, do you ever think “should I pass on this worthless overcall and take away their support double?” To my opponents who love to make aggressive and questionable overcalls, keep it up, we couldn’t get to our best contracts without you!

Unlike the negative double which is always made by responder, the support double is always made by the opening bidder at his second opportunity to bid. The bidding goes 1d/p/1s/2c/?: You hold Axx, Kx, AQxx, xx. You show 3 card support for partner’s spades by doubling 2 clubs. This bid does not limit the size of opener’s hand, it merely shows 3 card support, denies 4 card support and transfers control of the hand to responder. If responder has a 5 card spade suit you are going to play in some number of spades, depending on the size of responder’s hand. If he has only 4 spades, he can try for no trump or play the 7 card trump suit.

Suppose on the same bidding you held Axxx, Kxx, AQxx, xx. You now need to tell responder a different story; that you have 4 card support. With this minimum hand you would do that by bidding 2 spades over the opponents 2 club overcall. Note: here you can also show the size of your hand. With 12-15 bid 2 spades, with 16-18 bid 3 spades and with 19+ bid 4 spades.

Assume we change the bidding to 1d/p/1s/x: With three card support as in my first example, make a support redouble, it means the same thing as “double” in our earlier context. If you have the second hand, simply bid 2 spades to show 4 card support. Support Doubles or Redoubles Must be Alerted.

What do you do if you do not have either 3 or 4 card support. If you don’t have a strong hand you can always pass, partner will have another bid. If you have some defensive tricks and are strong in the opponent's overcalled suit, you must pass and hope that partner will double back in so that you can pass his double for penalties.

Is making the support double or redouble obligatory with 3 card support? I think the best rule is to play that you must show the support if you have it. Max Hardy says that opener has an obligation to double or redouble if he has a 3 card fit for partner’s bid suit. One advantage of playing support doubles “mandatory” is that you know when opener passes he has 2 or fewer cards in your bid major. I believe that with this understanding it is appropriate to alert the pass as denying support.

Use support doubles only when you do not know whether responder has a 4 or 5+ card suit. If responder’s bidding clearly indicates that he has either a 4 card suit or a 5+ card suit, then support doubles are off. So if the bidding goes 1d/1h/1s/2h/, we know that partner by bidding his spade suit, rather than making a negative double, is showing 5 spades, so a double of 2 hearts at this time would be for penalties! I credit my partner, Howard Christ for this analysis, but I like it.

If you agree to play support doubles (as each of your should) it is important to decide how high to play them. Here is a workable rule: Play support doubles on every conceivable auction up to the level of 2 of responder’s bid suit.

Bob Scarbrough and I were playing recently when Bob opened his hand with one diamond. I responded one heart, and my LHO bid one spade. Bob held Qx , QJx, AQJxxx, xx and choose to rebid his 6 card minor suit and eschew the support double. As it turns out, I have a 5 card heart suit and we can compete effectively in hearts. I tactfully whispered “Support Double.” Bob replied, “Do some research, I want better authority.”

Mike Lawrence in his book “Double” (2002) gives us this hand. 86, KQ8, J10, AQ7842. The bidding is 1c/p/1h/2d/?. Mike says don’t rebid your 6 card minor, you must make the support double. If you have a really big hand you can rebid the minor on the next round. Max Hardy in his book “Advanced Bidding for the 21st Century” (2000) on similar bidding shows K84, 84, AKJ1062, J8. and says make a support double, it is more important to show 3 card support for spades than your 6 card diamond suit.

For the record, the controversy is still unresolved, as Bob maintains that Mike is too old and Max is dead. It is nimble thinking like that keeps us going! Who can quarrel with that cogent analysis?

Making Negative Doubles Postive (Part 3)

In my recent blog Making Negative Doubles Positive (Part 2) I referred to Mel Colchamiro’s "Rule of Nine.” To use the term “Rule” is sort of a misnomer, as they are really guidelines. What is the distinction? Guidelines can be breached, but if you do, you better be right!

The Rule of Nine is used for determining when it is appropriate to convert partner’s take out double to penalty double. In Part 2 of my recent Negative Double blog, the rule was mentioned in the context of a reopening double in a sequence like 1h/2d/p/p/x/p/? Partner’s double here is effectively asking you to bid, but sometimes you will have passed with a trump stack in overcaller’s suit hoping that opener will re-open with a take out double and give you a chance to convert the take out double to a penalty double. This is overcaller’s worst nightmare—he has been caught speeding at the wrong time against the wrong opponents and is about to get a bloody nose, a dose of humility and a bottom board.

The Rule of Nine gives us a guideline as to when it is safe to pass for penalties and when we must bid, even though defending may look juicy. Here is the basic rule: Add together your cards in opponents suit plus your honors in that suit plus the level of the bid, and if they total nine or more, then smile and pass partner’s take out double. This rule can be applied to all situations where partner has made a take out double and you are thinking of passing.

Here is an example of the application of the Rule of Nine: Partner is the opening bidder. The bidding is 1h/2d/p/p/x/p/? You hold xxx, Kx, AQ987, xxx. You can’t bid a suit or make a negative double so you pass to see what partner will do. Happy Day, he re-enters the bidding with a take out double. You say, aha, lets see if we can count to nine! You have 5 trump plus two honors and the bid level is two so 5+2+2 =9 and you pass, hoping no one will notice the saliva on your chin.

If you have the capacity to remember a couple of refinements, then you can enhance your results: (a) when you have doubleton or trebleton honors such as AQ or KQJ etc. make it the Rule of 10. One of those honors may get smothered and be a non-counter (b) if you have two sure defensive tricks outside the trump suit, it is discretionary to let the double stand even though your count is only eight and (c) if the opponents open the bidding at the four level, it often will be correct to leave the double in even if you don’t meet the Rule of Nine, If you have a squarish hand and at least 1 defensive trick, leaving the double in will be better than contracting for 11 tricks in a minor or 10 tricks in spades. When you have length in your suits and distribution, then it is more likely to be correct to bid. If the basic rule is all you remember, you will be money ahead and right most of the time. There are no guarantees, but if you are correct 75% of the time, that will produce a nice score.

There are two further points to keep in mind. First, the Rule of Nine is a matchpoint rule and is not always correct if the scoring is IMPs. Second, this rule is not a rule telling you when it is correct to double opponents, it tells you when to convert partner’s take out double to a penalty double.

My favorite team game partners are Carolyn Waugh, Barbara Burgess and Patty Luther. Plenty of competitiveness, ample competence and adequate patience. They drag me along for comic relief. Last Thursday I was a spectator as Barbara and Patty were put to the test in a difficult hand. My post round analysis was flawless since I had forever to decide what to do and had just finished my blog on Making Negative Doubles Positive (Part 2). Barbara is the dealer and holds KQxx, xxxx, KQxx, A. Even I can get that opened with one diamond! LHO overcalls 1 heart and there is no further competitive bidding. Patty has to make a call with 10xxx, void, Axx, KQxxxx. Here is your first chance to stumble. I hope, like Patty, you ignored the club bid and made a negative double. Yes, even with those ratty spades and 6 nice clubs.

Back now to Barbara’s hand, she of course bid spades, but what is the correct level. Remember in my blog I said a jump bid in response to a negative double shows 16-18 points. I also said that this is not a hard number and subject to the usual valuation adjustments for fit and playability. Should Barbara jump to 2 spades? There is a fit, so how do you value the singleton club Ace? Remember, that the only game force bid is a cue bid in the overcalled suit. The obvious weakness is the 4 small hearts. Do you want to inspire partner or slow partner down? You pick!

Now we have it back to Patty. We know there is a fit and so we now have to revalue Patty’s hand and find the correct call. Patty’s nine high just got huge. Not only does she have the club suit with the KQ in the sequence (always better to have length and touching honors, this hand has both) but we also have a heart void and an Ace. What do you say, bid game, make a game forcing cue bid in hearts, or invite with 3 spades?

This the type of hand that can produce big swings in IMP scoring because it requires both partners to look beyond hcps and assess the true playability of the fit. If Barbara’s raise is 1 spade, then she has limited her hand and slam is not in the cards. But, if Patty now bids 3 spades, Barbara can pass, so my bid is 4 spades, I don’t want to play this hand short of game with IMP scoring.

If Barbara jumped the bidding to 2 spades, then I might make a game forcing cue bid of 3 hearts to get another bid out of partner before I give up on slam. Barbara could have as much as 18 hcps and still bid 2 spades. Since she is really on a minimum for that double raise, I would hope that she would spike the balloon by bidding 4 spades.

What did my partner’s do? I told you that they are good didn’t I. I will give you a clue, we won the round by 26 IMPs. In team games, it is only the end result that counts. Them things ain’t no beauty contest. But even if it were, my team would contend.

Making Negative Doubles Positive (Part 2)

When I started on Negative Doubles, I didn’t know there would be a Part 2. I thought all you had to do was “double” and now it becomes partner’s problem. It escaped my ever diminishing mind that half the time I would be the partner. We all remember the good times when we have the suit fit, and put behind us those awkward times when all we have is a misfit.

You are the opening bidder, opponents overcalled and partner made a negative double and it has rolled back around to you for action. It’s a happy day – we have a four+ card fit for one or more of the suits that partner advertised with his negative double. You may simply show support for that suit. The level of your supporting rebid will depend on the strength of your hand. I don’t want to minimize the importance of “hand evaluation,” so here is a guideline subject to adjustment for hand quality.

With 12-15 hcps make a single raise in the indicated suit, with 16-17 hcps make a jump raise and with 18-19 bid game. The only real decision will be on the 15 hcp hand. If it is over balanced with Aces and Kings, has good middle cards or has honors sequentially located in single suits, you might want to upgrade it to a jump raise. I might note that none of these bids are forcing. Also note that you are limiting your hand by the level of your supporting bid, but partner (the negative doubler) is still unlimited, so control of the hand is now with responder.

If you have a hand that is worth more than 19 hcps or that has some exceptional playing strength, but did not fit a 2NT or 2 club opening, you must tell the negative doubler that. The way to announce this “monster” is to cue bid the overcaller’s suit. This bid is a “tell me more bid” and “says nothing, nor asks nothing” about their suit. It is simply a game forcing bid (the only forcing rebid opener can make) and responder should further describe his hand as best he can.

Here are some examples: (a) The bidding is 1c/2s/x. As opener you hold (i) xx, AQxx, Qxx, AQxx. (ii) Axxx, AQxx, x, AKQx. (iii) xx, AKxx, xxx, AKJx. With (i) make a single raise, with (ii) bid game and with (iii) we have a very robust 15 hcps and I upgrade it to a jump raise.

Things have gone food so far, but what if you do not have the suit or suits that responder indicated with his negative double? If you have 6 cards in your bid major, you can rebid the suit. If you have a secondary suit that has not been bid or shown you can bid that. I hate rebidding 5 card suits, but if you have a very solid 5 carder and have no better bid, you may have to rebid it. If you have a stopper in the opponents overcalled suit, you can bid no trump. If you have to go to the 2NT level, you better hope that partner did not shade his strength when he decided to negative double, because you are going to need it. Remember the Rule of 23? If none of these solutions work, tell the best lie. After all, partner has to have something for his negative double, and if he does not, we will hereinafter refer to him as “ex-partner.”

Here are some examples. The bidding has gone 1d/2c/x. This shows both majors in my book and remember, while you could have bid 1 heart over 1 diamond without the overcall with 6 hcps, I recommend that you have 8 hcps in this sequence for your negative double. As opener you hold: (i) Qx, AQx, KQJxx, xxx (ii) Qxx, AQx, AQJxx, Kx (iii) Qxx, Kxx, AQJx, xxx. With (i) I may just bid 2 diamonds and hope that partner has at least 2 of them. The other alternative is bid 2NT, not at all appealing from my side. If partner has any extras and a club stopper, maybe he will bid 2NT over my 2 diamonds. At least the opening lead would come up to him. Two diamonds is my bid. (ii) With 18 hcps and a club stopper, I would jump right to 3NT. (iii) Who opened this hand anyway? A pass would have been nice with only 12 hcps and square hand. I rate to get murdered in 2NT. I am going to bid 2 hearts with only 3 card support and hope for the best in this 7 card fit. Where is Sonny Moyse when I need him?

What is responder saying when he passes an overcall? One of two things: Responder either has a stack in the overcalled suit and can’t double (since it would be negative) or partner does not have the strength or correct shape to take action.

Assume the bidding goes 1d/2c/p/p. What are opener’s obligations to reopen the bidding with a double. Remember that you heard it here: Be very careful about doubling back in if you have length in the overcalled suit. The more cards you have in the overcalled suit, the more it looks like the reason partner did not bid is that he’s broke. When opener is short in the overcalled suit, then the possibility that responder made a trap pass looms more likely.

If you have a minimum opening hand double back in at the 1 or 2 level if you have 2 or fewer cards in opponent’s suit. If you are doubling back in at the 3 level with a minimum hand you should have a singleton in opponent’s overcalled suit. Doubling back in with 3 cards in opponent’s suit is dangerous. Even with extra values, pass may be correct. If you want to see an example of a correct reopening double see example (d) (3) in part one of Negative Doubles. In my next blog I will explain Mel Colchamiro’s Rule of 9. When you have that you will know whether to leave the double in or pull it.

Now we finish off with responder’s rebid after his negative double. If opener has made a simple raise in your indicated suit, you can invite to game by a further raise. Alternatively, if opener did not bid your suit, you can venture to 2NT. Both of these actions require about 11 hcps. Responder can also bid a new suit not shown by the original negative double or actually bid one of the suits shown by the negative double. Responder bidding a suit after a negative double almost always shows a 6 card suit that could not be bid on the first response and is to play. Just as we saw with opener’s rebid, none of these rebids by responder are forcing. If responder wants to force to game he must cue bid opponents overcalled suit. Again this doesn’t ask for or tell a stopper, it just says “tell me more.” Responder has now taken charge of the hand. To cue bid after a negative double responder needs 13+ hcps

The requirements for negative doubles that I have laid out in my blog posts are the ones that I think will work the best for most club players. Get on the same page with your partner and when you see an overcall in front of you, before you think about bidding, always consider a negative double first. My guess is that in a normal club session, almost as many negative double are missed as are made.

Making Negative Doubles Positive (Part 1)

I learned all I thought I would ever need to know about bridge in the fraternity house over 50 years ago. The rules were simple. No matter what you held, you opened one club. Another time honored rule was that you doubled whenever you were really ticked off, often over an overcall to intimidate the opponents and get partner’s juices flowing. Doubles were an omnibus bid like 1 club, and were only negative in the sense that if partner did not save you, the opponents would usually make the contract with several overtricks. The redouble was also frequently used, not as SOS, but as a bluffing macho move. The only other thing you needed to know was the phrase “not through the iron duke” which was repeated every time you covered an honor with an honor. In the end we seldom knew who won or lost, and if you did lose, you accused the opponents of using hand signals. Rubbing an eye brow was much in vogue!

This is a long explanation of why 50 years later negative doubles never seem to jump to the front of my brain. It is not uncommon for me to write on subjects that don’t store well in my mind, so here is a basic review of negative doubles—a primer if you will for others who may have experienced something like fraternity/sorority house bridge.

1. Recognition: True negative doubles only occur when partner has opened the bidding at one of a suit and his LHO has made an overcall. So in all bid/direct overcall sequences, you first instinct should be to see if a negative double will work to more fully describe your hand and keep the bidding one level lower.

2. Distribution: Since this is basic, let me make this very simple. In all bid/overcall sequences other than the major/minor or minor/major sequences, your negative double shows 4 cards in all unbid suits. In the major/minor sequences, you negative double shows 4 cards in the unbid major only.

3. High Card Points: Again, trying to demystify, you can make a negative double if you would have bid your suit had there been no overcall. For example, if the bidding is 1c/1h/x, you are showing a 4 card spade suit. Since without the overcall you would have bid 1 spade with a bad 6 hcps, that is all you need to negative double. There is one exception, if the bidding is 1d/2c, look for 8 and not 6 hcps. You will find out why in time!

4. When is a Double Negative? Until you have a reason to change the rule, make negative doubles “ON” through 3 spades. Mark this on your card and make sure you and partner are on the same page. Thus, if opponents make a 4 club or 4 diamond jump overcall, a double is for penalties. Gobble Gobble!

5. Five Card Suits: We have assumed until now that the suits shown by the negative double are 4 cards in length. What do you do if you hold a 5 card suit? You bid the suit rather than make a negative double so partner will know that you hold 5+ cards in the suit. There is one significant exception to this rule. If you hold a 5 card suit, but do not have sufficient points to make a free bid (e.g. 10 points at the 2 level), then you can make a negative double to show the suit even though it is 5 cards in length.

Testing the Basics: (See answers at the end).
(a) The bidding is 1c/1s/? You hold (i) Qx, Kxxx, xxxx, xxx? (ii) Axx, xxxx, Qx Kxxx (iii) QJx, KQxxx, Qxx, xx.
(b) The bidding is 1d/2c/? You hold (i) Kx, Qxxx, Kxxx, xxx (ii) xxxx, xxxx, Kx, KQx (iii) Kxxx, KQxx, AKxx, A.
(c) The bidding is 1s/2h/? You hold (i) xxx, Qx, Axxx, Kxxx (ii) x, QJxx, AQxx, Kxxx (iii) xx, xx, KQxxx, Kxxx.
(d) The bidding is 1h/3d/? You hold (i) KQxx, Jx, xx, Axxxx (ii) Kxxxx, AJX, xx, Axxx (iii) Kxx, Kx, AQxxx, xxxx.

My bidding Choices:
(a) (i) Pass. The Queen of spades is probably dead meat and this may be a 3 hcp hand. (ii) This is a nice negative double despite my 4 small hearts. I also have some defense if opponents get too high. I also like my spade stopper if partner wants to play no trump. (iii) With 5 hearts and 10 hcps I bid 2 hearts. Now if partner has 3 card support we have found an 8 card heart suit. If the hand only had 8 hcps and not 10, I would make a negative double.

(b) (i) I am going to pass without four spades to go with my four hearts. What do I bid if partner bids 2 spades over my negative double? When you figure this out you can change the rule! (ii) The same strength as (i) but with 4-4 in the majors I make a negative double. My minor suit honors make this a very attractive no trump hand as well. (iii) Negative double of course. I have 19 hcps, but the negative double is not limited in hcps. This smells slamish and with my single club may play better in a major suit contract if we have an 8 card fit. There is plenty of time to show my strength after partner further describes his hand.

(c) (i) I have the right holding for a negative double but I also have 3 card support for partner's spades. Support majors with support! I am going to bid 2 spades and forget the negative double. It will be the last chance I have to show my spade support at the 2 level. (ii) I am going to make a negative double to show my 4-4 in the minors. With my 12 hcps and good hearts, the right spot may be 3 NT, but a negative double is a good way to start to describe this hand. (iii) Over 1 spade I would not bid 2 diamonds (not enough for a free bid) so I am not going to negative double. Pass and wait to see what partner does.

(d) (i) Since negative doubles are on through 3 spades, I am going to double to show my nice 4 card spade suit with a negative double. Note that negative doubles are on over jump overcalls as well. Forget about your 5 clubs. (ii) With 5 spades I bid 3 spades, hoping to catch partner with 3 card support. (iii) Pass smoothly. Partner has a diamond shortage and will assume you have made a trap pass and double back in. When he does make another smooth pass and get out your calculator.

Once of my favorite subjects is the pitfalls of "meaningless overcalls." Have you noticed how much easier RHO’s overcall has made it to describe some of these hands? Absolutely essential in many cases. Think about that the next time you consider making a crap overcall! Part 2 of the sequence will deal with bidding action following the negative double. Happy Thanksgiving to all readers.

Mel's Rules of 23

Earlier on this Blog I reviewed Mel Colchamiro’s Book, How to Play Like an Expert (Without really being One). One of the ways to be successful in bridge is to have enormous natural talent. Just as we have Savants in every other endeavor, we have them in bridge. Sadly, there are a lot less of those than players who profess to be. The rest of us rely on bridge standards, partnership agreements and following a bunch of rules. One of the rules that Mel’s book hands down to us is the Rule of 23. Actually there are 2 Rules of 23 according to Mel, and he ought to know, it is his book.

Here is the 1st Rule of 23. After the first round of bidding, neither partner will bid 2NT unless he can determine, with reasonable certainty, that the partnership has at least 23 hcps. Actually, I added the words “reasonable certainty.” I know, you are thinking a lawyer always has to use “weasel words” to add maneuvering room. Well, you could look at it that way, but my emphasis was more to prevent inventing the best possible hand that partner could have and then adding that total to your total, getting 22 and saying “close enough.”

Why do we have this rule? Only because it takes 23 points to make 2NT! I know, you are saying, “Wait a minute, I was in 3NT last week with 22 points and made 4.” Believe me, remembering and recalling all of your big success stories is a significant hindrance to long term success. Soon they become a standard in your mind. Your anomalous hand of the decade has not changed the basic math of bridge. Assuming good defense, it still takes 26 points on average to make 3NT and 23 points to make 2NT. If you have fewer than 23 hcps, experience has shown that you are better off playing a contract in a suit at the 2 level, even if you have to play it in a 7 card trump suit. Remember, in a suit contract your little trump will often cash.

If it is your turn to bid and 2NT is an option, you simply count your points and then add to them the minimum hand that partner can have given his bidding. Note that I said minimum, not maximum. So if the bidding has gone 1d/1NT (6-9), you would have to have 17 hcps to now bid 2NT since partner has a minimum of 6. If the bidding went 1c/1h/1NT (12-14), don’t bid 2NT unless you have 11 hcps.

I saw this rule in application in a recent Frank Stewart bidding quiz. You hold KT, xx, AQxxx, KQT3. You open 1 diamond, partner responds 1 spade, you bid 2 clubs, he bids 2NT, what action you take? If you can rely on partner to apply the Rule of 23, you know he would not have bid 2NT unless he could guarantee our combined holding to be a minimum of 23 hcps. Since your bidding has shown no more than 12, he must have at least 11. While your hand only has 14, they are a strong 14 (3 kings, an ace and concentrated honors ) so you should bid 3NT. The good news is so did Frank Stewart, and he didn’t even know the Rule of 23. Unlike some of Mel’s Rules, this is one that can be applied unilaterally with any disciplined partner.

Here is the 2nd Rule of 23. If the game is match points and you are in a competitive auction, if from the bidding you can ascertain with reasonable certainty that you and your partner have a combined 23 hcps, either you play the contract or they play it doubled. Is this risky business, stuff authors write about, but that mortals never apply? Not at all, after all these rules are supposed to make us play like an expert. It would be helpful if you defend like one as well. Will you "take the pipe" on occasion? Of course, and you get all those insidious grins that go along with it, but it is a good long term percentage play. Remember, this is match points and two bottoms and 3 tops still average 60%. Mel’s take on this is quite interesting, he says if opponents make a contract when you and partner hold a combined 23 hcps, you likely were fixed either way, so not much was lost with the double.

How are you going to remember the Rule of 23? For me it’s 23 Skidoo. Adios.

Getting Life and Bridge in Balance

Despite major efforts of the ACBL and the club directors throughout our ACBL domain, the major complaint about our bridge populace is that as a group we are still intimidating, take ourselves and the game too seriously and at times can be downright rude. I know, you have heard it all before and you are all smiles and sweetness. It’s just those other people who can’t take a flaming fix and congratulate the opponents on their success and creativity. Let’s all make a special effort in 2009 to make friends for ourselves and friends for duplicate bridge as well. You will like yourself better and others will like you better as well.

George S. Coffin was a noted bridge expert, writer, publisher and a well respected competitor. In 1970 he wrote “Grace at the Bridge Table” for the MIT Tuesday evening bridge club. I feel whether you are religious or not, the sense of his writing is worth repeating here:

Grace at the Bridge Table

Oh Lord, grant us this session of bridge for our enlightenment and bring forth only the good from the alleged Devil’s Picture Book, the 52 pieces which thou has snatched from Hell and rendered so beneficial.

Please show us we came here not to inflate our vanity by winning but to train and salve the soul in humility and good fellowship.

May we learn from Thee, in life as in bridge, the habit and power of constructive thought, the growth of reason, the development of imagination and self control in all things that we do; also how to befriend our enemies by communication and cooperation.

Please teach us, Oh Lord, that bridge is a relaxing hobby and only a game to play for fun. Let us play now as if this were the last session on earth, yet plan as if we are going to play forever.

Blessed are the losers, for they shall inherit all the bridge games on earth. Amen

Let’s all take the sense of George’s thoughts and make bridge a better place than we found it. Tomorrow is not to early to start. Practice makes perfect.

Bidding Control Cards (Part 2)

In Rule 5 of my last blog post, “Cue Bids and Control Bids (Part 1)”, I made the statement that the partner in charge of the hand initiates the control bidding process. I also said that the initiating bid may or may not show a control. Actually, most of the time it does show a control (ace or void), but the point is that it really doesn’t matter since the initiating partner is interrogating the responding partner about his controls and also has the ultimate responsibility of evaluating slam probabilities and setting the contract. The reason for the initiating partner to initiate with a control is to avoid stepping responder’s control and forcing him to show it one level higher. The ultimate object is to make it as convenient as possible for responder to show any controls he has at the lowest possible level. A few examples will best illustrate the process.

Strong Playing Hands with Voids:
As noted in part 1, discovering the viability of slams where one of the hands has a void is a prime use of control bidding. Assume I hold AKxxxxx, KQJ, KQx, void. After the 1s/3s sequence, I am interested in slam even though I have only have 18 hcps. As responder you hold QJxx, xxxx, Ax, QJx. I assume that you must have at least one Ace to make a limit raise, but I need to know if the Ace is in diamonds or hearts (and bid 6 spades) or in clubs (and settle for 4 spades). I am in control and I want to ask you to show your controls. As long as my next bid is not in spades and is more than 3NT, your only duty is to tell your story. My initiating bid in this case is 4 clubs! I am making an efficient forcing bid to make it easy for you to show any of your first round controls. With none you would bid 4 spades.

You respond 4 diamonds showing the Ace of diamonds and, since we bid controls “up the line”, your bid denies holding the Ace of clubs. I now start to bid 6 spades, but wait, you could also have the Ace of hearts and then I want to be in 7. I can now bid 4 hearts, asking you to show any higher ranking control cards that you might hold. The 4 heart bid does not say anything about my heart controls, it simply minimizes the level of the bidding and asks you to continue. In this case you bid 4 spades denying the ace of hearts so I now bid 6 spades.

Strong Playing Hands with Worthless Doubleton:
In a second example I hold AKxxx, AK, KQJx, xx. I want to be in slam if you have the Ace of clubs, but in 4 spades if you do not hold that card. You hold QJxx, QJxx, xxx, Axx. No matter how many points we have, if opponents have two tricks off the top, we want to stay at the 5 level. I initiate the cue bid process with a convenient bid of 4 hearts. If you bid 4 spades I know you are aceless. Actually, you bid 5 clubs showing first round control in clubs, and I now want to play this hand in at least 6 spades. You could also hold the Ace of diamonds or the King of clubs, or both (a really good day). Since we bid controls up the line and first round controls first, your bid of 5 clubs did not deny holding either of those cards. How would you continue the bidding to make a further investigation? See my suggestion at the end of this post.

Low Level Exploration:
In my last example I hold AKxxx, x, KQxx, Axx. The bidding is the same 1s/3s. An optimist (we will call him Howard!) will see partner holding (a) Qxxx, Qxxx. Axx, Kx. Slam is just there for the taking. A pessimist will realize that partner may well hold hand (b) Jxxx, AQx, Jxx, Qxx. The pessimist bids 4 spades and considers it may be a better than average board if some other pairs get too ambitious, make a key card 4NT probe and potentially get set at 5 spades.

Howard will see that he can pursue slam and get vital information without going past the opportunity to stop at 4 spades. He bids 4 clubs asking for controls. If partner holds hand (a), he bids 4 diamonds (the Ace of Diamonds). Howard now knows that 11 tricks are not a risk so he bids 4 hearts to see what else partner might have. After all he showed 10-12 points and we have discovered only 4. When he hears 5 clubs, this both shows the King of clubs and denies the Ace of hearts. He now bids 6 spades for a high board.

Let’s assume partner actually held hand (b). Our bid of 4 clubs is going to roust out a bid of 4 hearts from partner showing the Ace of hearts but denying the Ace of diamonds. Since this is the suit in which we hold a singleton, we sense that there may be a duplication of values and that partner’s points may not working points. In reality we can see it is not a high percentage slam, and we would do well to simply bid 4 spades and get out. The point to be made is that he got out at 4 spades and not 5 spades.

Avoiding Gerber Confusion when No Trump is Bid.
My convention cards have always stated that if the first or last bid is no trump, then 4 clubs is Gerber. I am not sure where I got this "pearl of wisdom", but it recently caused me to contract for 12 tricks when on a good day the hands could only make 10. Part of the confusion was ignoring my own card and bidding 4 clubs asking partner for controls. Although no trump was not the opening bid, the bid last preceding my 4 club bid was 3NT. According to our card, partner correctly took my 4 club bid as Gerber, and responded accordingly. The rest was not pretty! I have since consulted the wisdom of my old college pal, Eddie Kantar. The rule according to God is that 4 clubs is only Gerber if partner’s first bid is 1NT or 2NT. Your card probably already says this, and mine does now.

As a parting shot, what if partner asks you to show your controls and then you hear him bid 4NT after your initial response. Believe me, we not playing this sucker in NT, that is an ace or key card asking bid. The two treatments are not mutually exclusive. Partner is entitled to “change horses.” Show your Aces or Key cards as the case may be.

I strongly urge you to start using control bids in your slam bidding a supplement to, and not a substitute for Blackwood or key card asking bids. Just follow the simple rules I gave you in Part 1 and don’t over complicate the process. If you get all tangled up in your underwear, bail out and try again on the next opportunity.

Bidding Continuation on Hand 2. I bid now bid 5 diamonds, a continuing inquiry. In the example hand, since you have no move controls you bid 5 spades. If your hand also contained the Ace of diamonds, but not the King of clubs, you would next bid 6 diamonds instead of 5 spades. If you held the King of clubs, but not the Ace of diamonds, you bid 6 clubs to show 2nd round control of clubs. With both those additional cards (Ace of diamonds and King of clubs) you just bid 7 spades. If that contract isn’t right, tear up your partner’s ACBL card. If he is a life master, I would recommend a tin snips!

Cue Bids and Control Bids (Part 1)

Are you ever confused about that all inclusive bridge term called a “cue-bid?” In modern usage a cue bid no longer shows a full out game forcing powerhouse as it once did, and often says nothing about first or second round control. Some of the old uses prevail such as the Michaels Cue Bids showing a 2 suiter, and Western Cue Bids asking for a control in the pursuit of a three no trump contract. Those are nice accessories to round out a partnership agreement, but they are not essential to success at the game.

In bridge today, a cue bid most often is used by responder to show trump support for an opening bid where opponents have intervened with an overcall. By bidding overcaller’s suit you are telling partner that you have support for his opening bid and limit raise values or better. So 1s/2c/3c! shows 3 or 4 card support for spades and 10+ hcps. The cue bid is also used to show support for an overcall that your partner may have made. So, 1c/1s/p/2c! shows 3 or 4 card support for spades and limit raise plus values. Note the "plus," it is really an unlimited bid. In most partnerships, 99% of the time when you hear a cue bid, it will have this meaning. Use it whenever you can, it sends an unmistakable message to partner and will help you avoid missing makeable games.

There was a time that bids showing either 1st or 2nd round control cards in pursuit of a slam were also called cue bids. In an effort to reduce confusion, these control showing bids are now called “control bids” and not cue bids. A nod of thanks to Bridge World magazine for the clarification. Control bids are not just for experts, they should be used in partnerships at all levels of expertise and in their basic form require only a few rules of the road.

You might ask “Why do I need to complicate my life with learning control bids?” "I just advanced from Blackwood to showing Key Cards (1430 or 0314) and now I can count partner’s controls including the King of Trump! " Just being able to get a count partner’s controls has a fatal weakness in some slam going hands. It is on the occasion when you must know which control partner has that things come apart.

Suppose you have a distributional hand with 4 Losing Trick Count (“LTC”) strength, one of the main features being a void, but you are missing two aces. While some good players open these 4 LTC hands with a 2 club forcing bid, let’s leave that discussion to another time. Assume the bidding goes 1s/p/3s (limit raise) and you now bid 4NT (Blackwood) asking partner for aces. He shows one of the two missing aces! Which ace is it? There is no way to tell, and now all you have done is force the bidding one level higher, and you still have to guess whether the hand will make a slam. In this sequence, the slam is 50/50, and in matchpoints it is a long term loser to be bidding 50% probability slams (unless you want 50% games).

Alternatively, in a second hand you have another 4 LTC hand with 2 aces and a worthless doubleton in clubs. The bidding is the same as shown in the first example. Over 3 spades you now bid 4NT and partner shows 1 Ace. Does partner have first round control in your doubleton, or are you going to lose 2 tricks off the opening lead? In both of these examples, if you do not use control showing bids, you are better off bidding 4 spades and putting an end to the guess work.

There are occasions where you may want to use control bids merely to conserve bidding space. If in a spade bidding sequence you bid 4 clubs as a control asking bid, and the diamond or heart ace are essential to going forward, if partner is aceless and bids 4 spades (a sign off), you can pass one level lower than Blackwood would permit. This facilitates more speculation with out attendant risk.

Control bids are easy if you just apply some simple rules and do not overcomplicate the process. These rules seek to make sure (i) that you realize when partner is asking you to show controls and (ii) that when you respond, partner will know not only what first round controls you have, but even more importantly, what first round controls you do not have.

Rule 1. A bid can never be a request to show control cards unless the partnership has agreed on a trump suit. Thus 1s/3s is trump agreement. If you play Bergen Raises, so also is 1s/3c. Likewise, 1c/1s/3s is agreement. Either partner can initiate the control asking process, but usually it is better to have the partner with the bigger hand in control.

Rule 2: A request to show controls will always be a bid in a suit that has not been bid.

Rule 3. Any bid under 3NT is not request for you to bid controls. Thus 1s/2s/3c is not a request for controls. It might show a suit, a stopper or be a game try, but you are not being asked to show controls.

Rule 4. We always show all of our 1st round controls (Aces or voids) first and we show them “up the line.” Bidding controls up the line helps partner know when you are showing a 2nd round control. For example, if partner over 3 spades bids 4 clubs, and you bid 4 hearts, you have shown the Ace of hearts, but have denied the Ace of diamonds. If partner now bids 5 clubs, you can safely bid 5 diamonds showing 2nd round diamond control, since you have already denied 1st round control. Alternatively, if partner had bid 4 spades, he is not interested in your King of diamonds, so pass.

Rule 5. The partner initiating the cue bid process is in control. The initiating bid may or may not show a control and you, as responder, do not have a need to know what it shows as long as you know partner wants to hear about your controls.. As long as you are not in control of the hand, all you need to do is respond to partner until he stops the control bidding process by returning to the agreed suit.

In our second installment we will demonstrate by specific hand examples how bidding controls can work in practice. Since the rules that we have discussed will apply, you may find it convenient to make a hard copy of this post so you can refer to it. Just select what you want with your cursor and print in your normal manner. Be sure when you get to the print command page you designate “selection” so you don’t get a lot you don’t want. This is worthwhile, it is something to discuss with your partner and then put into practice. If you get confused, just bid the agreed suit and sign off and consider it a learning experience.

Further Bidding after a Weak Jump Shift Response

In our last blog we demonstrated the use of the 2 level weak jump shift by responder and contrasted it with the treatment of bidding the suit at the one level and then rebidding the same suit at the 2 level. In either instance, responder breathes a sigh of relief and assumes he is off the hook. But what if opener has a hand where he simply is not satisfied to quit despite the grim news from partner? Well, first let me tell you that you better get this right, because if you do anything other than lay down the pass card, you have just taken control of the hand and your partner as well.

As noted in the last post, the weak jump shift should show a 6 card suit and 2 to a bad 5 hcps. In order to make game against responder’s WJS you will need a hand that was almost a 2 club opener, something in the range of 19-20 points, probably a 4 LTC hand and at least three card support for partner’s suit. If you hold that nice 19 hcps hand, but only a single in partner’s suit, then trouble is just over the horizon. Either you pass or wish you had.

Contrast this with the responsive hand that bid and rebid the suit showing 6 cards and a good 5 to 9 hcps. The only difference in the requirement for making a forward going bid is that you can make it with hands that are a little weaker. It is always hard to talk about hcps, because so much depends on playability, but I would want 16+ to show further interest.

The results of forward going bidding can also depend on responder’s hand. He will not always have 2 hcps when he makes a WJS and his other 7 cards will not always be 322 (a real goat). If responder has some shortness in one or more suits, it could fit well to produce some additional tricks provided that opener started with the requisite 3 or 4 card support. The death knell for opener to try to find a safer place to play when he lacks support. Ridiculous! Repeat it again, Ridiculous!

With 3 or 4 card support, opener also has an opportunity to further the preempt with minimum values. Even with three card support we have 9 trump don’t we. Being LOTT guys, we are not going to let opponents buy a contract at the 3 level. Old stuff, but equally applicable to this setting. Opponents may not have a game, but down one is often very good, right Bob?

I see you, jumping up and down in your seat sitting on KTx, Axx, A, AKQxxx. You have 20 hcps, 8 1/2 tricks and 4 LTC. I would hope that my partners would have the discipline to open this 1 club -- my aspirations may be too high, but I love them all anyway. I hold QJxxxx, x, xxx, xxx. In response to 1 club, I jump at the chance to bid 2 spades and get out of Dodge! Partner, with justification, has continued interest, but needs to find out more about my hand. What is the best approach?

Well, the start is easy; you bid 2NT which is forcing of course. Now you need agreement with partner what this means. In this context if this is “feature”, you may wish you had some other agreement.There is a better way to proceed.

A preferred way to have partner further define his hand is "Ogust." This is not hard to remember if you use Ogust over weak 2’s. However, there is a twist here.You have to redefine the trems “good hand” and “good suit.” A “good suit” is one where the meager high card points you hold are in your suit. A “good hand” is one where you have a single or a void. Thus, in Ogust speak we respond to 2NT as follows: 2c= bad hand and bad suit, 2 diamonds= bad hand and good suit, 2 hearts, good hand and bad suit, 3 spades= good hand and good suit. With this hand I proudly bid 3 spades over 2NT. I obviously have either the Ace or Queen of spades, perhaps accompanied by the Jack. I also have a single or a void. It makes a comfortable 4 spade bid, but the slam potential of the hand is limited by the fact that I do not know the location of the shortness.

If you are really “uptown” card player (boater, spats and a cane) there is an alternate bid that you can add to your arsenal. This bid does not subsume 2NT, that bid remains Ogust. It is a "do-dad" that lets you pin point any shortness in responder's hand if that is important. Instead of bidding 2NT, you bid 3 clubs. This asks partner do you have any shortness and if so, where is the shortness. Without shortness responder replies 3 spades. With responder’s shortness in hearts as in my example, responder bids 3 hearts. If responder had Qxxxxx and nothing else, you have a hand that is too good to play anywhere other than 6 spades.

No matter how well you play, if you do not get to the best contract, it makes no difference. All your talent is wasted on inferior contracts. The first half of a bridge deal is all about communication. As in real life, those who have the best toys often enjoy it the most. If you don’t think so, send me your best real life toy.

The Weak Jump Shift and its Counterparts

Strong jump shifts by responder have been left for dead. They are now road-kill. The reason? With enhanced bidding techniques for strong hands (2/1, Bergen, Jacoby, etc.) they have outlived their usefulness. A corollary to owning an ACBL card is that you never leave a bid unused for more than a week. Weak jump shifts are an excellent example where that principle makes sense.

Let me get by some definitional issues. The only weak jump shifts that I am talking about are the 6 jump shifts by responder that do not go beyond the 2 level. I am not an advocate of Criss Cross Inverted Minors, but if you use that convention, the 1c/2d sequence is already taken to show a limit raise for clubs, so that would reduce the number to 5

Partner opens 1 club and as responder you hold K10xxxx, xx, J82, xx. Assuming you don’t bid 2 spades with this hand, what action do you take? Well, first you can pass with 2 card club support, a 6 card major and no defense. Don’t like that? Neither do I. Well fine, then bid 1 spade! Now partner bids 2 hearts (a reverse)! Now do you find any action you like? Bidding 2 spades at this point would clearly misrepresent your hand. Now you have worked yourself into a definite case of the “creeping shorts.” What you would like to do is back this auction up, mark WJS on your convention card and respond 2 spades immediately. As I just demonstrated, the WJS allows you to make a bid on a hand like the one described above and not risk a “runaway” auction that progressively slumps you farther and farther down in your seat.

There are some other benefits to using the WJS. First, for simplicity my example did not show competitive bidding, but in a real life setting if the bidding goes 1c/p/p, or 1c/p/1s, there is no way your are going to get LHO to be silent. Alternatively, if you had responded 2 spades you probably would not have heard any chirping on your left. We hate chirping! Second, you have achieved the ultimate in bridge bidding, a “twofer.” You will have told partner not only about the distribution of your hand, but also about your lack of hcps in a single bid.

The biggest mistake by those using WJS is that they don’t use the bid on very weak hands. With Q9xxxx, xx, 82, xx (bid 2 spades without blinking an eye). The opposite is also an equal problem, they use the WJS on hands that are too strong such as KQ9xxx, xx, Q82, xx (bid 1 spade, not two). Max Hardy in his world renowned book, Advanced Bidding for the 21st Century (2000) states that the proper range for the WJS jump shift is 2 to a bad 5 hcps.

You might ask what do I achieve by limiting the bid to such rotten hands. Why not 4-8 or some other more flexible range? The reason is that we have another bidding treatment for the 6 card suit in the good 5 to 9 hcp range. With hands like KQ9xxx, xx, Q82, xx we are going to respond 1 spade and at the next opportunity we will bid 2 spades. By rebidding our suit we will show the 6 card spade suit, but with a hand that may have as much as 9 high card points. Notice that by adopting this discipline, we have very precisely sliced and diced the range of 2-9 hcps, differentiating the WJS from the “suit rebid” response, and thus giving partner a very precise picture of your hand strength and card distribution.

Weak jump shifts are commonly used in competition and over a t/o double. Should they also be used when there is no competition from your RHO opponent? Of course they should. And for all the same reasons. Just because your RHO has not bid doesn’t mean that all is quiet on the Western Front. If you pass that nice 3 point hand, or bid 1 spade, it is a guaranteed that the Terrorist on your left is about to try to steal this auction from your side. Challenge your LHO to bid at the 3 level; it’s like throwing a grenade. Are you safe? Off course you are, you have described your hand to partner in detail. Unless he makes a forcing call, your obligation is over. Remember to check the box on the convention card that says that WJS are used when not in competition. Note that it is marked in “red” and must be alerted.

To wrap up this section let’s talk about what action responder takes when he has a 6+ card suit and 10-11 hcps. Assume you have KQ9xxx, xx, Kxx, Q8. Your partner opens 1 club, there is a pass on your right and you respond 1 spade. Partner now bids 2 diamonds. You must not bid 2 spades. That bid says I have 6-9 hcps and in the above example you have a nice 10 hcps. Jump your second response to 3 spades to show your 6 card suit and invitational values. Partner with a single spade and minimum hand can pass, but more times than not you will happily be in 4 spades. With the above hand if I had another spade or another point or if partner had rebid 1NT, I would bid 4 spades rather than 3 spades.

In the next post to our blog, we will continue this discussion and look at opener’s rebid options when he holds some significant extras and wants to ignore your warnings.

My Vote for Best Bridge Book of 2007

Summer has gone and so has my reading list. I didn’t read every new bridge book published in 2007, and perhaps they are saving the best for last, but if Mel Colchamiro’s book, “How to Play Like an Expert (without having to be one)” is not at the top of the list, somebody should conduct an investigation. This is Mel’s first effort at writing a book, but many have enjoyed his monthly column in the Bridge Bulletin, “Claim with Colchamiro.” The book does touch on some of his previous writing, but not to excess and always for the right reasons, adding more clarity and depth (and occasionally correction) to the practical advice he has previously given to us.

As the title indicates, the book does not address bridge experts. If you can declare at the “double dummy” standard, defend like a demon, recite all the percentage plays and intuitively figure out everything “on the fly” without ever being out of tempo, then this book is clearly not for you. But if you were in that category, your name would appear on the back cover along with Eric Kokish, Paul Soloway and Bobby Wolff.

Instructional books should be judged on clarity, good organization and how well they meet the expectations of their target audience. Mel tells you that his targeted audience is “us regular folk”, and at the risk of being intellectually whipped by the words “overly simplistic”, he takes dead aim on that audience. Mel’s teaching experience shows through and enables him to carry his message in a series of clear, concise rules, somewhat in the style of Ron Klinger’s “Better Bridge with a Better Memory.” It takes over where the Rules of 11 and “Eight Ever, Nine Never” leave off and takes us through more than a dozen easy to apply guidelines that for the most part can be calculated on your fingers. No move worries about “do I or don’t I” or “should I or shouldn’t I” or “what would Mel do now.” For many of those common dilemmas, Mel tells you how to make the same decision he would make without paying the tuition.

One thing I like about the book is the application of most of the rules are not dependent on a partnership understanding. Would it be better as a partnership read? Yes, but its value does not generally require mutual partnership understanding. Another plus, the book is replete with graphic examples that greatly aid the understanding.

If you think you are not an appropriate audience target at the conclusion of Chapter 4, then skip ahead to Chapter 14 and start to work your way through 60 pages of “Balance of Power” Doubles. While Mel makes a gallant effort to put “action doubles”, “BOP doubles” and “penalty doubles” into distinct and identifiable cubby holes, it still is a humbling experience. My advice is don’t get lost in the forest. Look for the major summarizing rule at the end of the chapters, and then go back and worry about the subsets. Here is where it would be nice if you and partner got on the same page.

Those who know my bidding style know that I come from the Larry Cohen camp, generally subscribing to the maxim that "you can’t leave opponents undisturbed if 1NT is opened on your right." The only thing worse that defending 1NT is defending 1NT doubled. Those waiting for the perfect hands to utilize Cappelletti, Hamilton and other “beefsteak” 5-5 no trump killers are doing a lot of waiting, no balancing and getting a lot of average minus boards. Mel has developed a system to get you into the auction whether you are in 2nd or 4th seat. The entire system is circumscribed by two rules explained on pages 10-25. Here is a summary of those rules:

(a) If your RHO opens 1NT (15-17), count the number of cards in your two longest suits, subtract your Losing Trick Count (LTC) and bid if the result is greater than 1. For reasons explained in the book, Mel calls this the Rule of 8, but I prefer to think of it as the Rule of 1.

(b) How do I get into the auction? Use the “DONT” defensive bids. I like this, Mel likes this and more importantly so does Larry Cohen, arguably the strongest match point player ever.

(c) If the bidding goes 1NT/P/P, partner obviously did not meet the Rule of 1, but that doesn’t mean that he doesn’t have some stuff. Here you apply the Rule of 2. Bid (DONT of course) regardless of your hcps or vulnerability if you have at least 2 “shortness” points. Example: T643, QT95, T, Q965. Bid 2 clubs! If partner followed the 2nd seat discipline, the probability is that our side has a total of about 19.5 hcps. Remember there is no penalty double in DONT, and partner could hold KQxx, Kxx, Axxx, Kxx and not have a call. In this example his longest 2 suits = 8, less 7 LTC= 1. This is not more than 1, so partner is required to pass. He is very thankful when you take a bid. So now you know that defending against No Trump is in fact simpler than 1-2-3, it is as simple as 1-2! I would recommend reading Chapter 4 before you read Chapter 3, I think it puts it in better perspective.

If you are looking for page after page of tedious “play of the hand” problems, then this book is not for you. If you are completely undisciplined and do not like rules of application and want to be left in your current quandary of applying instinct in an ad hoc fashion, then save your money.

The book is available at www.melbridge.com and at other book resources. The cost is $21.95, it is paper bound and 276 pages. Did I buy the book? Yes, but if I had it to do over again, I would recommend it to you and then read your copy.

The Odds and Ends of Bridge (Post Graduate Course)

Until poker became a TV star, everybody thought Poker was mostly bluff and luck and that duplicate bridge was a game of skill. Today we know that even the lowly internet poker players calculate the probability of finding an “out card” and live and die off pot odds. Conversely, club game bridge players largely consider bridge probabilities as an annoyance that only ruins an otherwise beautiful afternoon game. It can only be explained by the difference between money and masterpoints. If you don’t want me to ruin your beautiful afternoon, just exit this blog and go back to the novel. This is not easy stuff, but I hope that sometime it will form a useful reference. This is my last blog post on “Odds and Ends” and soon we will return to entertainment.

While bridge probability tables are helpful and avoid some difficult computations, the odds set forth in these tables are known as “a priori” odds, since they measure the probability of chances on any given hand prior to the play of any of the cards in that hand. As soon as one or more cards are played on the deal, these a priori odds are history. Sometimes the resulting change in the odds will be miniscule, but other times will be substantial. Probabilities calculated after the commencement of play are called “a posteriori” odds. These possibilities are too numerous to fully capture on any printed table.

The Deletion Principle

Let’s look at a simple example where we hold a seven card suit AKQxx opposite xx. If the suit splits 3-3 we will be able to take 5 tricks in this suit. When opponents hold 6 cards in a suit the “a priori” odds for the 3-3 split are 35%. The odds for a 4-2 split are 48%. With 6 cards outstanding there are 64 possible card divisions, 20 of them being 3-3 and 30 of them being 4-2 or 2-4 and the rest being nightmares.

Now, starting our analysis and play, assume that both defenders follow suit on the play of the Ace and King. We now know that the distribution of the suit was not 6-0 or 5-1 (our so-called “nightmares”). We have eliminated the 2 possibilities of the 6-0 break and the 12 possibilities of the 5-1 break, leaving only the 50 possible combinations of 3-3 and 4-2. By reducing the denominator, we have increased the odds of a 3-3 split from 35% to 42%, and the odds of a 4-2 split from 48% to 57%, but also note that the relative probability of the two suit divisions to each other has stayed the same. The probability of the 3-3 split is still less than 50%, and will remain less than 50% even if West follows suit on the third lead.

This example demonstrates an important principle of bridge probabilities known as the “deletion principle.” It can be stated as follows:

“When the opponents follow to the play of a suit with insignificant cards, the impossible distributions are deleted but the probabilities of the remainder of the distributions retain their relative proportionality to each other.”

Note that I have highlighted the words “insignificant cards.” You might at first think the holding of the J or Q by a defender would be significant. But in this example, the only division that will obtain 5 tricks is the 3-3 split, so the appearance of the Jack or Queen at anytime during the play of the suit would have no significance to the final result. If West held Jxx, and false carded the Jack on the second play in the suit, it would be an insignificant false card since we still have only one play that works for 5 tricks, the 3-3 split. We have no choice but to lay down the honors and hope that the jack was a false card. That is why all the opponents cards in this particular 7 card arrangement are considered insignificant.

Now let us change the cards a bit and demonstrate a holding in which the Jack does become a significant card and note how that changes probability of the 3-3 split. Assume we have AKQ10x opposite xx. Again we lead our two top honors with both opponents following suit with insignificant cards (not the jack!). As in the first example we now eliminate the fourteen 6-0 and 5-1 suit distributions, but there is another suit distribution that we can also eliminate in this case. We know that neither defender held Jx or we would have seen the Jack on the second round of play. Thus, we can also delete those 4-2 combinations that would have included a Jx doubleton by either opponent. Of the 30 possible 4-2 combinations, 10 of them involve Jx doubleton. While the probability of the 3-3 split remains unaffected at 35%, the probability of the 4-2 split has been reduced from 48% to 32%. Now in relative terms, the 3-3 split has a 52% probability and the 4-2 split a 48% probability.

Unlike the first example, we could delete the 4-2 combinations involving JX because a defender holding those cards will not make things easy for declarer by playing the Jack on the first or second lead if he held Jxx. Since now we know that the 3-3 suit split has become a slight favorite when our 7 card suit includes the AKQ10, we simply plunk down the queen and hope the odds work in our favor. The unwashed will sniffle that you got lucky, but we should let our non-readers suffer the consequences of not checking into Tommy’s Bridge Blog.

A10xxx opposite Kx. This example demonstrates that the favorable odds will also occur where there are two significant cards outstanding, the Q and J. The deletion process is a little different. Here we can delete the 4-2 combinations that include a Qx or Jx (18 cases out of 30) and the 3-3 combinations where either defender has both of the honors (8 cases out of 20). Again the combination of these deletions works out to a 52% probability in favor of the 3-3 split. The play is to ruff out a small card after taking the A and K, hoping to see the Q and J fall on the third lead. It’s a favorite! You might say, “Duh, how else would you play it?” Well the important thing is that you realize that you have now vaulted over that 50% threshold, and spiting the 7 card suit is now a preferable line of play to taking a finesse in another suit.

What you want to be on the lookout for in these situations are the combinations where opponents hold one or more significant cards and you don’t see any significant cards after the first two plays in the suit. What really makes an honor held by the opponents a significant card is that your 7 card suit holds a “threat card” (such as the 10 in my first example). This eliminates the possibility of a false card.

Here are examples of other layouts where the deletion principle enhances the probability of the 3-3 break to a 52% probability. The point being that you should try to split the 7 card suit, rather than take a finesse in another suit as an alternative. (i) 109xx opposite AKx. The play for 3 tricks in this suit is A,K and small to the 10. The 3-3 split is a 52% probability. (ii) A opposite KJxxxx. Play the A, K and ruff a small card if neither defender shows out. The 3-3 split is a 52% probability. (iii) AQxxxx opposite x. Here the 52% play is to play the Ace and ruff 2 small clubs trying to split the suit. It is also a 52% probability. It is not so obvious that the 6th card in one hand is the threat card, so memorize it!

The deletion principle is also the reason for the popular saying “8 ever, 9 never.” I won’t waltz you through the numbers, just keep repeating the old saying.

Looking for Additive Opportunites

Howard Christ is the Executive Director of the Ocala Duplicate Bridge Club in Ocala Florida. When I am in Florida, he is further distinguished (my choice of words) by having me as a partner 6 days a month. I think Howard really keeps me around to demonstrate that he does, indeed, have limited tolerance for fools. It is nerve wracking to play with Howard since he is one of those players that always seems to know what is going on at the table and never fails to identify an opportunity if there is even a whiff of it lingering over the table. One of his great pearls of wisdom is his thought about opportunity at the table: “You won’t see it if you are not looking for it!”

Frank Stewart’s bridge column for Saturday, September 15 reminded me of the need to look for those opportunities, no matter how slim they may be, as long as it doesn’t cost you anything to explore. Here is the set up in Frank’s column:

^^^^^^^^^^^^K
^^^^^^^^^^^^54
^^^^^^^^^^^^9432
^^^^^^^^^^^^AK6532

JT962^^^^^^^^^^^^^^^^^Q873
K87^^^^^^^^^^^^^^^^^^^JT9
Q876^^^^^^^^^^^^^^^^^^JT
8^^^^^^^^^^^^^^^^^^^^^JT97

^^^^^^^^^^^^A54
^^^^^^^^^^^^AQ632
^^^^^^^^^^^^AK5
^^^^^^^^^^^^Q4

The contract is 3NT. The opening lead is the 3 of spades, up steps dummy’s K. As all good match point players do, you look at the array of potential contracts that could have been reached by the field on this deal and see if the club suit breaks, you are going to take gas on this board, since either 6 clubs or 6 NT are high probability contracts. You now have to hope that the club suit doesn’t break 3-2 and that those slam bidders get heartburn. You note that your 3NT contract also has problems, as the only remaining entry on the board is in the club suit. If you play small to the club Queen and back to the high club honors, you will get exactly 3 club tricks on a 4-1 club break, This will leave you one trick short unless the heart finesse works.

Many players would simply resign themselves to the heart finesse, a 50-50 proposition, as the only back up to a failed club play. The best declarers who are always looking for a small edge will see that the heart finesse can always be tried, but that there is a slim chance for another line of play that can be explored first without losing the later chance for the heart finesse.

Noting the 4 diamonds to the 9 on the board, they will see that the QJT of diamonds are outstanding and that if RHO has any two of those honors doubleton, the 9 of diamonds will set up as a trick if an entry is preserved to get at it. Yes, finding the JT doubleton East is a long shot, about an 8% probability, but nothing is lost by trying the diamond play before you take the heart finesse. Play a small club to the Queen and lay down the A and K of diamonds, and lo and behold, the bank vault opens up, the J and T fall under the A and K. Now you can play the third diamond toward the 9 and the 9 becomes a good trick when West takes his Q of diamonds. Since you still have the club 6 to get to t he board ,you can reach that diamond trick. Now you no longer have to count on the heart finessse for your 9th trick.

This comes under the category of “if you are not looking for it, you won’t see it.” Perhaps “timing is everything” would also be appropriate. Note that you have to try the diamond play while you still have a club entry, so if you make the mistake of laying down 2 clubs to try the club suit first, you are dead. You can still promote the diamond trick, but you can’t get at it. When the clubs don’t break, you can still try your heart finesse, but you have then given up on the additive diamond play.

This is not an easy problem, and is in this post simply as a teaching tool. First, look for additive opportunities if they do not jeopardize your existing chances. If you are not looking for them, you will not see them. When you have multiple play options, and one of them involves a 7 card suit, even though the odds are against a 3-3 break, always try that solution first before taking your finesses. If the 7 card suit doesn’t work you can usually still take the finesse, but often if the finesse doesn’t work, it is too late to try the 7 card suit. Alternatively, you can do as I do, get Howard Christ to play these hands for you!

Odds and Ends of Bridge (Part 4)

^^^^^^^^^^A10
^^^^^^^^^^943
^^^^^^^^^^AK65432
^^^^^^^^^^K

Q964^^^^^^^^^^^^^87532
Q3^^^^^^^^^^^^^^^K762
9^^^^^^^^^^^^^^^^^J1087
QJ10985^^^^^^^^^^None

^^^^^^^^^^KJ
^^^^^^^^^^AJ108
^^^^^^^^^^Q
^^^^^^^^^^A76432

The above hand is from Frank Stewart’s Bridge Column on Sunday, September 9. Let me digress a moment to discuss probabilities before I get to the play of the hand. The probability of the division of the 8 card diamond suit prior to the play of any card in the deal is:

5-0 or 0-5 = 3.91%
4-1 or 1-4 = 26.26%
3-2 or 2-3 = 67.83%

The Queen of Clubs is led and East discards the spade 2. We now have completely discovered the division of the opponent’s holding in the club suit as West 6- East 0. We learned in Odds and Ends of Bridge (Part 1) about the Law of Attraction, that a long suit in one hand tends to attract another short suit and that a long suit tends to reject another long suit. The probable distribution of the 8 card diamond can now be recalculated to:

5-0 or 0-5 = 8.44%
4-1 or 1-4 = 35.22%
3-2 or 2-3 = 46.34%

This simply drives home the point that the initial table odds that you so frequently see and hear about can change rapidly once the complete division of any second suit is known. In this case the odds of a 3-2 spit in the diamond suit have been reduced from 68% to 46% by reason of the club division. While ordinarily the probability of an 8 card suit dividing 3-2 is far superior to taking a simple finesse in another suit, the aberrant division of the clubs has now made the 3-2 split in diamonds a decided underdog to a finesse. The point is not the arithmetic or memorizing probability tables, but when the cards around the table in one suit start to do funny things, don’t expect everything else to be normal – make a disaster plan.

The bid contract as published was 3NT. Assume the scoring is matchpoints. You are on the board with the King of Clubs. If the diamonds split 3-2 you can make 12 tricks by playing a small diamond to the queen and then back to the board with the spade, running the rest of the diamonds from the top. If you decide to “Pig-out” and go for 12 tricks, you actually can make only 8 tricks since the diamonds split 1-4 and you now do not now have enough board entries to try the “split honors” finesse in the heart suit.

At matchpoints we take the line of play that will both fulfill our contract and, at the same time, present us with the greatest probability to net us the maximum number of overtricks without jeopardizing the contract.

In Frank Stewart’s analysis he did not put all his eggs in the “3-2 diamond split basket,” since he knew that the 6-0 split in clubs was bad news. He played the diamond Ace from the board (Queen from his hand), then the King of diamonds hoping for a 3-2 diamond split and 5 diamond tricks. When East showed out on the second round he put Plan B in motion leading a small heart losing to West’s Queen. He won the club return in his hand, used his spade entry to get back to the dummy, led is 9 of hearts and let it ride, ultimately winning 2 spades, 3 hearts, 2 diamonds and 2 clubs.

Frank’s line of play was a heavy favorite to make 9 tricks, and at the same time he preserved his long shot of finding the diamonds 3-2 and making 5 diamond tricks for a total of 11 tricks. There is a superior line of play to the one chosen by Frank that will preserve the same opportunities, introduce no further risk and at the same time make an overtrick for top board. Did you find it? Hint: You don’t need to smother your own Queen of diamonds!

Odds and Ends of Bridge (Part 3)

Well ,you had to know that Odds and Ends (Parts 1 and 2) were laying the groundwork for more serious discussion to follow. I would be content to let well enough alone and have my readership bask in the comfort of reviewing stuff they already know, but since part of my mission is to drive those bridge intermediates up a notch or two, I can’t let everybody get too comfortable. Actually, the principle of Restricted Choice is not all that complicated, since the hard part of any sophisticated bridge play is recognizing when it confronts you. In Restricted Choice, it really hits you over the head since you unexpectedly see an opponent drop an honor in the first play in the suit.

Playing Rule for Restricted (Free) Choice Situations

The application of this playing rule often presents itself in a 9 card suit where declarer holds A9xxx in one hand opposite KTxx in the other. With QJxx outstanding, the initial plan is to split the suit 2-2 and drop both honors with the second round played. You start with the Ace from your hand, and, lo and behold, East drops the Q or J under the Ace (it does not matter which, since the math solution ignores the possibility of a false card by East). Now you have to decide whether East holds QJ doubleton or a single honor.

If he was dealt a doubleton honor, then you have to continue your plan to drop the other honor. If East was dealt a singleton honor, that means that West was dealt Jxx or Qxx, as the case may be, and the correct play is to play toward the K10 in the dummy planning to finesse against West for the other honor (Q or J). While the rule with a 9 card suit generally favors a “drop strategy,” this combination of events is an exception to this rule. It is called the Rule of Restricted Choice, although more modern authors generally refer to it as “Free Choice.”

In my example, on the second lead toward the K10x, you should insert the 10, finessing West for the missing honor. This seeming anomaly is mathematically correct and supported by the laws of probability. The correctness of the rule, often disputed in the past, is now conceded by all experts.

Here are the Rules and Odds for Restricted Choice Situations:

(a) In a nine card suit when there are two missing equivalent honor cards in a suit (e.g. Q, J) along with 2 small cards, if on the first lead one of the opponents plays either one of the honors (Q or J), it is almost 2:1 odds that the honor played is a singleton and you should finesse the other opponent for the remaining honor if you can.

(b) If you have an eight card suit (e.g. K765 opposite A1098) and there are two equivalent honor cards outstanding (Q and J, along with 3 small ones), if on the first lead one of the opponents plays either one of the missing honors (Q or J), the odds are approximately 5:3 that the honor played is a singleton and you should finesse the other opponent for the remaining honor if you can.

(c) If you have a seven card suit (e.g. K76 opposite A1098) and there are two equivalent honor cards outstanding (Q and J, along with 4 small ones), if on the first lead one of the opponents plays either one of the honors (Q or J), the odds are approximately 3:2 that the honor played is a singleton and you should finesse for the other opponent for the remaining honor if you can.

Other restricted choice positions are AKQ9 opposite xxx. If on the lead of the Ace you see the 10 played, lead a small heart from your hand and insert the 9. The J and Ten are equivalent honors.

Here is a little different twist. Dummy has J9x and you hold Qxx. Unfortunately, neither opponent led this suit for you, so you have some work to do. Lead small from the dummy toward the Queen, assume this is taken with the Ace by West. Since the Ace and King are equivalent honors, it is unlikely that West holds both of them. The correct play is to come to your hand and play toward the J9. If West plays a small card, insert the 9, since East is a favorite to have the King. If he also has the 10 there is nothing you can do about it, but if West started out with A10x, you will make a trick in this suit.

One final example. K109 opposite xxx. You play small and insert the 9 which loses to either the J or Q. For the purpose of Restricted Choice applications, the Q and J are equivalent honors. We know that it is more likely that any honor played is not likely to be accompanied by the adjacent honor. We need to lead again toward the K10, and if West plays a small card we put in the 10, not the King. East may have the Ace, but the odds favor West holding the Jack and we hope that the 10 will force the Ace in the East hand. If so, we get a trick in the suit.

What is the common denominator? It is that you are missing two equivalent honors in the suit and on the first lead you see one of them, bet that it is a single and take the finesse (if available) against the other opponent.

In Part 4, I will wrap up all this high math with a discussion of the “Deletion Principle”, demonstrating that middle cards can make a difference and that some 7 cards suits can actually be favorites to break 3-3.

Odds and Ends of Bridge (Part 2)

I. Remembering Suit Splits When Declaring

Are you tired of trying to memorize all those a priori suit distribution tables? Here is a short cut that is easier to remember and just as good.

If the number of cards you and dummy hold are an even number, the probability is that the odd number of cards held by opponents will split as evenly as possible. The probability of this division is always more than 50% and gets greater as your holding progresses from 6-8-10 cards. Remember the Rule, forget the specifics.

If the number of cards you and dummy hold are an odd number, the probability is that the cards in the suit held by opponents will split unevenly. The probability of an even split increases as your holding progresses from 5-7-9 cards, but never reaches 50%.

The 11 card holding is an exception to that rule. Always play the suit to split evenly, 1-1. The odds of a 1-1 split are 52% and the 2-0 split 48%.

There are other applications for these rules. If you are declaring 3NT and LHO makes a 4th best lead of the 4 of spades, you can’t always tell with clever defenders whether the suit is 5-3 or 4-4. We know from our rule that an 8 card suit held by defenders is more likely to be 5-3 than 4-4, so in calculating the number of times to hold up in the suit, we might take that into consideration. Actually, there is another rule that makes that “hold up” decision simple for you. It is called the Rule of 7. You total the number of cards in the suit in your hand and in the dummy and subtract that number from 7, the result is the number of times you hold up in the suit. (e.g. If you count 5 cards, hold up twice if you can!)

One final thought before leaving this subject. Sometimes you have the option of splitting the outstandikng cards in your 7 card suit 3-3 or taking a finesse, and either chance will enable you to make your contract, but if you let the opponents in, they will take their setting tricks. There is a right way to do this so that you can preserve both chances. Always try to break the suit first. If that doesn’t work, you can still try the finesse, but if you do it the other way around and the finesse loses, you lose your second chance. While the finesse alone has only a 50% probability, by combining both chances you increase the probability of success to 67.5%.

II. Rules for Single Finesses

To avoid a lot of card table arithmetic, we have some general rules for simple finesses. These should comfort you, because most of them will be familiar to you.
a. If you hold 11 cards in a suit missing the King, you play for the drop. It is a slight favorite over the finesse.
b. If you hold 9 or 10 cards in a suit, you are correct to finesse against the King, but not the Queen or Jack. For example with AQJxx opposite xxxx finesse against the King. With AKJxx opposite xxxx, play AK from the top. Remember “ 8 ever, nine never”?
c. If you hold 7 or 8 cards in a suit, it is usually correct to finesse against the King or the Queen, but not against the Jack. For example with AQJxx, or AKJxx, as long as you hold 7 or 8 cards in the suit, finesse for either the K or Q. With AKQ10x opposite xxx, play for the 3-2 split.
d. If your opponents hold 5 or 6 cards in a suit, it is correct to finesse against the King or Queen, but not against the Jack. For example, if you hold AKQTx in your hand opposite xx, you would play the suit from the top and refuse the finesse on the Jack. Missing other honors, you finesse for them.
There are some further exceptions to these rules, but they will put you on overload. One prominent (but often misunderstood) exception is the “Restricted Choice” play. See Odds and Ends of Bridge Part 3 in next blog post.

III. Working with the Probability of Split Honors

If 2 honors are missing in a suit, bridge probabilities greatly favor finding the two honors split between the two defenders. If you see in the dummy AJ10, AK10, AQ10, these combinations all benefit from the split honors presumption. To demonstrate look at AJ10x in the dummy and xxx in the hand. There are only 4 relevant possibilities, K/Q both with West, K/Q both with East, and the two possibilities (yes 2!) of the missing honors being split between East and West. You will fail to make 2+ tricks only in the single instance where both the K and Q are held by East, one chance out of four so we say the success rate is of making 2+ tricks is 3:1 or roughly 75%. You surely want to try this when one suit that presents a split honor finesse before taking a 50% simple finesse in another suit.

Even if you only have AQ9 opposite xxx, put in the 9. With the A/Q you always have the finesse as a 50% probability. If you also hold the 9, you increase you chances for 2 tricks. If West holds J/10 doubleton, it will go x,10,Q,K on the first lead. On trick 2, you now drop the J making the A/9 good. The probability of the J/10 doubleton is 12.5%, so total probability of making 2 tricks from this holding is now 62.5%, not 50%. You should always go to this combination before trying a simple finesse in any other suit.
One split honor combination that is often overlooked is QJx in declarer’s hand. You will make a trick and have a stopper in 75% of the cases (where the honors are split or the A and K are both held by the East). Note the difference between this holding and Qxx in the hand and Jxx in the dummy. In this last holding, if the honors are split (again a 75% probability), you get no tricks and have no stopper. This is a suit that you never want to lead since if opponents lead it you gain a trick. If LHO doesn’t lead that suit on the opening lead, declarer can be reasonably certain the honors are split, since if LHO held the A and K in that suit, he would probably have led one of them.

You have probably been wondering why in certain situations we don’t just play for the drop of the Queen when we have the A and K in the suit. If it is a 9 card suit, we do – it is a 52% probability. If it is an 8 card suit, playing for the drop of the Queen doubleton with either opponent (a 27% probability) is a decided underdog under almost any circumstances.. Thus, if you have a choice to break a 7 card suit 3-3 (a 35% probability) or to drop the Queen doubleton from an 8 card holding (an 27% probability), go for splitting the 7 card suit 3-3. It is a significant favorite to be the preferred line of play.

Bridge is not an arithmetic test, but having a general awareness of the laws of probabilities will give you a better feel for the game and significantly better results. I know that any developing player’s mind is already on overload, so just start out by trying to recognize whether any particular play has a probability of greater or less than 50%. You don’t always have a choice, but when you do, try to take the plays where you have the odds working for you.

The Odds and Ends of Bridge (Part 1)

I. Chance and Probability Theory

The likelihood of the occurrence of any event in Bridge is called a probability. For example, probabilities can refer to the location of specific cards, high card points, or distribution of the suits among the four hands. Probabilities are not guarantees. On one deal or a single play of the cards, calculated probabilities may lead you to an aberrant result, but over the long run probabilities will prove out within a very small variance. The moral of this story is that if you want the probabilities and odds to even out, play more bridge. The usefulness of probabilities is not to determine whether an isolated line of play will work, since if you have only one line of play, it makes no difference what the probabilities are, it either works or it doesn’t! On the other hand, if you have two or more chances to make your contract, and you are able to choose among them, then it is helpful to know which chance is more likely to succeed.

II. Using Probabilities to Help You Find Specific Cards

The underlying math of bridge sees 52 individual cards and each of 4 players having 13 pockets where cards can be located. Each time you identify that “x” pockets of a defender are occupied by certain cards, that defender has fewer empty pockets. If you also know the number of cards in that suit held by the other defender, you can fill up some of his empty pockets. We are only concerned with the opponents empty pockets!

For example, if LHO opens 2 spades and you end up playing a contract in 4 hearts, you can reasonably assume that LHO has 6 of his pockets occupied by spades, so he has now has 7 empty pockets. If Declarer looks at her hand and sees 2 spades and also sees 3 spades in the dummy, she knows that RHO started with 2 spades, so now RHO has only 11 empty pockets. This empty pockets stuff is the backbone of all probability calculations in bridge, called the Law of Vacant Places.

How can we make this useful at the card table? Let’s look at the above example. Assume that the success of the contract depends on locating a specific card in a suit other than spades. Since RHO has 11 empty pockets and LHO has only 7 empty pockets, the odds are 11 to 7 (64%) that RHO will have the card you are looking for. This little calculation can be applied any time you have the distribution in any single suit completely identified between the two opponents.

An adjunct to this principle is called the Law of Attraction. Length in one suit attracts shortness in another suit. Conversely, shortness in one suit attracts length in another suit. In this context, the terms “length” and “shortness” speak only to the relative holdings of a defender in two different suits, predicting that when the defender has length one suit he will have shortness in another suit. This is better explained by example.

Again, looking at our first example, since LHO has length in spades (very likely 6), the probabilities are that RHO has greater length in any other suit. Assume declarer has AJx in diamonds and dummy has K10x in diamonds, a two way finesse. Is it simply a random guess as to who has the Queen of diamonds? On this deal, declarer should always finesse RHO for the diamond queen. Two reasons:

1. Remember the “Law of Attraction?” We reason that LHO with 6 spades is likely to have the least number of cards in the diamond suit. At this point, it doesn’t matter how many more diamonds RHO has, as long as we recognize that the odds are that he will have more. Since RHO is most likely to have more diamonds, he is the most likely to hold the missing Queen of Diamonds (or any other specific diamond for that matter). What is important is not how many diamonds RHO has, as long he has more than LHO. If the seven diamonds break LHO 3 and RHO 4, the odds are 57.1% (4/7) that RHO has the Queen I.

If you remember the Law of Attraction, you don't even have to do the arithmetic or memorize card distribution tables. All you are trying to do is figure out which way to take a 50% finesse and you know the person with more diamonds is the favorite to hold the Queen! We don’t really care what the likelihood of success is, as long it is more than 50%. Alternatively, if your contract requires one of two finesses to work, in either diamonds or hearts, and one goes through RHO and the other through LHO, take the one through RHO for the same reasons. These conclusions come with the usual caveat about "all other things being equal." If you have seen the Q of diamonds fall out of LHO’s hand, don't ignore it!

2. I said two reasons. Here is the second! LHO opened a weak 2 bid. He likely has 6-10 hcps. Let’s say on average 8 hpcs. It is also likely that he has at least 5-6 of those points in spades. We could put a fine point on this, but this is not an arithmetic lesson. With 2 or 3 points outside of the spade suit, the odds are simply better that RHO has partner has the Queen of diamonds. This simply reinforces our decision to take our 2 way diamond finesse through RHO.

I have gone to great lengths (with endless repetition) to make this understandable for those who like to know “WHY?” It is better if you understand the analysis, but even if you forget, if LHO makes a weak 2 bid, just take all your finesses through RHO if you have a choice, and remember to save an entry to the dummy!

This example teaches another good lesson that even seems to escape good players. There is always a cost to entering a competitive auction. That cost is the information (strength, location and distribution) that you furnish by bidding, particularly when there is no substantial likelihood that your side will end up declaring a contract. One of the “Hallmarks” of good players is that they listen to the opponents during the auction and use the information they obtain against them.