Sunday, April 29, 2007

Bridge Rulings- Did You Know This?

A funny thing happened as I was vigorously pursuing yet another bottom board. It is match point duplicate, we are red and they are white. Your author sitting East is the dealer and passes. South bids 1 diamond, my partner passes, North bids 1 heart, another pass by me, south now bids 1 No Trump. My partner then makes a balancing double, but I do not see his double card go down. North passes the double and I reach down and pick up the pass cards sitting in front of me thinking that the auction is over and that I do not have another bid. At that point south looked at me and said “you’re passing?”

It was like somebody kicked my leg, so I looked around quickly wondering why she said that. I then saw my partners double of 1NT and indicated that I had missed his call in error and that I wanted to bid. The director was called and confusion reigned. IT WAS RULED THAT I HAD PASSED SINCE I PICKED UP MY CARDS EXPRESSING AN INTENTION TO PASS.

Steam was coming out my ears as 1 No Trump Doubled made 4
(-480). Now it’s your turn to rule. Your choice: (a) the director was correct (b) the director was wrong and I was abused (c) it doesn’t matter since we got what we deserved for making such a crappy balancing double.

Since there was no committee, there was no appeal. Still frustrated, I wrote to Mike Flader at the ACBL (Rulings Director) and asked if the ruling was correct. In a written opinion Mike said:

“According to ACBL regulations, a call is made by placing a card on the table So, tapping the table or picking up the cards on the table do not measure up to the requirement for making a call. If the director judges that you think the auction is over and that you do not have another call coming, he should allow you to make a call and continue the auction. If not, then the auction is over. In the facts stated in your letter, you thought you did not have another call coming. If that is the case, then, you should be allowed to make another call and continue the auction.

What’s the point? The point is that I was right, something that rarely happens in bridge. Much more satisfying than 1.5 black master points to a bridge career boarding the “Last Train to Clarksville!!”

Friday, April 13, 2007

Rate Yourself as a Partner

Do you think you are a good partner? A steady stream of smiles and “thank you partners.” Lots of sincere consolation at the end and a refrain of “we will do better next time.” Here is a chance to test just how good you really are as a partner. The following list comprises some of the match point lessons that I have learned the hard way. Look at all 12 of them and say “yes that is me” or “no that is not me.” If you get between 11-12 “yes” answers, you are surely going to “partner heaven.” If it is 9-10, you have been taking notes while I make mistakes and are probably sought after as a partner. If your affirmative answers are 7-8 you really need to copy this post and read it every day at breakfast. If you only get 5-6 on the “yes” side, you are a candidate for the Gong” show!

1. Do you identify vulnerability before the cards come out of the tray and make vulnerability part of your bidding strategy? If vulnerability is unfavorable, don’t be carried off the battle field on your shield. If vulnerability is favorable, don’t let them play a contract if you can hold your losses to down 1 or even 2. Remember that when opponents play the hand, a score of -90 to -120 is the “death zone”. Even the best players find it near impossible to double low level contracts, and the urge to take another bid, rather than suffering the ignominy of letting the hand be stolen, is almost irresistible.

2. Do you give expert players a little respect? The “David and Goliath” scenario hardly ever plays out at the bridge table. If your opponents are known to frequently play at the 55+% level, you will do well against the field holding them to an average board. Find another time, place and opponent to demonstrate your cleverness.

3. Have you accepted that in match point duplicate that you are not the master of your own result? In match point games, inequity plays out on every hand. Good players defending will steal an extra trick from poor players and good players declaring will do the same thing. Play the hand for its full potential and don’t worry about the “gifts” that other teams may be getting on the same hand. Pouting about “fixes” is the quickest way to fix yourself. “If you want justice, go to night court!”

4. Except for checking our score for accuracy, I never look at travelers. Do not look at travelers. Can I say that again? “Do not look at travelers”. Once the hand is done, it is over. You are never going to see that hand again; the odds are 1 in 465 billion! Looking at travelers only will set in motion mood swings of highs and lows (more lows than highs) and will prevent you from playing with equanimity. Don’t give away the next board worrying about the last one.

5. I accept the fact that a badly defeated contract can still be a great board. If you are in a contract that is going down from the minute the dummy hits the table, play extra hard to minimize your losses. One way to do that is to mentally reset the contract on what you think is a reasonable expectation and then make that your goal. If you have bid the hand correctly, other teams will be in the same contract and going down as well. I recently saw a hand where –300 was an average+ board for declarer.

6. I realize the value of average plus boards and their place in determining overall results. Good results in match point duplicate are not produced by a massive array of high boards. High and low boards will frequently even out. At the end of the day if you have more boards in the “average plus” range than in the “average minus” range, you will have a good result. Have patience. Trying to force high boards will only diminish your chances for this strategy to work

7. I would rather be a winning coward. Grand slams are for bridge heroes. Heroes are usually carried off on their shields. The risk-reward ratio is out is whack because we are competing against teams composed of imperfect people and not robots! Bidding and making a small slam in the right denomination will invariably get you an average plus board even if the hand makes 13 tricks. A special note: The “right denomination” is not always no trump.”

8. I am a tranquil declarer. When you declare, do not panic. You can’t develop a playing strategy if your mind is running in all directions. Tranquility is a state of mind and no battle plan was ever created in the middle of a full retreat. Don’t be overwhelmed by the problems and risks in the hand. Focus only on developing a reasonable plan that will let you control your own destiny rather than conceding the momentum to the opponents.

9. I "plan my work and work my plan." Once you have a plan, execute it with confidence. Don’t appear to be frazzled and torn by indecision. Thank partner for coming down with exactly the cards that he bid (effusively if you are disappointed). If opponents think you have it “in the bag” and are about to “claim”, they might just fall asleep and start pitching cards carelessly. Never give the opponents even the slightest reason to kindle their hope.

10. I leave creativity to bridge bloggers. Don’t look for “creative” maneuvers. More often than not the party at the table who is deceived is your partner. The most important element of a bridge partnership is “trust.” Misleading partner undermines partnership confidence and is the fast lane to disaster. Once the seeds of distrust are sown, it is hard to recapture that partnership magic.

11. I bid on the KISS principle. If you have two choices, make a bid that you are sure partner will understand. Game day is not a bidding examination. If there is any concern that your bid will send partner “into the tank”, then it is wrong even if it is 100% right. Save the bidding lesson for later.

12. I reward partner for balancing. If partner acts courageously in a balancing situation, give him a little room for his bravery. Don’t hang him out to dry. Remember that he has already bid some of your points. It is not necessary or advisable for you to bid the same points again!

If you think your partner does not read this blog, copy the post and give the test to him or her. Remind them that they can always see my posts at www.tommybridgeblog.blogspot.com

Tuesday, April 10, 2007

Jacoby 2NT Convention

This post gets me back to a segment of my audience that I may have ignored recently, the novice/aspiring intermediate. Jacoby 2NT is a direct 2NT conventional response to a major suit opened by your partner. It shows 4 card trump support and game going values. If you play Bergen raises, then you already have a bid for the hand that has 10-12 hcps and 4 card support, so you could reserve Jacoby 2NT for hands with 13+hcps. If you do not play Bergen raises, then I think it is all right to drop the requirement down to the 12 hcp range. In final result, shape makes a great deal of difference and in valuing the hands, responder should consider that he is a supporting hand, not an opening hand.

In an earlier post I discussed splinter bids at length (see January 07 archives). There is some overlap between Jacoby 2NT and splinter bids. My rule is that I do not use Jacoby 2NT if I have the requirements for Jacoby 2NT, but also contains a single or void. I would make a splinter bid instead.If you don't usae splinters, just ignore this concept.

Here are the standard responses to a Jacoby 2NT bid:
1. If opener has a single or void, he bids that suit. That is the first priority no matter what the size of the hand.
2. The next priority is to show the size of the hand if there is no single or void.
(a) With a minimum (14 hcps or less) bid 4 of the major. This is the fast arrival concept and warns partner that you do not have any significant extras.
(b) With 15-17 hcps and no single or void, bid 3NT.
(c) With 18+ hcps and no single or void, bid 3 of the major.

Note you jump to game when you have a minimum hand and slow bid it when you have extra values.

One minor point. If you have a good 5+ card suit (AK10xx or AQJxxx), you ignore all the rest of the instructions and make a jump bid in that suit. So the sequence 1h/2NT/4C shows a good 5 card club suit. Literally, a source of tricks on which responder may be able to pitch losers. Some prefer that the jump bid show a void to distinguish it from a singleton, but I like it the way I have explained it. If I have a void and think it is something that partner needs to know, I will bid the suit at the 3 level and bid it again a the 4 level if I have the chance to do so.These are refinements that rarely arise and can slow you down, so don't get bogged down here.

You can see that opener is describing his hand, so responder must be the Captain of ship in these sequences. If Responder has any interest in pursuing slam, he should not bid 4 of the major, as opener will correctly pass. One way to invite slam is to go directly to Blackwood or whatever you use to ask for Key cards. Unfortunately, there are some hands where you can only pursue slam if partner holds a specific Ace. An alternative to Blackwood is to bid first round controls up the line. Look at these hands:

(Opener) AK10xxx, xx, AQxxx, Kx (16 hcps)
(Responder) Jxxx, AKxx, Kxx, Qx (13 hcps)

The bidding: 1s/2NT/4S (no single or void and 12-14 hcps). Responder has a great hand with 2 doubletons and lots of Aces and Kings. He does need to know about the Ace of hearts since if opener does not have it, he would have 2 losers off the top. The best way to invite with this hand is not Blackwood, but rather by showing the diamond Ace by bidding 5 diamonds and asking opener to further describe his hand. We have already established that spades is our fit, so this can only be a first round control showing bid, not a new suit at this level. Your plan is that if partner bids 5 hearts showing the Ace of hearts, you are going to play 6 spades and if partner doesn't have the Ace of hearts, he will bid 5 spades to play. On the above hands we get to a cold slam on 29 hcps. There is no other way to get there other than to guess.

Note that if partner has the Ace of Clubs and not the Ace of hearts, he has to ignore it and bid 5 spades. You cannot show a control beyond the 5 level game. If you are going to use Jacoby 2NT, it is a good thing to discuss it with partner in advance, since many players do not understand it beyond the 2NT bid, and you are better off without it if you do not know the basic concepts and continuations.

Thursday, April 5, 2007

Quasi Smolen for 2NT Openers

In a recent post (“Smolen, Schmolen”) I discussed alternative ways to show 5-4 in the majors with a game forcing hand when partner opens 1NT. I concluded that a treatment named “Smolen” probably accomplishes this most efficiently without getting the hand wrong sided. Briefly, Responder uses Stayman and when opener bids 2 diamonds, Responder now jumps in the 4 card major. Opener with 3 card support for the opposite 5 card major bids 4 of that major and with 2 card support bids 3NT.

As usual, just when you think you have thought of everything, you get one of the 635 billion possible bridge hands that you never thought about. With my hand I did not open 1NT; I opened 2 NT with 20-21 hcps. My hand will follow later.

Partner held:
Jxxx, Jxxxx, Axx, x.

You are Responder, how do you find the best contract? There is not enough bidding room for traditional Smolen, so you have to be more creative than that.

Now you know that the moment you transfer, partner will bid 3 hearts and when you bid 3NT he will pass with 2 card support. Worse yet, he will come down with a 4 card spade suit. That is just the way life goes! That crash you hear was you falling to the bottom! So, now having a second chance you are going to use Stayman, but Opener bid 3 diamonds. If you now bid 3NT, you are going to hear that crashing noise again. Opener had had 3 spades and 3 hearts and you did not find the 8 card major suit fit.

Is there a solution? Of course, or I wouldn’t be posting this. After 3 diamonds, responder must bid 3 spades (the 4 card major). What could this be other than 5 hearts and 4 spades? Now with a 3 card heart suit, opener will bid 4 hearts. Why is responder’s 3 spade bid forcing? Because Responder would not have bid 3 clubs (Stayman) without game going values. Did you think this was garbage Stayman? Also notice that we have the contract right sided. A major concern when Opener has 20-21 hcps.

My actual hand was:
AKx, KQx, KOxxx, Kx.
Playing 3NT you find that RHO has not only the Ace of hearts, but also the QJx of clubs. Now don’t you wish you were in 4 hearts? At 4 hearts you lose a heart, spade and club for 620.

My hand could have been:
AKxx, KQ, KQxxx, Kx

Repeating responder’s hand for convenience:
Jxxx, Jxxxx, Axx, x.

Now if you try to transfer to hearts, you are going to bury your 8 card spade fit. Again RHO holds the key cards that beats 3NT, but 4 spades is high probability game. You will find it by using Stayman and you don’t have to worry about continuations.

So now we know how to deal with one more of those 635 billion hands? When partner opens 2NT and you have a game going hand and 5-4 in the majors, use Stayman, and if partner bids 3 diamonds, now bid your 4 card major. The treatment is based on Smolen principles, but you don’t jump in your 4 card major. That whoosh you hear is your high speed elevator going to the top. You will get a good result on these hands if bid them correctly, as most opponents probably will not find the optimum contract. If it works, tell them where you got it.

Wednesday, March 28, 2007

Culbertson's Valuation by Visualization

Ely Culbertson was one of the great geniuses of contract bridge. Ely was born with dual citizenship in Russia to an American father. His family lost everything in the Russian revolution so he came to this country in early adulthood with the only asset he had, an ability to earn a living playing cards. He married a bridge teacher from New York, and with his wife, Josephine, became a major force in auction bridge. When Commodore Vanderbilt invented contract bridge in 1929, Ely quickly grasped its commercial potential, grabbed the game by the throat and took it from the card room at the Cavendish Club to every kitchen in America. Soon he was publishing a magazine (The Bridge World), writing a bridge column, writing the seminal work on Contract Bridge in 1930 (The Blue Book of Contract Bridge), hosting a weekly radio cast featuring a bridge challenge match, forming and operating about 600 bridge teaching studios around United States and partnered with Josephine, playing high stakes bridge marathons against other pretenders to his throne. To give you an idea of his impact on the game, in 1939, when United States was still in the depths of the 30’s depression he made more than $1,000,000 from bridge related revenues.

He was a player’s player with marvelous instincts for the game. Jeff Rubens, the current editor of the Bridge World, said that Ely was known as a brilliant theoretician, yet he literally had dozens of rules relating to all phases of the game which he relied upon to make decisions about his own play. One of these rules was “Valuation by Visualization”.

To paraphrase this rule, it says that in making decisions about whether to make a game try or slam try, you should do so only if “a perfect minimum hand for partner will make the contract a lay down.” You first decide the minimum strength partner can have for his bid, and within that limitation you can logically place specific cards in partner's hand. It must now be a laydown and not be finesse dependent. If you read Frank Stewart’s Bridge column, you often see him employ this technique to justify a bid by saying “partner could hold….” and then giving him a minimum hand.

There is a story about a little known bridge blog author playing in his 2nd National tournament in Atlanta with even a lesser known bridge director. The game was a knockout and IMP scoring was in effect. Toward the end of the 4th set of boards the author picked up:

Void, Kx, Axx, KQxxxxxx.

Across the table he hears director open 1 heart. The match is close and author really didn’t want this on his shoulders, but he bid 2 clubs (not 2/1 game force). Author’s LHO now overcalls 2 spades! Director, for his opening bid, held:

Jxx, AQxxx, xx, Axx (with 2 1/2 quick tricks it meets minimum opening standards for this pair).

Director goes into the tank a minute and finally lays down the 3 club card. (This director administers the rules but doesn’t always follow them). After a pass by the other opponent, author takes a pause in the action. First, to silently thank LHO for his useless overcall in spades, and second to put on his superman suit. Trying to visualize director’s hand, either he psyched and then raised, or he has significant values in the heart suit at least 5 deep and the Ace of clubs. Author, determined to bury partner if he is mucking around at this level, asks for key cards. Director bids 5 hearts (2 without the Q). Now, assigning director a minimum number of points for his opening bid (11) author starts to place key cards in his hand. Author gives him the AQ of hearts and the Ace of Clubs. Based on the bidding the Ace of Spades seems very likely to be with LHO for his 2 level vulnerable overcall. The opposing pair at the other table will surely get to 6 clubs, and it now or never to put this match out of reach, or alternatively look for a new team.

The rest is history recorded with the ACBL. Author quietly slid down the 7 club card, and only after LHO led the Ace of spades did he realize that he had to play it. Fortunately, the hand meets Ely Culbertson’s other criteria, it is a lay down when director tables his hand. It was not until after all the smoke cleared and the “high fiving” ended that director pointed out that author had just bid a Grand Slam at a National Knockout with only 23 combined high card points and "off" one Ace.

If it were not such a good example of valuation by visualization, I would probably tell this story sooner or later anyway. That’s what you get for owning the blog!

Monday, March 26, 2007

In a Minor Key

In a recent talk to the Ocala Duplicate Bridge Club, Jon Shuster of Gainesville presented a selected analysis of 717,102 computer generated bridge hands. One part of his inquiry involved the usefulness and frequency of occurrence of the preemptive jump raise when using the Inverted Minor (“IM”) convention.

For the IM analysis he limited his inquiry to only the preemptive raise to be made with less than 10 hcps, and broke that down into a minimum raise of 1-6 hcps and a good raise of 7-9 hcps. Some criteria need to be mentioned to fully appreciate the IM analysis:

(a) With the minimum preemptive jump raise (1-6), Jon permitted the preemptive raise to be made holding a 4 card major.
(b) With the minimum preemptive jump (1-6) raise he stipulated 5 card support in both clubs and diamonds, but with the good preemptive jump raise(7-9), he permitted the raise to be made with 5 clubs or 4 diamonds (but not on 4333 hands).
(c) Most importantly he imposed a minor suit opening protocol of always opening 1 diamond unless the hand held 2 diamonds and 3 clubs (4423).

It is not necessary that you agree with Jon’s assumptions. Without assumptions analysis cannot be made. Other assumptions may vary the conclusions.

In one part of this analysis he tested the effect of permitting the good preemptive jump raise (6-9) FROM 1 club to 3 clubs with only 4 card club support to determine how this affected the frequency of finding opener with a 3 card suit. His results showed that the frequency of finding opener with a 3 card suit when raising to 3 clubs with only a 4 card club support is anywhere from 2-3 times more likely (depending on the seat in which opener opened). Central to this conclusion is Jon’s assumed protocol in the opening of minor suits.

If you changed the assumption to open “better minor”, I am confident that the relative difference of three card suits would be smaller between clubs and diamonds since you always open the better of the two suits. That is not a pitch for “better minor” nor is it a recommendation that you make a good inverted raise with 4 clubs. Assuming you apply Jon’s criteria, he found that when you make a good IM jump raise with 4 card diamond support, you expect to find opener with a 3 card diamond suit only about 8% of the time. It is easy to see that your support protocol has to be tied into your minor suit opening protocol to make a comfortable decision about the level of diamond support required for a preemptive jump raise.

The more important revelation from Jon’s study of IM preemptive raises deals with their frequency of occurrence. Let’s assume you play duplicate bridge twice a week or 104 times a year. If you use only minimum preemptive minor suit raises (1-6), you will see one about every 4 months. If you use only good preemptive minor suit raises (7-9), you will see one about 11 times a year or once every 9.5 sessions. If you use both minimum and good preemptive minor jump raises, you will see them 15.5 times a year, once every 6.7 sessions.

What are the practical aspects of this. Unless you play several times a week, you have to question whether using inverted minors is worth the effort. Every convention takes up "gray matter," so if you have reached your “Peter Principle”, this might be a good one to consider eliminating. Conventional bids also raise the possibility of missing an alert or missing the bid entirely, which could lead to disaster,

Finally, there is much more to the inverted minor suit raise convention that just the first response. If you are not familiar with the recommended continuations, you very likely will end up with a poor result. My view of this was substantiated by a comment made by Frank Stewart in his bridge column on March 25, 2007. After a discussion of an inverted minor hand, Stewart concluded:

“I don’t care for inverted minors, not because I think the idea itself is theoretically unsound but because the development of the auction will be confused unless a pair spends considerable time in discussion.”

I’ll give you a clue, I think the only correct places to pay these hands is either 3 of a minor or 3 no trump since you don’t have 8 major suit cards. Even with a single raise (10+) you can bet that either 3 of the minor or 3NT will be a top board, but unless you find opener with stoppers in both majors, getting it right can be an elusive proposition.

On the other hand, with long minor suit support and less than 9 points, a part score in no trump is often the best contract. It will be easier to find that contract if you do not take up your own bidding space with IM. The better advice is to simplify your convention card and leave those problems to someone who needs them.

Sunday, March 18, 2007

Losing Trick Count (Part 2)

In Part 1 on Losing Trick Count we learned how to make a LTC count of your hand and also to estimate the LTC of parter's hand. In this second and final post on the subject, we will see how to use the LTC information to make vital game going decisions.

Rule: Once you know your LTC and have estimated partner's LTC, simply add them together and subtact the total LTC from 24. The remainder is the number of tricks you are likely to take on this hand if you have an 8+ card fit.

(1) Opener’s Hand: AKxxx Kxx Jx QJx. (14 hcps/7LTC). Opening Bid is 1 spade. Here are some responses and analysis.

(a) Partner responds 2 Spades. Jxx Qx Qxxx Kxxx (8 hcps/9 LTC). Formula 24- (7+9) = 8. We are predicted to make 8 tricks in Spades. Opener should Pass.

(b) Partner responds 3 Spades Qxxx QJx Axx Kxx (limit Raise). (12 hcps/8 LTC) Formula 24-(7+8) =9. We make 9 tricks in spades. Opener should Pass. Here you would probably bid 4 spades on points alone, but LTC denies that. Note that despite the fit the hand is too square.

(c) 2NT (Jacoby) Qxxx Ax Axxxx Ax (14+ points/7 LTC) Formula 24-(7+7) = 10. We can make at least 10 tricks in spades. With no shortness and a minimum, opener bids 4 spades.

(2) The bidding goes 1s/2c/2d/?. As responder you hold Qxx Qx Axx AKxxx 15 hcps/7 LTC and spade fit. Opening hand vs. 15 hcps. Formula 24- (7+7) = 10. We are favorites to take 10 tricks in spades. Bid 4 spades.

(3) The bidding goes 1c/1s/3s/? Opener is showing 4 card spade support and about 15+ hcps. You estimate it to be a 6 LTC hand . You hold QJxx QJx Axxx xx (10 hcps/8LTC). Quit worrying about the hcps, you have only 8 LTC, so if partner had 6 LTC you ought to make 10 tricks in spades. 24-(6+8) = 10. On the other hand if you held Kxxx Kxx Kxx xxx (9 hcps/9 LTC, pass 3 spades, it looks like you can take only 9 tricks. 24- (6+9) = 9.

(4) Opposite a minimum raise, it is often difficult knowing whether to pass, invite to game or bid game. A good guideline is to bid game directly with 5 LTC, invite partner with 6 LTC and pass with 7 LTC. To accept an invite, partner needs to be on top of his raise and holding a 8 LTC hand. Something like Kxxx Kx QJxx xxx.

The Weak 2 Bid: Setting aside all of the theoretical discussions about disciplined and undisciplined weak 2 bids, if partner opens with a weak 2 bid, it is safe to assume that the hand is 7-8 LTC. If it is 8 LTC is would look something like KQxxxx xx xxx xx. If partner has 7 LTC the weak 2 bid hand could look something like KQxxxx xx QJx xx. If you have a 6 LTC hand, it is too good to be opened with a weak 2 bid, you are liable to pre-empt your own partner. If you have a 9 LTC hand, you better have an understanding partner.

Three level Pre-empts: Do not make the mistake of opening at the 3 level every time you hold a 7 card suit. If you do, some of your hands may be too weak for a 3 level pre-empt (8 LTC hands) and some may be too strong (5 LTC hands). At the 3 level, vulnerability is very important. Until you gain confidence in your own judgments, a good rule to follow is to open a seven+ carder at the 3 level with 7 LTC if non-vulnerable and with 6 LTC if vulnerable. As you move up to the 4 and 5 level with your pre-empts, subtract 1 LTC from each of the 3 level requirements for each level you go up.

Responding to Pre-emptive Bids: Knowing when and how much to raise a pre-emptive bid is one of the hardest judgments in bridge. Start with an assumption about partner’s LTC, and then count how many of his losers you can cover with winning honors in your hand. Assume, for example, that partner bid 2 spades on KQxxxx xx xx xx (7 LTC). To produce game you will need to cover 4 of his losing tricks to bring the total losing tricks down to 3. Counting high card points is not very reliable as Queens and Jacks don’t count for much in this analysis. Your “cover cards” will roughly equate to your Quick Tricks. Thus, you can raise to 4 spades with Jxx AQx AQx Axxx (4 Quick tricks/7 LTC) and have a reasonable play. If you have a singleton, you can also count that as a cover trick if you have at least 3 supporting trump. Thus, Jxx, AQJx, KQxxx x (6 LTC) will give you a play for game.

LTC is not for novices who still need to focus on basics. Using hcps is the only practical way to learn the game, but once you have mastered hcps (advanced novice), you need to learn when to forget hpcs (distributional hands) and use the LTC technique. Pat Peterson teaches LTC in her advanced bidding courses. Again, the book is Modern Losing Trick Count by Ron Linger. Good bridge is a lot of work, but also a lot of fun. If you could buy a good bridge game, who would be interested in playing?