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.
Sunday, September 30, 2007
Sunday, September 23, 2007
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.
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.
Tuesday, September 18, 2007
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!
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!
Wednesday, September 12, 2007
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!
^^^^^^^^^^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!
Friday, September 7, 2007
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.
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.
Thursday, September 6, 2007
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.
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.
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