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Here is a way to get a rough estimate of the probability of success. I find this calculation useful since it is doable at the table if you are comfortable doing basic mental arithmetic with fractions.

Use the fact that each of the 3 suits can be guarded by one defender. Ignore the fact that vacant spaces get limited to approximate these events as independent coin flips. Then

S guards both C & H ~= 1/2*1/2 = 1/4 N guards both C & H ~= 1/2*1/2 = 1/4 First two does not happen but S guards both majors ~= 1/2*1/2*/12= 1/8

Squeeze succeeds ~= 1/4+1/4+1/8 = 5/8 = 62.5%

When none of this happens there is still a small chance of HJT falling in 3 rounds or SQ falling in 2 rounds, guesstimate the conditional probability of that as 1/4. (The exact value of this is not as important as remembering to avoid double-counting it.)

Play succeeds with probability ~= 5/8 + 3/8*1/4 ~= 62.5% + 10%~= 72.5%.

We have been overestimating the probabilities by ignoring vacant spaces, so take a reasonable haircut on this estimate. I usually take it down by 5-10%, so one would get ~65% here, not far from Kit and David's exact figure above.

Finally, the alternative play of cashing H honors instead of S honors that I and several others have suggested above gets to exactly the same probability of success, although the two lines succeed/fail differently on different layouts.

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♦A, 3 rounds of ♥, ♣A. Then start running the diamonds, pitching 2 clubs and a spade. On the last diamond, pitch ♥9 if it is not good. In the 3-card ending, I play for the black suit squeeze to have succeeded and play spades from the top. This line will succeed if (i) S guards H and N guards C, or (ii) S guards both H and S, or (iii) either defendant guards both C and S.

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How about just one national per year? I understand the large number of tournaments serve the pros and some retired people well, but I feel this (especially, regionals and sectionals) devalues their significance.

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Yes, but RHO already opened 1♥ in the first seat. In case A, we have the remaining hearts, so partner is more likely to have 4+ spades than the other cases.

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Richard, it is true that 11 tricks are normal. But I expect that those 11 tricks will score 50-60% for the declarer in a typical club game, while 10 tricks would be about 20% and 12 tricks above 90%. So, one should pitch the spade only if one believes it is better than 50-50 odds that partner has the 8. I do, given what has transpired so far, but it is a close decision. Risk appetite as a partnership and whether we need a good result vs. playing safe would also come to play.

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Partner seems to be pretty careful with his play of the spot cards, giving us all the information he could. As Ben says, the fact that he played ♠2 in the second round of the suit tells us that he likely has the 8 and didn’t play it thinking it might be important. If that is the case, he would be quite disappointed if we don’t find the ♠10 pitch.

Another factor favoring this play is that things have gone quite well for the declarer so far and we will not do well if he scores another heart trick.

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I have too many losers if I lose to trump Q. My plan is to play for doubleton Q and get 3 spade ruffs in the hand. That would get me to 11 tricks (one spade, 3 diamonds, 3 spade ruffs, two hearts and two clubs). I still need another trick, which could come from hearts or clubs, but I don't have to decide on which yet.

I start with ruffing the SK and cashing AK of trumps. Seeing the first wish come true, play HA, spade ruff, HK, spade ruff. Now CA, seeing CQ drop. Now we'll pull the outstanding trump and decide on the source of the 12th trick. From the play so far, it is more likely that CQ was a singleton, but I'll have a problem if I play a H, West will win HQ and play a H and I have to lose a club. So, I have to end play East in clubs. So, pitch a heart on DJ, cash SA pitching the last heart and duck a club at trick 11.

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I completely agree with Nikos. I buy almost every bridge book that gets published, but won't buy or read this one. I do not consider this a bridge book.

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I see, you are right about 2-4 hearts. With 4-2, you will have to find CQ (i.e. ruff West's heart exit with CJ or, more likely ruff with CK and finesse the other way). Let's assume you get that decision right 50% of the time and run some numbers.

P(S) = P(surviving the spade ruffs without an overruff) = P(4-4) + P(3-5) + 0.5* P(5-3) = 32.7% + 0.75*47.1% = 68.0%

P(H) = P(succeeding in the heart end play) = P(3-3) + P(2-4) + 0.5*P(4-2) = 35.5% + 0.75*48.5% = 71.9%

Ignoring the correlation between the two events, we get P(success) = P(S) * P(H) = 48.9%.

Now, the much less elegant play of playing the trumps from the top succeeds with probability P(2-2) + 0.25*P(3-1) = 40.7% + 0.25*49.7% = 53.1%

It is pretty close and I suspect it will even be closer since P(H given S) > P(H) and also because West is unlikely to stay quiet with 5 good spades or a good 4-4 in the majors.

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Kieran's line succeeds if it avoids the spade overruff (i.e. spades are 4-4, or 3-5, or 5-3 with CQ onside) and hearts are 3-3. There is also an additional chance if it avoids the spade overruff and hearts are 4-2 but clubs behave (2-2 or stiff Q).

Using a priori probabilities for suit distributions, I get 41.5% for the probability of success, but it might be slightly more (will survive some 6-2 spade splits and also the odds of 3-3 heart split increases once spades are 4-4, etc.). The straightforward line of pulling trumps succeeds with 53.1% probability, so it seems better.

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I agree it is a great play. My point is that it is not that difficult to default into it if you have the right reflex to ruff a second spade and then test trumps.

This hand would make an excellent example in a textbook on declarer play.

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This is a nice play, but I'd expect most world-class declarers to find it. At the table I was watching, the declarer (who was also in 5♣ and got the same spade lead and heart shift) missed the opportunity by winning the heart shift in the dummy. Now, he was one entry short to complete the elimination of spades and diamonds.

Edit: I see that only two declarers were able to take 11 tricks in clubs (one in 6 going down), so I might be wrong. Only a diamond shift by West at trick 2 beats 5♣ by taking away an entry, and I don't think that would be found in most tables. Perhaps Kalita's play deserved more credit than my initial assessment which was apparently colored by seeing the layout.

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So glad to hear the point of view expressed by Justin, Max, et. al. I think this is too rare of a perspective for the good of the game.

I also think that UI and its treatment by the average player has become horrible. I would venture to guess that about 50% of the field in a regional tournament is using tempo as a defensive signaling mechanism (pause before leading a side suit doubleton, pause before cashing an ace without the king, pause of before ducking with the ace, etc. etc.), and about half of that 50% do not even notice that they are doing it because it has been ingrained! As stated above by others, it is often a free shot to take advantage of these situations. Unless top-notch players demonstrate by action at the table that this is not OK, this will continue. I.e., I'd like to see more examples of playing the ace on a slow doubleton lead without a bridge reason to do so. It is simply too convenient to duck with a pause and then rationalize that you knew it could not be a singleton.

In summary, I'd like to see more examples of falling on the sword due to active ethics. We need many contemporary anecdotes similar to Al Roth's “I thought you had the queen!”.

Murat Azizoglu

Murat Azizoglu

Use the fact that each of the 3 suits can be guarded by one defender. Ignore the fact that vacant spaces get limited to approximate these events as independent coin flips. Then

S guards both C & H ~= 1/2*1/2 = 1/4

N guards both C & H ~= 1/2*1/2 = 1/4

First two does not happen but S guards both majors ~= 1/2*1/2*/12= 1/8

Squeeze succeeds ~= 1/4+1/4+1/8 = 5/8 = 62.5%

When none of this happens there is still a small chance of HJT falling in 3 rounds or SQ falling in 2 rounds, guesstimate the conditional probability of that as 1/4. (The exact value of this is not as important as remembering to avoid double-counting it.)

Play succeeds with probability ~= 5/8 + 3/8*1/4 ~= 62.5% + 10%~= 72.5%.

We have been overestimating the probabilities by ignoring vacant spaces, so take a reasonable haircut on this estimate. I usually take it down by 5-10%, so one would get ~65% here, not far from Kit and David's exact figure above.

Finally, the alternative play of cashing H honors instead of S honors that I and several others have suggested above gets to exactly the same probability of success, although the two lines succeed/fail differently on different layouts.

Murat Azizoglu

Murat Azizoglu

Murat Azizoglu

I agree with David Caprera that the ruling seems to be sensible.

Murat Azizoglu

Murat Azizoglu

Murat Azizoglu

Murat Azizoglu

Murat Azizoglu

Another factor favoring this play is that things have gone quite well for the declarer so far and we will not do well if he scores another heart trick.

Murat Azizoglu

I start with ruffing the SK and cashing AK of trumps. Seeing the first wish come true, play HA, spade ruff, HK, spade ruff. Now CA, seeing CQ drop. Now we'll pull the outstanding trump and decide on the source of the 12th trick. From the play so far, it is more likely that CQ was a singleton, but I'll have a problem if I play a H, West will win HQ and play a H and I have to lose a club. So, I have to end play East in clubs. So, pitch a heart on DJ, cash SA pitching the last heart and duck a club at trick 11.

Murat Azizoglu

The solution as outlined above by Nigel G. is quite brilliant.

Murat Azizoglu

Murat Azizoglu

P(S) = P(surviving the spade ruffs without an overruff) = P(4-4) + P(3-5) + 0.5* P(5-3) = 32.7% + 0.75*47.1% = 68.0%

P(H) = P(succeeding in the heart end play) = P(3-3) + P(2-4) + 0.5*P(4-2) = 35.5% + 0.75*48.5% = 71.9%

Ignoring the correlation between the two events, we get

P(success) = P(S) * P(H) = 48.9%.

Now, the much less elegant play of playing the trumps from the top succeeds with probability

P(2-2) + 0.25*P(3-1) = 40.7% + 0.25*49.7% = 53.1%

It is pretty close and I suspect it will even be closer since P(H given S) > P(H) and also because West is unlikely to stay quiet with 5 good spades or a good 4-4 in the majors.

Murat Azizoglu

Using a priori probabilities for suit distributions, I get 41.5% for the probability of success, but it might be slightly more (will survive some 6-2 spade splits and also the odds of 3-3 heart split increases once spades are 4-4, etc.). The straightforward line of pulling trumps succeeds with 53.1% probability, so it seems better.

Murat Azizoglu

This hand would make an excellent example in a textbook on declarer play.

Murat Azizoglu

Edit: I see that only two declarers were able to take 11 tricks in clubs (one in 6 going down), so I might be wrong. Only a diamond shift by West at trick 2 beats 5♣ by taking away an entry, and I don't think that would be found in most tables. Perhaps Kalita's play deserved more credit than my initial assessment which was apparently colored by seeing the layout.

Murat Azizoglu

Murat Azizoglu

Murat Azizoglu

I also think that UI and its treatment by the average player has become horrible. I would venture to guess that about 50% of the field in a regional tournament is using tempo as a defensive signaling mechanism (pause before leading a side suit doubleton, pause before cashing an ace without the king, pause of before ducking with the ace, etc. etc.), and about half of that 50% do not even notice that they are doing it because it has been ingrained! As stated above by others, it is often a free shot to take advantage of these situations. Unless top-notch players demonstrate by action at the table that this is not OK, this will continue. I.e., I'd like to see more examples of playing the ace on a slow doubleton lead without a bridge reason to do so. It is simply too convenient to duck with a pause and then rationalize that you knew it could not be a singleton.

In summary, I'd like to see more examples of falling on the sword due to active ethics. We need many contemporary anecdotes similar to Al Roth's “I thought you had the queen!”.