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I don't know how BBO generates hands, but the above statistics prove that it can't be in random fashion.

No, it doesn't. It doesn't “prove” anything.

Let's grant that the 1000 deals you chose were randomly dealt out hands (as opposed to the robot competition where I believe there are intentional biases built into the hand selection). Let's also grant that your manual calculations are accurate (which we have only your word for, and even assuming you are honest about this people have been known to make errors tabulating this sort of thing).

According to my off the top of my head calculations (which I admit aren't necessarily accurate), your results are on the order of 2.5 standard deviations away from the expected value. Some statistician out there can come up with the exact number. That isn't a likely event, but longshots do occur. All your results would say is:

If the dealing were truly random, the probability of getting these results is about 1 in 5000 (or whatever the number is). Unlikely, but possible.

Thus, we can interpret the results in one of two ways. Either:

a) The dealing program is flawed, causing this bias b) The dealing program is not flawed, and these results happened by chance.

Whichever interpretation you choose to make is your judgment. But do not say this is any kind of proof. Statistics never prove anything. All they do is give us a basis from which we make our judgments about reality.

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Yes, on that exact hand my play will fail with best defense. This needs East to have specifically the king of clubs and the queen of hearts for his 2 outside honors (which he might not have). Saying this layout is a reasonable expectation as to what he might hold is quite an overbid.

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That is my understanding also. Playing online, I will routinely make claims without a statement which would be far too loose for normal play. If an opponent doesn't see what I am planning they simply reject the claim, and I play it out. If my claim was wrong, that will be determined in the play. I can't imagine a director ever being called for a claim online.

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Definitely win the first trick. I'm going to be losing several tricks in the other suits along the way, and I can't afford to be losing a spade trick. If East opened a 5-bagger and has an entry, I'll pay off.

I will start by leading the jack of hearts. West will have to cover if he has the queen, in which case I will duck. Now I can set up a heart trick as well as throw West in if he has 4 hearts, and he will have to give me something. It is hard to see how this will fail on normal splits.

If West doesn't cover, he doesn't have it. I will play AK and a heart. If the hearts are 3-3, great. If not, I will again be throwing West in for multiple end-plays, and probably emerge with 9 tricks.

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John,

I will grant that that even though you won't be able to find out about partner's distribution and side card location, game is more likely to make if partner has a maximum than if partner has a minimum.

It may be the case that game is a favorite to make over the range of hands partner would consider a maximum, while it is an underdog over the range of hands partner would consider a minimum. If this is the case, the 2NT inquiry would be correct if you were in a bidding contest.

You are not in a bidding contest. There are two opponents at the table. By bidding 2NT, you give LHO a relatively cheap 3-level overcall or a free double, which may aid his side in finding a good save, a good make, doubling your eventual contract, or finding the best opening lead. By bidding 4♠, you force LHO to commit himself at a very high level. IMO, the gain from putting this pressure on the opponents far outweighs any slight advantage which might exist from inquiring.

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First auction: Big spade raise

Third auction: Could be a variety of things. The overcaller will make his most natural call, and partner will follow up with what he thinks is appropriate having heard the overcaller's third bid.

Second aution. My agreements are that good-bad 2NT followed by 3NT shows doubt about notrump, presumably a single stopper. Partner should pull with a singleton in their suit unless he has sufficient fast tricks 2NT followed by a Q-bid shows a partial stopper.

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What's going on here? Partner would have responded 1♥ with 4 hearts, so declarer has 4 hearts. Declarer wouldn't have overcalled a 5-card spade suit to the queen, particularly holding 4 hearts, so declarer has 6 spades. This makes declarer's distribution 6-4-1-2. It means that partner has played a wrong count card in clubs for some reason, but that seems like the most likely inconsistency.

If this construction is accurate, my best bet is to shift to a heart and play partner for the ace of hearts. Would declarer have risked the heart ruff if this is the layout? Yes, because he does need a club ruff in dummy and doesn't know the spades are 2-2. Okay, I've convinced myself to shift to a heart.

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I'm not particularly concerned that the transfer gives the opponents more options. I want to maximize my ways of bidding my own hand. In my mind that has the higher priority.

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Yes, it is wrong to pass. You have a perfectly good hand, and a perfectly good suit, one you certainly want led against 3NT. You would open the bidding without hesitation with this hand, and diamonds is definitely where you live. What are you afraid of – going for a number in 2♦?

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We play that redouble by either of us shows the weakest holding possible in the danger suit. This gives partner a chance to sit if he has things under control. Thus, we will never be wrongly running unilaterally. Also, this gives us a chance to avoid being bluffed out when we have something like Jx opposite 10xxx, where both partners have better than the weakest holding possible.

At any rate, it is vital for any partnership to have solid agreements for this situation.

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For those who don't have the background to understand the mathematical analysis, here is the layman's way of calculating the odds:

Think of a 13-card hand being dealt one card at a time. For each card, it is necessary that the rank of the card not match the rank of a previously dealt card. So:

The first card can be anything.

The second card must not match the rank of the first card. There are 51 possible cards left. Of these, 48 do not match the first card. The chance of the second card being ok is 48/51.

The third cad must not match the rank of either of the first two cards. There are 50 possible cards left. Of these, 44 do not match either of the first two cards. The chance of the third card being ok is 44/50.

Continuing along this line, the chance of success for all 13 cards is:

(48/51) X (44/50) X (40/49) X (36/48) X (32/47) X (28/46) X (24/45) X (20/44) X (16/43) X (12/42) X (8/41) X (4/40)

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If players follow the proper policy of always asking about the meaning of an alerted bid regardless of whether or not the information matters to them at the moment, then there is no UI issue.

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Partner's heart spot is an attitude signal. A low spot says that from his point of view he wants hearts continued. A high spot says that from his point of view he doesn't want hearts continued. It doesn't show or deny the king of hearts, since if he had the king of hearts and a doubleton diamond he would have signaled his intentions by putting the king of hearts on the table.

Kit Woolsey

No, it doesn't. It doesn't “prove” anything.

Let's grant that the 1000 deals you chose were randomly dealt out hands (as opposed to the robot competition where I believe there are intentional biases built into the hand selection). Let's also grant that your manual calculations are accurate (which we have only your word for, and even assuming you are honest about this people have been known to make errors tabulating this sort of thing).

According to my off the top of my head calculations (which I admit aren't necessarily accurate), your results are on the order of 2.5 standard deviations away from the expected value. Some statistician out there can come up with the exact number. That isn't a likely event, but longshots do occur. All your results would say is:

If the dealing were truly random, the probability of getting these results is about 1 in 5000 (or whatever the number is). Unlikely, but possible.

Thus, we can interpret the results in one of two ways. Either:

a) The dealing program is flawed, causing this bias

b) The dealing program is not flawed, and these results happened by chance.

Whichever interpretation you choose to make is your judgment. But do not say this is any kind of proof. Statistics never prove anything. All they do is give us a basis from which we make our judgments about reality.

Kit Woolsey

Kit Woolsey

Kit Woolsey

I will start by leading the jack of hearts. West will have to cover if he has the queen, in which case I will duck. Now I can set up a heart trick as well as throw West in if he has 4 hearts, and he will have to give me something. It is hard to see how this will fail on normal splits.

If West doesn't cover, he doesn't have it. I will play AK and a heart. If the hearts are 3-3, great. If not, I will again be throwing West in for multiple end-plays, and probably emerge with 9 tricks.

Kit Woolsey

I will grant that that even though you won't be able to find out about partner's distribution and side card location, game is more likely to make if partner has a maximum than if partner has a minimum.

It may be the case that game is a favorite to make over the range of hands partner would consider a maximum, while it is an underdog over the range of hands partner would consider a minimum. If this is the case, the 2NT inquiry would be correct if you were in a bidding contest.

You are not in a bidding contest. There are two opponents at the table. By bidding 2NT, you give LHO a relatively cheap 3-level overcall or a free double, which may aid his side in finding a good save, a good make, doubling your eventual contract, or finding the best opening lead. By bidding 4♠, you force LHO to commit himself at a very high level. IMO, the gain from putting this pressure on the opponents far outweighs any slight advantage which might exist from inquiring.

Kit Woolsey

Kit Woolsey

Third auction: Could be a variety of things. The overcaller will make his most natural call, and partner will follow up with what he thinks is appropriate having heard the overcaller's third bid.

Second aution. My agreements are that good-bad 2NT followed by 3NT shows doubt about notrump, presumably a single stopper. Partner should pull with a singleton in their suit unless he has sufficient fast tricks 2NT followed by a Q-bid shows a partial stopper.

Kit Woolsey

Kit Woolsey

If declarer has 5=4=1=3 shape, I can't imagine him overcalling 2♠ rather than making a takeout double.

Kit Woolsey

If this construction is accurate, my best bet is to shift to a heart and play partner for the ace of hearts. Would declarer have risked the heart ruff if this is the layout? Yes, because he does need a club ruff in dummy and doesn't know the spades are 2-2. Okay, I've convinced myself to shift to a heart.

Kit Woolsey

Kit Woolsey

Kit Woolsey

Kit Woolsey

5♠ is meant to shock everybody at the table.

Kit Woolsey

Kit Woolsey

Kit Woolsey

At any rate, it is vital for any partnership to have solid agreements for this situation.

Kit Woolsey

Think of a 13-card hand being dealt one card at a time. For each card, it is necessary that the rank of the card not match the rank of a previously dealt card. So:

The first card can be anything.

The second card must not match the rank of the first card. There are 51 possible cards left. Of these, 48 do not match the first card. The chance of the second card being ok is 48/51.

The third cad must not match the rank of either of the first two cards. There are 50 possible cards left. Of these, 44 do not match either of the first two cards. The chance of the third card being ok is 44/50.

Continuing along this line, the chance of success for all 13 cards is:

(48/51) X (44/50) X (40/49) X (36/48) X (32/47) X (28/46) X (24/45) X (20/44) X (16/43) X (12/42) X (8/41) X (4/40)

Kit Woolsey

Kit Woolsey