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Edit -- posted the below in too much haste. Withdraw. Agree. The possible layouts & probabilities (scaled from the prior probabilities) are just these two xx hxxx xxxx xxx (4/7) xxxx hx x xxxxxx xx xxx xxxx xxxx (3/7) xxxx hhx x xxxxx I'm still with you: xx xxx xxxx xxxx (3/5) xxxx Txx x xxxxx xx Txxx xxxx xxx (2/5) xxxx xx x xxxxxx I think we are agreeing that the possible layouts are therefore xx xxx xxxx Qxxx (1/2) xxxx Txx x xxxxx xx Txxx xxxx xxx (1/2) xxxx xx x Qxxxxx so the odds are 1:1. This seems a very complicated way to get to the answer. "That means that" suggests a linear line of reasoning, but 2/3 and 4:3 seem to be from thin air here. Anyway, I cannot follow. The only layouts I see consistent with Fred's formulation are these two: xx Hxxx xxxx xxx (2/3) xxxx Hx x Qxxxxx xx xxx xxxx Qxxx (1/3) xxxx HHx x xxxxx so I think the finesse is a pedestrian 2:1. I can come up with 8:9 if I consider xx Hxxx xxxx xxx (8/17) xxxx Hx x Qxxxxx xx xxx xxxx Qxxx (4/17) xxxx HHx x xxxxx xx xxx xxxx xxxx (5/17) xxxx HHx x Qxxxx but the last is impossible when RHO has played five little clubs. Seems right: xx xxx xxxx xxxx (5/13) xxxx Txx x Qxxxx xx xxx xxxx Qxxx (4/13) xxxx Txx x xxxxx xx Txxx xxxx xxx (4/13) xxxx xx x Qxxxxx

Instead of ♣J with RHO, this line needs both ♣J on the left and the last trump on the right.

The ♦A needs to live, so that really requires ♦3-3, plus somehow not losing a trick to the ♥10 in the last 4 tricks. Therefore, rolling along, it must be better to simply pull trumps -- ruff trick one, unblock ♦, pull trumps ending in dummy, discard all the spades if ♦J10 fall in 3, and finesse the ♣10.

Is "balla" Indian slang? I of course agree completely about logic. Detailed computation is nothing -- neither mathematics nor related to at-the-table bridge -- though I am somewhat proud of my program. The beauty of mathematics is in finding simple and sometimes surprising ways to see things. This principle is important to playing bridge because, I believe, thinking leads to mistakes. The more thoughts I churn, the greater the chance one is wrong. Therefore it's really beneficial not merely to be able to solve bridge problems but to have economical thought processes for doing so.

Agree closely. My automated calculation includes the above, also the negligible considerations of J alone of diamonds and the opening leader's presumed KQ of clubs. ♠Qxxx onside is more significant than we intuit. It occurs over 11%, and so even considering the necessary diamond luck you've shortchanged the finessing line by up to 6.6% (if my club-lead logic is fair). In summary I concur with the well yclept JLOGIC at 44.1% to 41% -- plus some singleton ♠Q cases adding the same 1+% to both numbers.

Yes, I think it's wrong in principle. If partner's thought processes are rational, it is always in theory possible to anticipate them. There is no such theory. It is tempting to assume an algorithm such as considering all possible partner hands and corresponding to each of them all possible layouts from partner's point of view, but there are two insuperable obstacles to that theory: it requires unlimited computation power, and it fails to acknowledge that "all possible layouts" is ambiguous, not well defined (because for example interpretation of the bidding is somewhat subjective). The logical fact is that partner's thought processes cannot always be anticipated, and to assume otherwise is to play a very high pressure style of partnership defense, high pressure because it must occasionally come a cropper and further such croppers are defined as mistakes by one of the partnership. How "occasional" or how stressful a style is right at the top level I don't know. Not to my taste but it may be the winningest route. I don't think I have ever suggested, in any discussion about bridge, either online or offline, that anyone should believe me for any reason other than the bridge arguments that I or someone else has advanced.I think that's right, and your good analyses and reasonable style make a positive impression which you may be stuck with. From partner's point of view, those are layouts where the contract will go down regardless of what he does. To discard a diamond is to play for an extra undertrick. Yes? Sometimes that's all there is to play for. That is correct under the theories that (a) each defender is responsible for anticipating all ideas that might occur to partner, and (b ) any misjudgment is an error. In this case the misjudgment would be that both defenders already know X (club play can't help), so we need to look elsewhere.

You gave an example of what partner's thought processes might have been. Unless you can provide an example of a hand that partner might hold where (1) he might conclude that throwing a diamond increased the chance of setting the contract, and (2) it would be right for us to cash ♠A, those thought processes led him to make a mistake. That's illogical. Whether partner made a mistake doesn't depend on whether I personally can provide an example, but only on whether it exists. And that's not quibbling, but a substantial point. I've proposed a certain philosophy about partnership -- to recognize the possibility that sometimes it may be impossible to guess what partner has in mind and therefore, in some circumstances, to make a play that is not justified by any interpretation you can think of for partner's play. In insisting that *I* must come up with an example here, you are simply side-stepping my idea. Do you think it is wrong in principle? If you disagree with it and argue against it, fine -- leveraged by your greater expertise and experience you may well convince me. But I am not quite so humble as to concede that my ideas are wrong by default. That said, here's the germ of an idea. Perhaps partner, holding, approximately QJxxx, xxx, J8, xxx and trying to imagine layouts where his defense matters, can only come up with declarer hands like A, AKQxxxx, Kx, xxx or A, AKQJxx, Kxx, xxx. I don't mean to imply that partner is too dumb to consider the actual layout, but rather as I've already said partner doesn't consider it plausible.

If people interpret my "I'd hate to posit partner made a mistake" as meaning that I posit partner made a mistake then I take partial blame for the misunderstanding. Admittedly sometimes people say "I hate to..." as a prelude to doing that which they hate. That's not what I meant so my choice of phrase was unfortunate. My opinion is that partner may legitimately see things differently, and I gave an example. I believe that there is such a thing as putting too much pressure on the partnership signals. Never mind that this may be an imperfect world (partners do make mistakes). Even that aside, it is an ambiguous world. Many partnerships signaling philosophy is "your signal should convey whatever information is most important to partner." I don't argue against that approach -- I subscribe to it myself -- but I do argue that in the interest of winning bridge as well as partnership harmony you should accept that it doesn't always work. Sometimes partner's view is very different than you imagine and your guess as to "what is most important to partner" will be way off.

Good point. I missed that. I can agree but that's splitting hairs. Neither one looks like a splinter to me. It may therefore be right to consider other explanations. I'd hate to posit that partner made a mistake, but it does sometimes happen that partner sees things in a different way than we imagine. For example if partner has no trump trick and reads the bidding as showing a solid heart suit, then partner might not feel a duty to make a signal denying a trump trick. Maybe partner therefore figures that for us to try the ♠A if we have it is can't-lose so giving count is pointless.

I like the *idea* of a 4th club -- it protects partner's trump trick if such exists (though only Qxx is really at risk. If partner has Jxxx (or Kx) any black card works.). But why should it exist? Though the OP didn't give a full explanation of the opponents' methods, from the clue of declarer's club holding it appears that it was intended mainly as choice-of-games. That means that declarer thought the heart suit is solid, not AKJxxxx. Therefore ♠A for me.

It would be helpful to know what bidding persuaded LHO to lead ♦10x, but offhand I would not play LHO for only ♠Jxxxx. Who overcalls 1NT with a scant stopper and 4-4 in the majors? I would cross in ♣ and run the diamonds both on general principles, and because it wins outright if LHO has Jxxxxxx,Jxx,10x,x.

Post prandial judgment maybe, but pass & 5♥ seems obvious to me. Pass over 3♠ because despite 10 card ♥ fit this is a 9-loser hand, marginally worth a 2♥ response to a double. The urgency to bid 2nd time around is partner may have extras -- to accommodate the worries about wasted ♠A, imagine --,AKxx,AKxx,xxxxx. Admittedly, LHOs strange bidding does give me pause; hate to let him get away with it.

I like pass. Of course it understates the spades, but bidding 6♠ with this seems like being stampeded; on average I think we'll do better going along with whatever pd guesses.

That's right. So why make North the declarer? Must have been a hand from play.

But now you have no entry in a threat suit to the dummy's ♥winner. The play has gone: ♠8,9,10,K South wins ♥x Q x x West wins ♣x x Q x East wins ♠x x x A North wins So far everybody wins. Now you can, for example, duck one more ♣ and cash the minor winners leading to a 4-card ending in which you endplay W to score your ♠7. But you don't score the ♥K, so you lose 2♥ and 3♣.

Combining chances is a great principle, but there is also a principle that a lot of small chances may not add up to much. Playing ♠A then ♣s is at most 30% total chance: Singleton king either side -- about 12% Long ♣ and long ♠ with RHO -- if lead shows ♥ length, about 10% ♣ 3-3 and RHO has ♠Kxx -- 7% Long ♣ and long ♠ with LHO (along with the long ♥s) -- 1%.

Trusting the problem setter is easier than working out whether declarer can always suitably rectify the count for a squeeze. Making N the declarer must be a devious move to trick the careless. Pursuing that assumption, the only reason it matters who declares is that West but not East can break spades. Therefore it must be that breaking spades is the key to defeating the contract by South, hence unbreakable from North.

If LHO has four trumps, you don't cash two rounds of clubs - you just exit with a turmp and claim. Hence this should be if trumps break 3-2, or if 4=1, or if 1=4 and long trumps has short clubs or the ♣Q drops. Right. I read the OPs line too literally, and I posted without first seeing your post. To summarize, your 2.5% differential is conditioned on 1=4 hearts, hence corresponds to an 0.3% overall success differential between the author's and the poster's lines of play.

How so? If trumps are 3-2, we're 3 longer in trumps than the opponent. If we let them in 3 times with ♠Q, ♦A, ♦J and get tapped each time, we'll have equal length (all trumps gone assuming we pulled trumps when able) and we'll be on lead. At that point we cash the long ♦. Hence the only cost from being tapped out is a possible extra down-trick when ♠ are 4-1. (I did see your first message in which you mentioned generally the danger of being tapped and I acknowledged that claim in my initial analysis.)

Assuming no inferences from the lead or bidding, just calculating a priori lies of the cards -- All lines lose if there's a void trump. Immediate ♣ finesse works if the ♣q is onside, or trumps break and no singleton ♣ onside. 78% Strip two rounds of ♣ and endplay works if trumps break 3-2, or if 4-1 and long trumps has short clubs or the ♣Q drops. 83% Strip only one round of ♣ and endplay works if trumps break 3-2, or if 4=1 as Little Kid points out, or if 1=4 and ♣Q onside, or 0,1, or 5 small ♣ onside. 90%

This may explain Jack's thinking, but I don't think it is correct analysis. Finessing loses the contract only if it loses, the opponents then get a diamond ruff, and they still score two diamond tricks. Unlikely the opening leader (East) has a singleton diamond, or will manage to shift from ♦AJxxx. Hence the danger is substantially the chance that West can win a ♣ shift and get a ♦ ruff. That's 4-5% assuming the imaginative ♣ shift from East. Finessing gains the contract when ♠Qxxx(x) is onside and there are two natural ♦ losers. Counting only ♠Qxxx, that's about 7.5%. Hence even if overtricks were negligible compared to the big fat partscore bonus :( I'd finesse as the best chance to make 2♠. But really, even the overtricks from finessing may well overwhelm the small chance of a ♦ ruff defeat.

I don't get it either. First, it's MP not IMP. So spurning the % play in trumps is investing some fraction of a trick, even after discounting because of the possible ♦ ruff. Being forced out of trumps doesn't seem to me a legitimate concern. If trumps are 3-2 or the ♦J comes down, you can't be tapped out. If trumps are 4-1 and the ♦J is a loser, then you have 6 losers and are down anyway -- except if it's ♠Qxxx onside, then only NOT finessing allows those bad things to happen.

It's not universally accepted, because I don't accept it, though I'll probably understand it next time you use it. It's also not accepted by the WBF. The Guide to completion of the WBF convention card includes these definitions: S/S: Short suit S/T: Slam try SPL: Splinter, or short suit which suggests the theory that someone once wrote "S/T" next to a slam try bid that happened to be a singleton, someone else misunderstood, and before long the error was being propagated. In support of that theory, consider that the alleged abbreviation pattern is not normal English. Does it have any precedent at all? Omission of letters is the job of an apostrophe, not a slash, isn/t it? The slash in S/S for example serves to separate the two Ss to indicate separate words, not to substitute for the intermediate letters "hort" (otherwise it would be S/S/ -- "uit" would be entitled to equal representation). There are many other examples of propagated errors in English -- misunderstandings that have been often repeated and even proudly defended by their errant users. One such example is "arrant nonsense", often misspelled as "errant nonsense." (Nice essay at http://www.nytimes.com/2006/01/22/magazine...n_safire.html.)

The trap to avoid on this hand is to not win the ♠A in your hand, but rather, win the K on the dummy and play a diamond to the 9 ... if they were 3-3, or there was honour ten doubleton on your right, you are at home. or dry ♦ honor(s) onside. Diamond 3-3 are equally likely as hearts 3-3. The extra chances in diamonds compare with the extra chances from clubs or endplaying LHO for a 4th ♠ trick. My feeling was that the club chances are better than the extra diamond chances, and the spade is a bonus. That's why I said the ♠K play seems improbable. I admit I did not calculate. Edit: We overlooked some additional winning cases for ♦ that may be important -- two honors dry with LHO. Depending on the bidding that could bring the ♦ chances up to 49%. However I still think the ♠8 play is clear. (1) it might win, (2) the extra club trick is around 20% (we'll have to start them with low from the dummy; RHO may not make the best play).

No one would believe the chances in diamonds are good enough to justify playing the ♠K at trick 1 so that's not the trap. Therefore I would do something like Hanoi5: assuming T1: ♠8,J,A finesse spade at trick 2 & if it wins the best shot I see is T3: try a low club, succeeding if the hearts break or something good happens in clubs, or if LHO gets endplayed for another spade trick. Not so tempted to play diamonds at trick 3 because that might force you to cash ♦A when in with the ♥K, at a time when clubs are still to be developed. But I don't see that as qualifying as a trap.