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I agree with Cascade as regards dealing probabilities. Given the trump break, 3253 is over 14% 2353 is under 10% 3352 is under 12%. However, there is a restricted choice argument that in the last case LHO might well discard a club from 5305, whereas in the first case with 5404 the defender has little choice because of the excellent bidding. So if I chose line 2 I'd tend to ruff a club.

Good lead -- whether from ♦AJ107x(x) or from 7x(x), other tables may not face this problem. Hence hoping for some luck: Win, ♠Q to the A, ♣Q and unless this is covered the hand is over one way or another. If LHO follows small, cash ♥s and finesse against the ♣10. If LHO follows with the ♣6 or 7, ♥ to Q, run the ♣8. Alternatively could play ♥ to the Q first. Saves a downtrick; loses most of the chance for a ♠ cover.

4♠. I sympathize with the worry that this might undercook for ♠ purposes, but other than that I don't understand the reservations. With a million hands like AQJxx,xx,xxx,AQJ, what choice has partner but to make (practically -- except for 4♣) the only forcing bid? If slam-going with diamonds, partner will be happy to hear of the double fit and will not pass. Even if partner might pass 4♠ on a few hands where 6♦ is best it is hard to imagine that failure to indicate the ♠ feature will lead to more accurate slam judgment on average over those marginal deals.

an unsatisfying example anyway, in that it's hard to construct an excuse for RHO to unblock both spots (one of them might have been count. Cherdano's idea seems plausible.) Except for the one story I cited, the scuttlebutt I've heard about his ability was muted so yes, I assume that he was a lesser light compared to the stars of his era but I don't have knowledge. I did play a round against him and Helen Sobel -- 1965 San Francisco Nationals I think -- and it was a privilege. We must have had a bad result and there was some glowering between my partner and me (mostly me I'm guessing) and Goren, as tactfully as it is possible to deliver so delicate a message, advised us (me?) to learn to behave better toward partner. Of course I was a little inwardly resentful at being dressed down but I couldn't object "Who does he think he is?" I knew who he was.

That's true. The chance of >17hcp is about double with the balanced distribution. But as against that it looks to me that 18-19hcp 3433 facing a minimum 1♥ response tends to be a poor game. If you consider instead the criterion that opener have a 5-loser hand, then the situation is more than reversed: In my simulation of 200000 deals (opener 5 losers and one of the listed distributions, responder 4+ hearts and either shorter spades or at most 4 spades), four times as many 2425 hands qualified (38 hands, 22% of the total, nearly 4-fold over-representing expectation based on distribution alone) as 3433 hands (5% of the total, more than 3-fold under-representing the 18% expectation based on distribution alone -- and all 9 of these hands have >19hcp, so nominally don't even open 1♣). I suppose the true rate of 4♥ bids is somewhere between the extremes of a rabid point-counter and a LTC zealot, but still expect that the expectation for 2425 is well ABOVE 1/8.

Maybe. I'm always interested in your experience. Sorry, I misled you by including the irrelevant information of "strong game". I'm using the hand from BBO only because it reminded me of my question and because the suit here seemed like a good illustration, not because I imagine that the actual pretty good declarer's oversight bears in any way on top level performers. I had more in mind examples like a (serious) London rubber bridge hand in which Bob Hamman overlooked a sure trick line because he missed a spot in the trump suit, and he didn't seem astonished to have done so. seemingly not yet, but no reason to suppose that the margin by which you fall short has anything to do with spot watching. Let's try to refine this a little. I've heard top players (sorry I don't specifically recall who) say that they figure they always know the spots when it matters, or that they figure they can always reconstruct the spots in a suit if necessary. That's consistent with what you say, but it's qualified. It doesn't rule out in fact probably implies occasionally being surprised by a suit where the spots rated not to matter but did (vide my example). There is a difference between "being able to reconstruct" and always being on top of the situation in real time.

Kibitzing a strong game the following occurred[hv=pc=n&s=shdc6542&w=shdc8&n=shdcakj&e=shdcqt973]399|300[/hv]West led ♣8, A, 10, x. Subsequently E followed suit (to the ♣K) and discarded his remaining intermediate clubs leaving himself ♣Q3 against declarer's ♣65. No one but a kibitzer noticed what had happened and the consequent potential for an extra trick. My feeling is that even the very top players do not track the exact spots reliably enough to have picked up this opportunity at the table. Maybe there are one or two exceptions -- Martin Hoffman perhaps? and it used to be said that Charles Goren could write down the exact hands after a session. What do others think? And do you think it possible and/or worthwhile to cultivate the ability?

The literal answer to your question is that you forgot one big thing -- the unequal probabilities of the various distributions. For 2425 I make the chance to be 0.0617 or nearly half of 1/8. In stipulating to ignore the extra comparative chance that 2425 would be worth bidding 4♥, you stipulated away a compensating advantage that could be quite large.

Mostly reasons to finesse. Probably LHO with J8x will treat J/8 as equals on the second round (and similarly for 108x if the first trick lost to the J). Therefore the strategy of drop 2nd round wins only against original KJ or K10 on the right; finesse wins against J10, J8, 108. Moreover there is a possibility that LHO will (and should) cover on the first round from J8x or 108x which further reduces the chances for KJ or K10 offside.

Point well taken.

My first thought was that percentage is win the ♣K (discarding a heart -- not "anything") and play ♦ from the top for two more discards which is 53% in the ♦ suit. The alternative of ruffing the ♣K and finessing ♦ for three discards is obviously <50% in the ♦ suit (actually 42% since 5-1 or 6-0 diamonds is no good) so superficially inferior. However, I posted wondering if my second thought that RHO's reluctance to break a red suit could indicate her actual ♦Qxxx (e.g. fear of squashing partner's ♦10xx) was valid or resulting. I take Rogerclee's point that it was hindsight. I overlooked the possibility of making when spades are 3-1. 4% + 2% 5%x? + 3% So unless my arithmetic is way off, the differential from 3-1 spade break successes for the two lines is dwarfed by line 2's need for a ♦ break.

I agree we are very thin for 5NT, but doubling and likely defending with a void is also precarious -- not so much that 5♣ is likely to make, but in that it invites a very random outcome. 5NT at least approximates our actual hand and so gives the chance for a very good result if partner has good offense.

[hv=pc=n&s=sakhkj85dakt95ck6&n=sqt98643hq74dj6c5&d=w&v=0&b=1&a=ppp2np3hp3sp4sp6sppp]266|200|Club honor led to the A. Low club returned.[/hv]How would you play? This hand is from a BBO Cayne match and East seems to me, as one would expect, a good player though I don't recognize the (Italian) name. I had one idea at the time; a different one later. I don't recall the exact lead but assume it was Q or J so East would know a club continuation was at least "safe" if not safe.

Tricky. Your sig includes the nice bit of snide about 2/1 from gnasher, forestalling my temptation to assume MP since not stated. At IMPs I'd go for the throat with a low diamond. Assuming ♥ length < 3 in dummy (else little hope to defeat) the underlead has reasonable compensatory prospects. At MP, ♥.

Re Phil's analysis the postscript about considering the opening bid seems relevant. 60% for the combined chance of dropping a major suit queen seems about right, but the probability of winning a ♠Q finesse through the opening bidder is similar and there are additional indications from trick 1: leading ♣4 from ♣9x(x)4 may counterindicate outside honors; RHO ducking trick one is less likely with both ♦AK and hence suggests ♠Q more strongly. But rather than the technical chance via cashing aces and kings I like Nigel's play: Collect 52% equity by cashing top trumps, then instead of simply spade drop try for an endplay via (1) ♠Q with RHO, (2) defenders fail to cash RHO's ♦ top(s), (3) we read the distribution. But what is the ♠ finesse line really worth? If you would choose it, surely exploring in ♦ per dake is nearly cost-free. It helps a lot -- the very weak indication from trick 1 play that RHO hasn't got ♦AK, ♣A has turned into a strong appearance that RHO had ♦A10x. (Are these birds clever enough to defend this way when RHO holds ♦AK10x ♣AJ108x rather than trying the ♣A instead of the small ♦? By the way why not ♣A in any case? What does RHO know from the opening lead?) Therefore the opening bid seems to place the ♠Q onside. Of course it was a little lucky to get such telling information from the diamond suit. There are imponderables but it's maybe a 1/3 chance that LHO has a diamond top and a 1/4 chance that we learn about it. Assuming you take 60% via cashing tricks when the ♦ plays aren't informative and nearly 100% by ♠ finesse the 1/4 of the time like the actual hand, the net is 60%(3/4) + 1/4 = 85%. If you believe that estimate it's hard to beat.

By "which makes slam nearly certain" I do mean the same as "which makes the slam depend on two out of three finesses (that are supposed to work on the bidding)" (though 6♦, if you can find it, may be a shade better yet). To say that slam being good is conditional upon East having some useful cards is true enough and goes without saying but is not what I meant. By bringing up the positional value of West's aces I meant that slam is very good compared to what it would be based on the same E-W cards but no knowledge of the opening bid. My first instinct was that while West is more than minimum for double-then-3♣, I wasn't going to put any blame. But on reconsideration of the potential in West's aces I decided West is a lot more than minimum and since East has given the partnership an opening to go further West should take it. Slam may still not be reached.

West should have anticipated the positional power of his aces over the opening bidder, which makes slam nearly certain.

It's an interesting card combination but on this particular hand I don't see how declarer can establish 10 tricks without creating 4 for the defense. For example even if North wins the ♥J and exits with a ♦, there's still time for the defense to score its ♠ trick.

If you play on ♦ -- seems a better chance for the contract than ♥ -- it would clearly be advantageous (e.g. South has xxx,A10x,KJ10x,xxx) to play high from dummy at trick 1. However, since the contract is absolutely normal and the game is matchpoints, playing on ♥ seems justified on the grounds that it maximizes the expected number of tricks.

5♥. To make 6♥ partner would need a fine vulnerable 4♥ bid, which is against the odds to hold when bidding 4♥ not vulnerable and is rendered much further unlikely in that it requires a low-hcp construction for the 5♦ bid. More typically 5♥ is already a save with say xx,Q109xxxx,--,QJxx opposite.

Edit -- sorry dup

♥ is better than ♦ if declarer is 3307 (or Axxx??,Kxx,--,AKQ10xx). Assuming declarer controls ♦ -- which is perhaps indicated by the 6♣ bid and possibly supported if the "hmm" expresses ironic surprise at dummy's diamond controls -- and assuming partner hasn't led a low heart from ♥x4 or opened 1st seat vul with a 5-card suit, If declarer has ♣AKxxxxxx the only chance is Kxx,x,x,AKxxxxxx and a ♠ shift. If declarer has ♣AKQxxxx, a ♥ will work and a ♠ will be ok also vs. Kx(x),Kxx,(x),AKQxxxx (which helps explain the weak 2). If declarer has ♣AKxxxxx, a ♥ will work, a ♠ may be ok (if partner ♠A), and a ♦ works if partner has 7 ♠. If declarer has ♣AKQxxx, a ♥ will work, ♠ as previous, ♦ will work. If declarer does not control ♦ then If declarer has 7-8 clubs, the only chance is a ♠. If declarer has ♣AKQxxx, a ♥ will work if partner is 7123, a ♠ if partner is 6313 or 7123 with ♠A, a ♦ if partner is 7303 (maybe KJxxxxx, Kxx, --, xxx?) If declarer has ♣AKQxx a ♥ will work only if declarer bid surprisingly to ignore 3NT, a ♠ will be ok if partner isn't very light for the opening bid, a ♦ is good if declarer is Axx,x,J10xx,AKQxx which seems a very optimistic 6♣ bid. There seem to be a lot of imponderables, such as explaining the opponents' bidding. ♠ makes the most sense to me, perhaps because I am not used to 7303 weak twos.

Of course (hits head). One could expand the model putting f=probability the finesse line will win and writing Pf instead of P/2. Then the condition for playing the fake finesse becomes approximately 0.4 + 0.6 Pf > f, or 0.4 > f(1-0.6P), satisfied either by large enough P or small enough f -- in particular f<0.4 no matter what P is. At this point, having discussed the hand, it is easy to grasp why RHO should not cover the ♠J and therefore to suppose it is obvious and no top player would go wrong. But if we allow that even Zia would take a moment to work it out and imagine that at trick 1 we manage to cover the opening lead within a couple of seconds and Zia plays along in tempo, and then at trick 2 as we cross in clubs he follows suit without betraying any wistful delay as if getting ready for the next trick, and that at trick 3 when the ♠J is led he of course follows low in tempo, then we have evidence for the smallness of f (evidence that he doesn't have the ♠K), a good case for going up with the ♠A.

Thanks for the analysis. Definitely helpful. Yes, I underestimated the ♠ finesse line by underrating its chances against ♠Kxxx(x). It seems to be about 48%. Those figures even seem to me to be generous, especially the 13% which neglects that ♣ must still break. Overall I get only 40%. There's about 32% when every line works. In the relevant sense that finessing picks up twice as much of the remainder as discarding it does seem not very close. To be fair, whether Zia would cover doesn't depend merely on whether it's right or wrong on analysis. Surely he will only do as much thinking as he has time for in advance, so if we play like Hoffman we get more edge. Second, there is at least a slight chance that even if Zia doesn't see any advantage to covering he also won't clearly see the advantage to ducking, and on some of those occasions of ignorance he'll go wrong under the time pressure of second hand play. I don't see offhand how to estimate the necessary chance for Zia to cover from the foregoing figures, and the wording is confusing as well.

If you go for immediate discards, dake hit the point that ♦ first is right because you have a chance to recover if RHO ruffs the 3rd one. However, on simple % calculation I think the trump finesse is a few % better. The imponderable question on which I hoped for insight is whether, in view of the small difference in the various probabilities, that even though Zia might be better than most at ducking the ♠J, he might still err often enough to make it worthwhile to test him then switch horses if he does not cover the trump J. Most players can't hope to outclass Hamman and Zia, but still hope to beat them somehow. Hence you hope that they make mistakes than you. Is the best strategy just to hope by chance that the cards deal them more opportunities for wrong decisions than they deal you? Or should you actively push them when the opportunity arises? In practice declarer Siebert (I forget which brother) ran the trump J and went down. All suits split.