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[hv=n=shakjxdck10&w=shxxdcjxxx&e=sxhqxxdcax&s=sah10xxdxxc]399|300|South plays ♦, dummy ♥, East ?[/hv] The instinctive play from East is to keep the same shape as dummy. No doubt it's the wrong play (and any counting East knows the lie of the cards) on sufficient analysis. A moron defender throws a spade hoping that the next trick will never come. But it takes a very alert East, not just a non-moron, to realize that declarer is planning to discard ♥J rather than ♣ on the next trick. Justin's idea of saving the spade to play as the squeeze card brings to mind Nabokov's explanation of a "quiet move" in chess in Invitation to a Beheading. The idea is so simple it's easy to overlook how subtle and strong it is.

♠A then low to the ♠Q. I think it's a very close but interesting question. I make the nominal percentages (absent lead inference) to be (double finesse -- run the Q) 71% (ace then low to the Q) 59% (low to the Q) 50% The lead inference is not strong. The bidding slightly discourages a heart lead (no double) and arguably the dummy has advertised minor suit controls. Even if we assume that LHO would always lead the ♣A when holding the ♠K but would lead it only half the time without the ♠K, the 59% for ace-then-low increases only to under 66%, seemingly decisive for double finesse. However, at the same time the double finesse probability decreases similarly, to 63%. Overall ace-then-low is therefore best provided LHO is dissuaded from at least about 4/9 of "random" (no trump trick) ace leads.

West has T9x of hearts and Ax of spades, EAST two clubs and Qxx of spades. You are down four if you play a spade and insert the king. The point about keeping track of the clubs is that you don't cash the last club unless it is safe to do so (or unless you have decided to play West for the ♠A). Given the defensive holding you mention and assuming the misguess of playing East for the ♠A the contract is down 1 if LHO has ♠A10 and down 2 if RHO has ♠Q10x. Not more. That is why you don't cash the club king (unless there is only one club left) when you decide to play E for the ♠A. As an aside, you would have a hard time taking the score back if you go down when EAST did have Qx of hearts, or maybe a creative QT doubleton of hearts.At the point of the matrix above you judge which heart holding to believe, having a lot of clues from the discards.

Minor point -- don't cash the 2nd heart early. Instead, come down to [hv=n=sjhj8xdck&s=sk9xhkxdc]133|200|[/hv] with the lead in the dummy and West of course retaining ♥109x. If only 1 club remains, cashing the club, playing a spade and misguessing is down 1. If more clubs remain then misguessing East for the spade (play a spade to the K) is at worst down 2, misguessing West for it (cash the club and duck a spade) is down 1. So there is no need to consider down 3 etc. If East was being playful with ♥Qx so be it. (But to make such a play East would have to hold the ♠AQ.)

Double. Intuitively it seems right to express the relative suit suitability of this hand. I'm not sure we'll get to 4H if partner has x,K9x,xxxxx,Axxx (though we might), but the example supports the idea of emphasizing suit play with a double. (Even if the spade x is J,Q, or K it looks better to play in hearts.)

Right. I was careless in claiming that ♥, ♦, and ♠ finesses all put you about equally at 75% if they work. Try the ♠ first and even if it gets you to 11 tricks, if you lose a trick in the process then you have only one finesse chance, not two, for the 12th trick. Hence while a successful (respectively unsuccessful) ♥ or ♦ start means 75%+ (respectively about 5%) chance to succeed, the corresponding numbers for a ♠ attack are more like 50%+ and 25%+. However, the 50% doesn't include the possibility (how much?) of LHO making a smooth duck to allow pilfering the ♠Q without losing a trick. (I posted a similar message several hours ago which hasn't appeared. Maybe it will, but in the past this forum always worked predictably.)

You also have LHO having ♦Kxxx and a chosen spade honour. After RHO wins the heart, he has to return a heart to stop you setting up the diamonds. You win, draw trumps, take a diamond finesse, ruff a diamond, then cash the trumps and hearts to squeeze LHO. You can't cash ♦A when you're in dummy, so you'll have to read the ending. I was unable to find such a squeeze. For example in the matrix below the last ♣ squeezes dummy, not West. (I also don't see that preserving the ♦A matters.) [hv=n=sq10hada10c&w=skxhxdkxc&e=sxxhxxdxc&s=saxxhjdcx]399|300| [/hv]

At first glance this is a two-of-three finesses hand. Assuming clubs break, you have similar very good chances (75%+) if you correctly guess on a winning finesse to try first (whether ♥, ♦, or ♠), and bad chances if not. For a second approximation consider the bad chances: If ♥ finesse loses, later find ♦KJ(x). If win ♥, pull trumps, & lose ♦ finesse, need ♥ finese & ♦J dropping doubleton. If win ♥, pull trumps, & misguess ♠, need ♥ finesse+♦finesse. Hence the ♠ play looks best because it is the only one that allows the full benefit of finding two of three cards right even when the first one you try for is wrong. I'm guessing that's a more important consideration than these additional issues: What does the lead imply about the chance for West to have the various missing honors? Comparing the "good chances" when the first finesse wins, what are the extra splinter chances? And last and least: Which line offers a better chance if trumps don't break?

Regardless of the way clubs are played to the first few tricks, collect 7 tricks (♣, ♥A, ♦'s) and dummy will have ♥KJ and some losing cards. The ♥KJ will both score, so that's 9 tricks. Sure, technically it's undeniably a squeeze in that East has to discard cards he'd rather keep. But unlike a fancy squeeze, the only thing that counts is your winners. The moral is that a "surplus winner squeeze" is some kind of junior version of the species, hardly worthy of the name.

I'd be inclined to play my top spade at trick 2. With weak diamonds declarer might have preferred a slower auction, so there's a good chance spades is declarer's weaker suit and that a diamond play will be more productive from partner's side. Besides, if declarer has say Q10xx,KQ,AKxx,xxx the best thing is to kill the dummy.

I was motivated to make some calculations by the fact that I guessed the worst line -- diamond ruff then trumps. Bottom line, the consensus views are right by a surprising margin. Assumptions: trump spots are split 3-2 (♣Q not doubleton), lead from ♥KQ. Simplifications: Calculated hundreds of distributions (considering "subsuits" such as ♦QJ), but ignoring several details such as ♦QJ doubleton or careful analysis when diamonds are 5-2. Begin with a ♦ ruff then play ♣ succeeds about 37%. Begin with a ♦ ruff then play ♠ succeeds about 46% (of which 10% comes from double shortness -- two black doubletons in the same hand) Pooltuna & Balicki got that part right. The squeeze is about 53% using Nigel's assumptions: RHO always exits ♦, LHO never, so Jlall et al are supported. Further I think my trump-loser assumption dis-favors the squeeze. Allowing for the guard squeeze and/or LHO's defensive choices is too complicated, but as a lower limit if the defense always plays a ♦ and we ignore our ♦10, the squeeze would be 43%.

For what it's worth, I've calculated almost exactly. Suprisingly, a noticeable edge to playing ♥ first -- about 13% where ♣ first is superior, nearly 16% for ♥. (In addition, 20% of the time both lines work because some Qx is onside or both Qx are offside, and a further 19% the line is moot because testing one round of both suits turns up a void or a Q.) To understand the idea, compare two similar example cases. Suppose the first suit you play finds xx offside. If you play hearts first, consider that it is 3.6% (given 1-6 spades) that RHO is dealt xxxxxx,xx,xx,Qxx -- heart drop fails, club finesse comes to the rescue. That compares with the 0% chance for the club-drop-first to succeed via LHO holding x,Qxx,???,xx since by stipulation both opponents have followed to two diamonds. Even without testing diamonds the same principle applies since a 7-1 split would be unlikely. Without the spade distribution information, clubs-first would be about 1/2% better.

The spade king must be off-side. Otherwise either RHO has overcalled on ♦QJxxx and out, or LHO has doubled 2♦ and led low from ♦1085. Unless the ♣8 is a singleton, RHO is playing a very devious defense. A devious defense is possible since RHO more or less knows declarer's hand, but still the odds are against it. Further, RHO's failure to continue diamonds suggests trumps are breaking. If all that is true, RHO is a favorite to hold the ♠J. Win the ♣, cross in ♦, low ♠ toward the 10.

That's good enough to persuade me to double. Does the lead even matter? Probably (notwithstanding Fluffy's reasonable idea) it does, if we take the mere fact that the problem has been posed as a clue. But that aside I would expect 6♠ probably down with or without a double. The bidding suggests that LHO has two non-solid suits and RHO hasn't much in spades (double of 5♥), so partner may have ♠Qxx and a ♦ holding sufficient to make the suit unestablishable.

Cherdano's point about partner not having 6 clubs because of opponents' silence is educational for me, but very subtle in that I would find it hard to estimate how much the slight extra distribution would influence the probability of the opponents finding another bid. Comments? A more simple-minded reason to suspect partner has only 5 clubs is that the six card suit is 6 times less likely to be dealt (though against that a six card overcall is much more likely to be acceptable without both top honors). EDIT-- AKxxx is 4 times more frequent than AKxxxx and 2.8 times more frequent than AYxxxx where Y can be either K or x. Allowing for the pro-rate chance to lose a trick to the K when overcaller has Axxxxx, the relevant operational ratio is somewhere in between. Why do I bother with these calculations?

I'm surprised at the unanimity of winning the ♦A at trick one. This in effect squanders a dummy entry (You feel it when late in the hand you cannot both force LHO with a good spade from dummy AND lead a diamond from dummy to establish the Q.) so right or wrong it is a somewhat unnatural play. Ducking is the convenient way to establish the ♦Q on the actual lie -- 2164 distribution with RHO, though it loses when RHO is 2371. It survives when LHO has 3 trumps -- if LHO ruffs our 10th trick we get it back with a club ruff in dummy -- or whenever spades break.

Strange where are ♣3 and ♣2 ? It seems to me that partner must have them and tried to fool declarer with returning ♣10, knowing that declarer would duck. When the ♣8 and ♣7 appeared partner rightly concluded that you could stand a switch to ♥. You now need to switch back to ♣ before the ♥ are established. Declarers hand: ♠Kxx ♥A9654 ♦Ax ♣Q84 Nice defense. Rainer Herrmann I'm sure you're right about the clubs -- from ♣Q843 declarer can't afford the 8 because it allows a fatal overtake by West when East has ♣A10 doubleton. But I have trouble visualizing declarer's hand. Isn't 2NT non-forcing? Even Kxx,Axxxx,Kx,Q8x seems a bit too strong. So I considered Kxx,Kxxxx,Kx,Q8x, but now the defense is entitled to 3 clubs and 2 red aces routinely, so why would East risk the low heart play? Nor does J10xx, A106x, Ax, Q84 with declarer completely make sense though from East's corresponding Kx,K987,Kxx,A1032 the defensive situation is less clear. Charles

♦Q, ducking if not covered. I must try to establish a long diamond, which entails losing one anyway, and I want to place the ♦K in order to guess how the clubs lie. If East wins then ♣K and ♥J may be entries for two high ♦ ruffs; finally ruff a black card in dummy, pull trumps with the ♥7 & cash a long diamond. If the ♦Q is covered prospects are not as good since the ♣K rates not to be an entry to bring in the long ♦. However there are various chances to make black tricks -- running the ♣10, leading towards the ♠10 as no doubt West has ♠KJxx. Very strange trick 1 though. No one leads the ♥9 from four trumps or even three of them; no one pops up with the ♥Q from 3 cards or even 2. So I have no explanation.

How? To be honest I had in mind your same line -- ♥A then ♦'s. That's tired because LHO can discard clubs on the spades and have enough cashing tricks to beat me. But after winning the 4th round of ♠ the remaining cards are [hv=n=shqxxdcq10&w=sh10dqxxck&e=shkj9xxdc&s=shaxxdk10c]399|300|[/hv] so I'll try a low ♥.

Cannot West profitably refuse to win the last ♦? If RHO is 4522 then ♣A, ♠ works. If RHO is 4423 I don't see any hope but ♥KJ109.

4NT. Maybe not at the table with an unfamiliar partner, but at least as a paper answer it seems about right. Encouraging, no minor suit card or control -- so trumps.

I'm mystified. Neither opponent redoubles 4♣ -- nominally denying 1st round control -- yet opener makes a grand slam try of 6♣. Responder skips over 4♦ yet later finds the muscle for 5♦. Does responder's 4♥ just mean a minimum? Or would 4♦ have been the ♦A and 5♦ is the ♦K? Of course they have their methods but I would like to be at the table to ask what they are. Absent that, I'll guess that opener HAS the ♣A and therefore opener's pass of 4♣x was NOT justified by hoping to hear a redouble. Hence, opener has NOT the ♦A. Therefore I'll lead ♦Q, either to build a ♦ to cash after winning a ♠ or possibly to cash 2 ♦ before declarer manufactures discards with black winners.

Duck the opening lead in dummy and if RHO plays low also let the ♦9 win.

If West holds Qxx,AQJ,KJxxx,xx, West can be endplayed with the 3rd heart. Win ♣K, ruff ♠, lead ♥. West (say) takes ♥A, exits ♣. Win ♣J. If ♣'s are 2-2, ♠A, ♠ruff, ♥K, ♥ and discard. If ♣'s are 3-1 it would have been better to play for ♦'s 3-3 (or ♦J10 doubleton in East).

What is the opponents' NT range?