ceeb

I'm not sure I follow the intended analysis. Ducking will be ok if spades are 5-1 and either diamond is onside and the ♣Q as well. By the vacant space argument both ♦ are wrong .4x.4=.16, so the double diamond finesse is 84%, and the club finesse 40%, for a net of 32%. That compares to 75% x 50% =37% when there is no vacant space consideration, so argues slightly for winning the diamond. Is that the idea? Winning the opening spade lead here works whenever both diamonds are onside, 35% plus or minus depending on what vacant space assumption you make, so already it's nearly equal with even the optimistic 37% for ducking. Add even a 5% chance of spades 4-2 with diamond honors split and Bob's your uncle. I like the argument that spades are 5-1 but surely it has to be mitigated by the huge dealing odds in the opposite direction. If LHO leads at random from equally long longest suits, the spade suit would be 70% 37% to be 4 cards. I can see halving that based on judgment about leading proclivities, but cutting it to zero? Ducking the first trick is taking an extreme position against even a small chance of ♠4-2. (Edit - on reconsideration the actual spot led increases the chance of 5-1 spades.)

As for the play, I'd like to know how the opponents implement "3/5 leads" -- some pairs take this to mean 5th best from 6 and if that is the case a 3-suit squeeze gaining two tricks is plausible against East. Also, I presume the ♠10 was played on the assumption that dummy did not play an honor. Assuming West takes the ♦A and returns another spade, against a 6=2 spade break I want to cash another spade with the option to discard a diamond from hand to keep all heart suit options open. East's discard if any will probably be informative. There are a lot of combinations and a lot of chances. If the opponents' carding is such that spades are likely breaking and again assuming a spade continuation, I will play on the assumption that if anyone is long in ♦ it is East (who ostensibly has five of them) so I may pick up one extra trick somehow then squeeze East between diamonds and either other suit. That suggests cashing the ♥K since if East has a singleton the minor suit squeeze (and club finesse) is likely. If all follow small to the heart it seems to get complicated.

I agree with Phil, Frances, and Gnasher's observation (e.g. "But strong opponents may duck the diamond twice, leaving you to guess what to do.") that my analysis of the slam being better than 50% was wrong. I was careless in my enthusiasm to make the point that *even if* it is a bit over 50% I still do not want to be in it. That said, a quibble of my own about Gnasher's analysis: Hypothesizing a line and showing that the contract is under 50% on that line is not a logical way to show the contract is under 50%. I mention this only in fun, and to show that I'm trying to surmount my bad habit of agreeing with Gnasher first and reading his analysis afterward.

It's a percentage slam -- diamond break or Jxx of clubs puts it over 50%. So it's worthwhile compared to game at other tables. But compared to 6H it would be better to settle for the cold game. Therefore unless playing IMPs against unusually strong counterparts I'd prefer to be in game.

I presume the spade lead is in the face of dummy having shown the suit. Even though there are several possible reasons for the lead -- looking for a ruff, bluffing a ruff, looking to give partner a ruff - nonetheless I think one can draw inferences from the lead that probably override the tiny nominal percentage differences among various trump plays. I figure the lead as one of 1) singleton ♠, probably without ♥K 2) bluffing a ♠ ruff holding ♥KJx(x) 3) long spades hoping to give East a ruff - unlikely with a void ♥ in decreasing order of likelihood. If #1 best is ♥Q first to avoid confronting a ♣ switch but that play implies a strong belief in #1 being the case. ♥'s from the top is a compromise mostly also catering to #2, if you reckon LHO has the bluffing mentality, and on my assumptions is 50% to be ok in the ♥ suit even in case of #3. So I like it. Not clear how to react if RHO turns up with ♥Kx(x) and puts a ♣ through. As for wanting to be in it: Trusting everyone's analysis that it is a moderately odds-on slam, judging that it's reasonably biddable by our counterparts, and taking into account that we're stuck a bunch, better to stay out of this one.

I don't know what IMP/MP scoring means, but maybe I don't need to know. At trick 3, cash the dummy's other high trump. Assuming both follow or LHO shows out, run the ♣Q planning if it holds, to continue with the ♣J. The fact that the ♣10 appears on the first round doesn't change this. RHO presumably covers the ♣J. Now it is nearly 100% safe to play a ruffing finesse in ♠ for an overtrick.

I feel very strongly that East has short diamonds (just kidding; I know what you meant), and probably short spades as well since the ♠Q, passing strange in any case, is risky hence extremely unlikely from ♠QJx. This is more reason to suspect ♥J86 with East.

I'd bid 1NT without agony -- the prospect of developing tricks is reasonable and partner likely has some ♥s if we are left here, and passing isn't my style. I don't mean that as patronizing, just that if I passed I'd be at sea later. Also, if partner has a long minor we want to have bid. Bidding 2♠ with only five isn't tempting at all.

I don't see much difference between the problem when the defenders keep 1♣ and 2♠, versus keeping 3♠. I compare these two defensive strategies: 1. The defenders keep one large spade each and one small (<♠6) spade between them (RHO discarding one small spade), no clubs, and three diamonds. So long as they treat the two small spade spots as described, LHO not revealing a small spade and RHO not revealing both of them, the ambiguity about spade length remains. 2. The defenders keep two spades, the long club, and three diamonds. Maybe #2 has a practical advantage in that even if the defenders mess up by revealing the spade position, the unknown club situation still disguises the distribution. Is that the point, or is there more? By the way, additional discarding strategies to consider are 3. The defenders keep two spades -- one big one little -- and four diamonds. of which 3a. The sleepy way: spades are 1-1; declarer must exit in spades. 3b. The unexpected way: one defender holds both spades and a singleton diamond honor, the other hold THREE diamonds.

After ♦A, ♥A, ♣Q reveals that the minor suit differential and therefore also the major suit differential is only one card, a major suit squeeze is unlikely. On the plus side, LHO is probably 3370 i.e. ♠ may break. Continue ♣J (and a 3rd ♣ if not covered), try ♠Q winning if covered. Finish pulling trump, cash ♦Q, play ♠s and hope the 10 or 8 comes down within 3 rounds. If the ♠Q lost there is the slight extra chance of a ♦-♠ squeeze if LHO had 108xx,xx,J98xxxx,--. If the ♠Q wins I see nothing better than ♥K, ♣8, ♣, ♦Q, and then ♠J catering for ♠3-3 or K10xx or K8xx on the left.

This does seem better. I would though cash the ♥A if the finesse wins. That avoids a defensive ♥ ruff in layouts such as RHO's xxxx,Kxxx,Kx,xxx, and also profits against RHO's xxx,Kxx,K7xx,xxx.

I don't read anything into the lead except a good chance that clubs are 4-3, hence a slightly diminished chance of very bad breaks elsewhere. Crossruff will require things to go well. We'd play to score 2 spade ruffs and 1 club ruff in hand, so roughly LHO must have 4 clubs and nothing too destructive in terms of short spades or the diamond 9. Roughly 50% for the clubs, 70% for the ruffing the 3rd spade, so about 35%. Finessing the red suits is probably better. Suppose ♦ to the 10, and eventually ♥ to the Q and ruff a small ♥. To a first approximation this succeeds if ♥Kx(x) is onside, or if ♦K(x) is onside. If the ♥ chance is 25% and the trump chance is independently 30%, that adds to 47%. I don't see any appealing line involving establishing spades.

Anyway, declarer knew what our signaling methods are, which is slightly more information than we have been given.

duck, cash spades, probably continue spades. That retains the chance to make if both black suits lie lucky and isn't much worse than guessing hearts for -1.

I suspect that when you have a complicated holding in trumps, more often than not there is a defensive layout such that whichever defender ruffs consumes a trump trick. This particular holding is nice to be aware of, but probably there are lots more layouts where the immediate 4th club loses ... ... and indeed in what way can playing the 4th club gain? After 3 clubs live I'd just duck a heart. If hearts break then there are 11 tricks; only if RHO wins the heart and plays a diamond must then the diamond finesse be tried. In particular on the given trump lie the heart duck brings in 11 tricks regardless of the location of the diamond king.