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[hv=pc=n&s=saqt863ha32dq9ca7&n=sj9hq85dak764ckq8&d=s&v=0&b=11&a=1sp2dp2sp3sp4cp4dp4np5dp6sppp]266|200|♥J led, Q, K [/hv] NS are U.S. players in IMP quarterfinal at US nationals; I guess they are playing 2/1 style. EW are Zia, Hamman in case it matters.

With regard to bidding 6♦ it's worth noting that you should not assume that ♦ will run for no loser. Accept for the sake of discussion the partnership decision to play Gambling 3NT. Assuming we play that 3NT shows a "running minor", just how running must it be? Even if the partnership has accidentally agreed "absolutely solid", in reality when you are dealt AKQxxxx the suit is a strong favorite to run for 3NT purposes -- especially if partner won't sit with a void. So given the stipulation that Gambling 3NT on AKQJxxx is a winning strategy, the case for opening 3NT with AKQxxxx is weaker by so slight an amount that it would be very surprising if the dividing line falls between the two. Therefore as a practical matter, if you play Gambling 3NT at all you will not flinch at using it with AKQxxxx. That being the case, how likely is the suit solid for slam purposes? Opener is known to have the AKQ and 4 of the remaining 10 cards, hence 40% to hold the J in which case the suit nearly always runs, but a 60% chance to be missing the J including a 1/3 chance to be missing both J and 10. In the last case it is only 35% to have a 3-3 break and no loser; with AKQ10xxx adding in Jx brings the chance to fractionally over 50% (54% that the J drops per http://dna-view.com/suitbreaks.htm, less 2% for singleton J). The net is only about 5/8 chance that a suit that is "solid" for NT purposes will run opposite a void. (I'm ignoring 8-card suits, but perhaps in that case as well opener can and should "cheat" by opening with AKJxxxxx.) On the present hand, 6♦ is almost surely off the ♣A so trumps will need to run. In addition, we may have a handling problem: likely need to cross to dummy with a ♥ ruff (though the actual ♣Q is a nice bonus) and a ♠ lead could be a killer (though the actual ♠Q is helpful). Bidding 6♦ is betting that the chance of losing a handling trick is under 20% (because 80% chance of no handling trick x 5/8 chance trumps run is 50%). I don't have a strong opinion about that; my point is just that if you bid with your eyes open you accept that a ♦ loser is substantial possibility and will blame fate, not partner, if it happens.

I like that message a lot, especially the part articulating why "safe" trump leads are really not.

True, I did not take your comment about 987x as you apparently intended. Sorry about that -- possibly neither of us read the other carefully. You are literally correct that no one explicitly computed the chance of recovering after RHO ruffs a ♥, but I did mention it. I also argued as you did against a short suit lead, but I took the inference further. Can you comment why you don't buy the theory that LHO would prefer an apparently safe trump lead rather than risk a heart from 987x into a possible ♥K10 say?

If your experienced judgment supports my suggestion that the lead means heart length then I'm reassured. But all that seems freaking obvious from that is that we shouldn't ruff any diamonds. That being the case there's no point in risking any accident in the heart suit. Why not just pull trumps -- if the ♥J is short it will still drop. And as Nigel said there is a guaranteed compound squeeze. I think it's an exceptionally easy one to read, as it seems we can run all five trumps discarding a diamond from dummy. If LHO retains a ♥ and a minor suit guard in the 7-card ending he will have only a single card remaining in the other minor. Cross in ♣, cash ♥A, then decide: If LHO guards ♦, cash ♣ to squeeze LHO then ♥ to squeeze RHO. If LHO guards ♣, cash the ♥ discarding ♣ and then the ♦s.

I stand behind my calculation and comments (i.e. stated assumptions). To recap, the most obvious and straightforward computation says you should not cash ♥s. Of course the vast majority of the time it neither helps nor hurts, but the obvious "hurt" greatly exceeds the obvious "help". However, I could stipulate and plausibly argue for assumptions under which cashing the ♥ tends to gain rather than lose compared to ruffing a ♦, and given that the full layout shows it is the winning play, it is tempting talk oneself into such assumptions. That's what I mean by results-influenced. I calculated and calculated, but tried to explain that all the calculations rest on imponderables. To calculate a hand like this manually strikes me as horrendously tedious. For a start the probabilities of various diamond breaks vary a lot according to what you assume about the heart break.

When the problem poser stipulates that the defense will be slapdash ("Somehow you know ... another trick in diamonds"), I think we can take it that "simple percentage" is ironic. The best legitimate line seems to me to be to duck a spade. Spades could be 3-3 and finding another red trick probably isn't hard. Assuming diamonds 2-5 and assuming RHO has about enough high cards to open, I figure the spade break or ♠QJ alone is 42% and requiring the ♥A onside leaves at least 35% overall chance of success. Playing on hearts works if RHO ♥AQ(x) onside -- around 25%. Just two honors onside is about 42%, but unless they are short there will be trouble. The problem is how the play goes when RHO has ♥AQxx,♦AKxxx if you win the ♦, cross in ♠ and lead the ♥10. RHO may take the ♥A and play a spade. Now a ♥ finesse and then what? If RHO is 3451, you are down. If RHO is 2452 you can strip RHO's black cards and endplay but this requires guessing that RHO isn't 3352.

Testing hearts with a trump outstanding does seem like a results-influenced line. It's not 100% wrong but justifying it does seem post hoc. Assuming one draws no particular distributional inference from the lead: Testing the ♥ gains compared to just ruffing a ♦ when an opponent -- presumably RHO -- has ♥Jx and someone has 3 trumps and short ♦. I make that about half a percent. A singleton heart on the other hand is 1+% on either side the majority of that percent or two the ♦ ruff line would work. So even if you figure you can often recover when RHO ruffs the second heart, you are down when LHO led a singleton so the total chance of loss must be over 1%. If on the other hand you figure LHO wouldn't lead a singleton then you begin to seriously analyze what LHO would lead from, and if you conclude as I suggested before that the answer is length then maybe the squeeze is best anyway.

I agree (we're conditioning on the assumption that all followed low to two rounds of trumps). In fact maybe 79% if you figure LHO would lead a diamond from QJ10(...), which increases the chances that they are breaking. Presumably the bidding was explained as showing ♥Q and ♣K in the dummy, and perhaps defender can deduce from the 7♠ bid that declarer has the fitting ♥K. But still, yes a heart lead from ♥J98 seems a little risky (plus some players just habitually play "honest" cards even though on lead against a slam is a good time to stop being predictable). But then so does ♥98x seem risky. What if declarer has ♥K10? Maybe there is an inference that LHO has heart length for this slightly surprising lead (why not a trump? Surely the bidding tells that either ♠Jxx or ♠xx is safe to lead from.) Accepting your assumptions I agree that the combination chance (drop ♥J or squeeze) amounts to well less -- 67% or so depending on detailed assumptions. On the other hand, if you allow LHO to have the ♥J, the squeezes get enough better that the case is much closer. I get 78% ot 74% favoring the ruff. As a "percentage" question perhaps this or the previous is the answer. However, depending on ones assessment of RHOs thought processes on lead, the probability of the ♥J dropping could be very high and that might change things.

I think there are situations where that logic is valid, but in this instance the opposite reasoning makes more sense to me. It's when 5♦ fails that we particularly want to make 5♥, in order to preserve the plus position that is our birthright. In the case that 5♦ makes, a small loss in 5♥ is less of a disaster. The net seems to me that the IMP odds angle makes finessing LHO for the ♠Q not exactly a good play, but at least better than it would be at rubber bridge. If you finesse through a singleton, the loss may be mitigated by teammates making a game. If you finesse through a doubleton you may get lucky and pick up the Q. Actually, on the odds we've already done well to bid 5♥. Suppose 5♦ is the contract at the other table. If it makes, we gain 8 or 13 IMPs depending if we make, but always a gain. If it fails, we lose 3 or 4 IMPs for going down and gain 11 for making which is a great bargain since we are obviously a favorite to make.

♠A then finesse RHO. The trump shift says RHO has some ♦ honors, but RHO passed over 2♦. Perhaps 5♦ is based on honors in both minors but only a tripleton ♦. That's also consistent with the idea of a trump switch holding a singleton ♠. By the way I don't understanding the bidding agreements. What would S bid if wanting to defend 5♦x? I also don't understand why, on this hand, S would want give N the option to defend nor why given that option N wouldn't simply pass holding A, AK.

Then we agree that the question is how to play based on the situation at trick 2, at which time the ♠ could be anything. So whatever line you choose, ♠7xx,♥x is a possibility, either a winning case or a losing case. The case has to be considered in the probability calculation.

The ♦ switch is quite strange. Presumably our 6♦ bid tells West where the ♦K is, so how does West know that it's not pickling East's ♦Q (whether or not West holds the ♦J)? I am not sure what to make of this clue but it may negate, for better or for worse, the blind probability analysis I considered before.

Sorry, I misread what you wrote, then blindly calculated without thinking about the logic until after I left the computer. According to my calculation yesterday it adds around 3%. Of course, I risk that. Since I'm planning to take the second club ruff in dummy with one high trump, it would be clearly wrong to ruff high in hand as well protecting against a singleton heart and losing to the far more likely ♠10xx. I assume the :) means you are joking. The hint also tells us the spades are in fact not 4-0, but it is a hint, not a stipulation. For example I found it interesting and useful because it makes the point that immediately testing the trumps is a terrible play.

That seems a good line. However, even when no ♠ void and no ♥ singleton it fails when LHO has ♠10xx,♥xx (or ♥KJx as you will misguess that in order to win against ♥Jx). Also when LHO holds ♠7xx,♥x it is not true that you can establish ♥ with ruffing finesses. So I think your main chance is more like 73% than 77%. On the other hand, you make against at least 1/3 of the 9% chance of 4-0 ♠ breaks, whenever the ♥ lie well (3-3 and some ♥Kx). And when ♥ are 5=1 you do not need 2-2 ♠; 3-1 is fine. That's 5% more. I figure 81% total. My main chance -- no ♠ void nor red singleton -- is about 77%, and I do about 1% better on 4-0 trump breaks than you do. By my calculation (and one could argue that my mistakes are biased in that I might quit when I am ahead) my line is 0.5% better. Probably that small difference is less than various things I didn't account for such as the opponents' silence in the auction, so I am not concluding either line is better than the other.

♦K, ♣ ruff, ♠K. If they are 4-0, there is still the heart finesse. If they are 0=4 there is also the trump coup, and in fact I think it's a better shot notwithstanding that it requires RHO to follow to 3 ♦s. If spades break, ♥A, ruff (in case the ♥K drops), ♠ ruff, ♦ to hand.

All valid, but 1. I'd be a little surprised to see a ♥ continuation from LHO after the ♣ duck. Possible I guess if LHO can read a lot into RHO's discard on the 2nd ♣. But at least on the surface from LHO's point of view declarer has ♥s bottled and both of the other suits are plausible switches. 2. If LHO does try a ♠ or ♦ we can more or less claim. If a ♣, back to plan A but if my misapprehension about the ♥ lie persists even after the defenders discard on the ♣ suit, I might misguess the ending. 3. If a ♥ is continued, I agree you can and have to duck it.

Agree with Nigel's agreement with Gnasher (not to imply disagreement with the rest of Gnasher).

4♥ is clear and X is obvious as well -- lots of defensive tricks, lots of losers. Dummy play hand -- The lead appears to be from ♥KQ9xx as neither leading a 4-card side suit nor false-carding makes sense on the auction. RHO's light 3rd hand opener and LHO's silence over 1NT, and lead, all portend 6-1 ♦s, hence fair chance for 4-1 clubs. So ♣Q, ♣ duck. Win heart return, run clubs and lead a spade from dummy to my remaining KQ10, --, A10x, -- Win the ♠K and judge whether to exit in ♠ or ♦. It shouldn't be too hard; possibly either exit will work.

A ♣ return is fatal if declarer had Ax, J1097, Axx, AKxx, but other than that the defense no longer matters. A ♠ would cost only against A,J1097,Axx,AKJxx or AK,J1097,Axx,AKxx which of course are not 1NT bids, and a ♥ return can never cost the contract. Failure to have ducked the ♥K might easily have cost: AKx, J1097, Axx, Axx.

I agree with benlessard that looking for slam after2NT is expecting miracles. Even considering 5♦ rather than 3NT seems to me very far-fetched. I question the 2NT response. I realize that it was stipulated as part of the problem but it seems a distortion. Add the system-imposed distortion of opening 1♣ and there seems no reason to expect the system can now right itself.

You might still succeed in this case but will need spades 3-3 or the ten dropping as you would have to use ♥A to shorten your trumps. Alternatively Hamman might have been planning, if RHO followed to the 3rd club, to cash ♦K, and if all follow low unblock the ♠KJ immediately. Seems an awkward line, but perhaps it is percentage as ♦Jxxx is a hefty 1/7 (i.e. 4 of the remaining 28 diamond lies) chance which is at least comparable to the risk of someone ruffing a spade when both minors are breaking. It does seem that he was assuming an extremely high probability -- 90+%? -- that RHO would falsecard when appropriate.

I agree as well. I overlooked MFA's point about the benefit of cashing a top spade, which has the effect that the chance for 12 tricks is double the chance for 10. In terms of matchpoint odds that means that, compared to other declarers who play in 4♥ and find MFA's line we have the identical expectation -- 1/3 of the matchpoints -- whichever line (MFA or safe for 11 tricks) we choose. The edge for choosing MFA's line thus comes from comparison with the remaining declarers in 4♥ or 5♥.

MP: Same as IMP, play absolutely safe (because the contract is 5♥, but gamble if it were 4♥). On trick expectation gambling for 10 tricks or 12, versus safe for 11, is obviously a somewhat close question By my calculation the best gambling line is strip then spade finesse, 21% for 12 tricks and 18% for 10, but the exact result doesn't matter, only that it's close enough that, correctly (which I think it is) or not, some 4♥ declarers will gamble. For the sake of MP strategy we can put aside the hands that make 11 tricks and assume the gamble matters. Just assume we make 10 or 12 tricks about equally often, about half of (the relevant) time each. Against the 4♥ declarers who gamble we are in terrible shape. If we play as they do, we expect only about 1/4 of the matchpoint -- half when making 12 tricks but nothing when making 10 tricks. Comparatively our expectation by playing safe is much better even though it is less than 1/2. Against the 4♥ declarers who play safe, we would get a slight edge by gambling but not nearly enough to compensate for what it costs us against the gambling 4♥ declarers.

I would impatiently play ♦Q a trick ago. Even KQJ10xx, x, AKJxx, x isn't a legitimate slam try -- needs 2 aces, diamond shortness, and trump length for a slam. Therefore RHO is having fun in the bidding. Partner however, if holding ♦32, wouldn't know that the 3♦ bid was a joke and wouldn't know continuing clubs is bad. Partner would only play diamonds with an honor or a singleton.