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Duck! A low ♠ from the dummy is needed when LHO doubled rather than overcalled with a bad 5-card spade suit. Regardless of many people's remarkable confidence that this approach is old-fashioned and has been proven inferior, LHO might not be so up to date. The ♠J is necessary when LHO doubled rather than bid ♠AQxxx -- surely far less likely. If LHO has ♠AQxx the ♠J play seems superficially beneficial but how much does it really help? Maybe an overtrick. For example if the ♦'s are guessable, then making the hand is on the ♦ guess, not on the spade play. If LHO has ♠AQxx, ♥Axxx, ♦xx, ♣Kxx the hand is unlikely ever to make.

I think you're right to be surprised if people say "about equal" when the difference is 10%. In partial defense of "people" though, the difference seems less extreme if you comparing winning %. The double finesse wins 76%, ace first 66%. Sometimes 76% vs 66% is less significant than, say 17% vs 7% (and in fact your 17% and 7% calculations didn't represent either winning or losing cases, but are just calculation made after eliminating the majority of cases in which the lines are equivalent).

Suppose we begin immediately: ♦Q, ♦K. All follow, maybe small maybe not maybe fire a spade from RHO. If there were a simple answer it would be the ♠ finesse -- slightly higher odds than the ♦ break. However, this ignores a few points. 1. If RHO wins & fires a ♠, I am disinclined to finesse. Even if we assume RHO is sure to credit me with the ♠J to come to a 22hcp hand, the spade play is risky if the layout is [hv=d=&v=&n=s qxhkjxdkjxxxcjxx&w=s10xxh10xxxd109xxcxx&e=sk9xxhxxxdaxc10xxx&s=sajxxhaqxdqxcakqx]399|300|[/hv]. 2. The defense should adopt a mixed strategy. West should of course duck the ♦A twice from any 3 or 4 card holding except ♦A109. East should duck sometimes but not always. If the declarer can assume the defenders ALWAYS duck twice, then it becomes % when ♦'s are ducked to assume they are breaking rather than to finesse the ♠. RHO must occasionally win the second ♦ from Axx (without the ♠K) and occasionally from ♦A9xx (with the ♠K) to avoid declarer being able to take advantage. If RHO is known never to win from ♦Axx then, when RHO wins and plays a spade, declarer gains an advantage by finessing. Conversely if RHO is known always to duck with ♦A9xx, then refusing the ♠ finesse when it is offered by RHO becomes an advantageous play for declarer. In summary, the defense should randomize among the four pure strategies that East wins the second diamond - only with ♦A doubleton - with ♦Ax or with ♦Axx - with ♦Ax or with ♦A9xx - with every length. 3. The ♦ spots may tell us something. --- It is a potentially complicated situation. Even ignoring my point about the RHO's possible reticence to play a ♠ and further ignoring the impact of the ♥8 in dummy, the are four possible strategies for each side. For declarer: play diamonds or finesse spade, each according as the defense ducks or does not duck two diamonds. Declarer may play a pure strategy of always finessing the ♠, but may do better by outsmarting the defenders or if I'm right about RHO's ♠ shift. The defense must use a mixed strategy to guarantee their birthright.

This is the line I should have suggested - for some reason I first cashed ♥AK too early, then thought that cashing them later meant I couldn't have ♥109 as one of my winning options. I can't understand why anyone thinks that a small extra chance in clubs makes up for giving up one of diamonds 3-3 or ♥Q doubleton. It's not as small as the red suit chances. If you try to combine chances via r1. club to the 10 (50+%) r2. a red suit cooperates (50%) r3. club to the Q (50%) then you have 3 50/50 (very nearly) shots, net of 7/8. The (second) best play in clubs alone is better than that. Play it: c1. Club to the 10 (50+%) c2. Cash club Ace -- Kx with LHO (4%) c3. Lead a club toward the Q -- 75%. Hence thanks to the preparatory play c2, c3 becomes equal to r2+r3. The vigorish from c2 not to mention dry red honors and power of the ♣7 are the edge.

♣A, low to the 10 then low to the Q is the % play in ♣, losing only when RHO has Jx (4 cases). By comparison, ♣A then low toward the Q (ducking) fails when LHO has ♣KJxx(x) (6+ cases). ♣A then low toward the ♣Q imagining RHO might hesitate with the King -- after we cashed the Ace -- means that one of us thinks the other doesn't belong on Vugraph. (Besides, there's no gain in playing the Q compared to ducking and leading to the Q later.) The play I suggest wins 90+% -- a little more if LHO would normally have led from 5 clubs, or if you think you can read LHO's fast duck as denying KJxx(x). I think it's also the % play for the hand, aside from free checking for trivial edges like ♦ or ♥ honors on the rail. (But low ♣ first is a reasonable alternative, losing by comparison only in the very unlikely event that RHO has ♣J alone.) Assuming the club 10 loses to the J, spade return: 1. Suppose you next cash ♦AQ and LHO drops x,J or x,10. Then a 3rd ♦ play is 2:1. However, a club play is 3:1, succeeding whenever RHO has either of the remaining clubs. So the ♦ restricted choice play is inferior 2. Can it be resurrected by first checking for ♥Qx? No, because you have to cash the hearts before you know the ♦ restricted choice option exists. Hence the 16% chance of the ♥Q dropping augments only the basic 50% basic chance in ♦, not the 2:1 chance, while ruining the chance to play another ♣ if the ♥Q does not drop. Edit: I see this is Codo's line. Also that the ♣7 is in dummy -- hence if RHO drops a high spot under the A there is a restricted choice play available, making the hand except when RHO has specifically ♣J4, J6, or 98.

This line and the variant where we duck a diamond instead of the last club are just down on 5-2 clubs offside. [and some compensation when 5-2 onside per gnasher, which may compensate for cases when the crossruff gets overruffed]. True, it's roughly equivalent to 4-3 clubs, which is 62%. As against that, pulling trumps fails a good (I think the ♦A is a favorite to be offside, but never mind that) 1/4 of the time when clubs do break, and succeeds only1/4 of the time that they don't. Hence as a farmer estimate, since the club break is >50%, better to settle for that than to swap part of that big slice for a similar share of a smaller slice.

♣A, K, Q & crossruff. Assuming I can read nothing from the club plays, continue ♣ hoping to score a ruff. Whether RHO follows (we pitch the last ♦ of course) or discards ♠ I need RHO to have 7 black cards in order to score my ruffs in dummy, and need LHO to have 7 minor cards to score ruffs in hand. Pretty much. Edit -- need LHO to have 6 minor cards as only need to score 2 small ruffs in hand, not 3.

I take your point. No. Under the given (reasonable) assumptions: 1. Declarer is equally likely to have QJ9x or QJxx 2. No other holding matters: By covering you win whenever partner has the 9 and possibly additional cases where declarer misguesses with QJ9x, so at least half the time. By ducking you lose whenever partner has the 9 and possibly additional cases where declarer guesses correctly with QJ9x, so at least half the time. Given that choice, it's not rational to lose at least half the time rather than win at least half the time. But every dog has its day.

No. Over 1NT, major transfer followed by 3♦, undecided as to whether we have a ♠ fit, is playable because opener can bid 3♠ forcing with ♠'s so cue bid can agree ♦'s. Wonderful. After 2NT, one level higher, of course 4♠ by opener in the in the corresponding auction can't be forcing. Therefore you either have to accept that cue bids over 4♦ are ambiguous -- catering for ♠ or ♦ slam is perhaps already more than we can manage, hence allowing for ♦ game as well is clearly too much -- or change the system. My preference is simply to agree to break the transfer after 2NT - 3♥ (the putative "super-accept") whenever assured of an 8-card fit. Even if thus lowering the bar is sub-optimal for judging ♠ slams (probably) or for bailing in 3♠ (probably not) it is only slightly so. In compensation, it simplifies the bidding in many sequences. In particular it becomes playable to bid 2NT 3♥, 3♠(no fit) 4♦ with this hand.

Me too. The main payoff for this idea is when RHO has ♥10x or ♥9x, rather than the singleton. Win ♣K pitching a ♦. CASH a ♦. ♥J, K, A, x. If RHO has ♥'s as stipulated and not more than three ♦'s originally I think we are home. For example -- ♦ from dummy. If RHO discards, win and continue with the ♦9, duck, ♠ discard. If RHO ruffs with the ♥9 then we can score the dummy's five trumps, one ruff in hand, and four top tricks. Other example -- LHO covers the 3rd ♦ (perhaps perforce from original ♦Qxx), ruff low, overruff ♥9. Win ♠ return, play winning ♦, ruff, overruff, pull trump, claim 10 tricks.

I had the same instinct so I calculated and was surprised to find it's not true. Disclaimer -- this calculation was before considering bridge aspects of the hand, in particular without taking cognizance of Fred's persuasive inferences about the ♦ finesse and the ♣ break. Hence this is just a sterile exercise of a priori probability: ♦ finesse, ♥finesse, ♥break adds up to 17.75% as 655321 said. (given odd club length, club ace known) ♥A, ♥ seems to win when RHO has ♥Kx (14%) but not against ♣Axxxx, so only a net of 10.3%. It also wins when LHO has ♥Kx (13%) if the ♦K is also onside -- net of 7.1% Total only 17.5%. Well, practically a tie, which is broken by taking into account intangibles such as the idea that the opponents choice of play may be influenced by the cards they hold.

♠9. Surely a ♠ -- could be easy defeat and ♥ is a wild shot. Maybe partner can find ♥Q switch with ♥J in dummy. IMP or MP?

♣A, K, ♣ ruffing low is around 72% for 12 tricks. same ruffing high is 67%. Hence paradoxically the line requiring a club break is better than the line requiring a trump break. The reason is that the two lines converge if LHO shows out on the third club. Clubs 4-3 is only 63%, but it is 75% of the cases in which LHO has not got xx. The chance of a trump break, by contrast, is not much changed by knowing about LHO's club holding. Cashing the spades early is wrong because releasing the trump jack loses to club xx on the left.

Finesse the ♦ now. From Billy's perspective you need AQJ of one minor or both minor Q's to come to 20hcp. If the former the play will not be complicated: you will run ♥'s & your minor. If the latter, then above all he doesn't want to help you run your AQxx -- maybe AQ10x -- suit. Therefore he would not discard a xxx or xxxx unless the other suit discard is worse. Hence the ♦ pitch suggests A. ♦Qxxx, ♣any three B. ♦xxxx, ♣any three C. ♦Qxx, ♣Jxxx D. ♦xxx, ♣Jxxx E. ♦any five or six These combinations are nominally in proportion 400:300:150:200:133. If that's right, then ♣A, K, Q wins in cases A+E -- 533 times. ♣A, 9 wins A/2+C/2+E/? -- much less ♦ A,J wins A+C+E- -- 650 times. Much as Billy might be inclined to make a tricky double-cross discard from ♦xxx, maybe, like the Stones say, he "just don't get that much chance." I'm sure your table feel is better than my reasoning, but for myself I like finding an approach that doesn't involve trying to out-psyche Billy Eisenberg. Edit: Hans' line obviously better -- no harm in ♣A, K before the ♦ play.

Pass. We probably have a diamond loser and despite knowing where the hearts are may not be able to pick them up. ♠K, ♥Kxx, ♦Kxxxx, ♣Axxx is possible but clearly more than we deserve. Transportation and finding the right suit are further worries.

Yes. Given that a non-passed hand would be promising a rebid, the difference here is negligible. Doubler is still unlimited. The distribution of possible hands for advancer is very little changed by being a passed hand because advancer to a full-value doubler, even a cue-bidding advancer, rarely has opening bid values. The point of promising a rebid is to make the bidding structure easier in case doubler is strong. Hence it's the passed hand status of doubler, not of advancer, which matters.

On ♠ lead -- Pull trumps discarding ♣, ♥, and if 4th round ♣. Play ♥A,K. If RHO follows twice or singleton ♥Q claim. Ruff a heart. If trumps were 3-2, then LHO has 5 minor cards remaining and the situation is: Dummy: ♠--, ♥Jx, ♦KJ, ♣A98 LHO: ♠--, ♥Q10, ♦XX?, ♣XX? Declarer: ♠J10x, ♥--, ♦A87, ♣x A. If LHO appears to have a doubleton club, play ♣, ♣ruff, and finish trumps for double squeeze with ♦ as pivot suit. Line C below remains an option if you lose confidence in the club lie after ruffing. Otherwise, cash two more trumps and decide whether to B. cash 2 diamonds then last trump for double squeeze with ♣ as pivot, C. finesse the diamond. Ostensibly the odds favor B if LHO has 2 trumps and C if LHO has 3 trumps. If trumps were 4-1 then a club has to go on the 4th trump, so line A is out.

I guess to lead a ♣. I hope to make at least 7♥ (including a ♣ ruff). 2♦ and 2♠. If I lead an early ♠. LHO may duck, allowing his partner to ruff. Nice point about the duck-and-ruff defense if declarer returns an immediate spade. There is, though, another way to look at it. A poor West will grab the spade willy-nilly, and if trumps are 4-0 that will be very helpful. A good West might decide to grab the spade rather than allow partner's trumps to be weakened; the duck defense isn't automatic. Finally, if you play a club at trick 2, a really good West can win it and play a low spade himself anyway -- especially if RHO's ♠x is smaller than declarer's ♠x. This defense seems to work against the actual lie. It's partly a psychological question whether excellent defenders (digression I know) are more likely to find the spade ruff if declarer plays a spade, or if they have to play it themselves.

Double About 40 years ago when I was young enough to have promise I had the pleasure to play a Los Angeles Bridge Week pair event with John Swanson. With a problem somewhat like this one I reckoned we were safe at the five level and I bid. We made the contract but John, whose mood at the table normally ranged from facetious to wryly humorous for once didn't hide his frustration and mentioned a rather obvious principle that I have not forgotten. "Look at how many tricks you have on defense."

There must be some flaw in the logic that compels 2♣, 3♣, and 4♣, all natural bids, on a four card suit. The partnership's firm rejection of NT is obviously, at least in hindsight, misguided. Therefore I suggest you had done enough NT denial with 3♣ and could have tried 3NT next time around. As for your partner's 3♦ call, preference on a doubleton honor is a great and unselfish bid when partner (you) may be begging for preference. That's less than normally likely given that you in turn were begged by the 2♥ call to do something. And it's less than normally attractive when holding a self-sufficient major suit as an attactive alternative bid.

I see nothing better than both kings onside: club to the queen and it better win. Then lead a spade from the dummy. If RHO discards, win, ruff with the 10 & weak defender overruffs. Now the winning diamond finesse sees us home. The strong defense is to discard a second diamond from an original K10, Q9xx, xxx, Jxxx, which defeats the contract. Perhaps it would therefore be better for declarer to play the spade from dummy at trick 3 and continue with the 4th spade ruffing (with the 10??). In any case, spade at trick 3 seems to me a more natural approach. Edit: If the club queen loses, still slight chance via ♠-♦ squeeze if LHO has Jxxx, x, Kxxxx, Jxx.

Here's another auction in 2/1: 1♠ - 2♥ 3♠ - 4♣ 4♥ <-- Natural? The issue here is that responder has, in no way, promised a good heart suit. It makes sense to agree here that 4♥ is not a shortness cue, but it does not make sense to offer 4♥ as a contract, since opener did not raise to 3♥. I agree that you can construct a few 6-3 hands that want to bid this way, but the default (and I believe, superior) agreement is to play 4♥ a cuebid. I also would not assume that 4♥ shows a tripleton; it's just heart agreement/tolerance in context. The context here is, to me, an obvious case of taking a preference. Perhaps in the 2/1 world 3♠ guarantees that ♠ will be trump. If that's the case then of course the "return to major" rule directly contradicts a rule you already have, which is a special problem. Both of your examples involve a "return" from ♠ to ♥. How do you feel about returning from a minor to partner's major?

♦. 12 IMPs? Then 5♣ made. (Alternatively, take the point of view that we should defend on that assumption.) Declarer has a singleton heart from the lead; if also a singleton spade I don't see how the defense can matter. Therefore we have a spade trick hence partner has not got the ♣K. Surely, then, pd has a black singleton. If Jx,KJ975, Q10xxx,x we have no chance; declarer will strip the hand then play a spade to the 9. Against 8xxx,x,J10x,KJxxx or 8xxx,x,xx,Kxxxxxx we can come to 2 spade tricks after a minor suit return. A ♥ will probably suffice in the first case. Against Jxxx,x,xxx,K9xxx a heart return might enhance our chance of a trump trick. (♠ similar(?), but more so had we won the first trick with the ♥Q.) This is a questionable 5♣ bid. Since 8xxx,x,xx,Kxxxxxx is the only clear-cut 5♣ bid I play a minor. I don't know the psychological effect of leading the ♣Q if declarer has K9xxx but won't go there. So a ♦.

Maybe a good idea to test the clubs first then. If you lead the ♣10 at trick 2 & rho reveals both honors -- by covering (e.g. QJ8x) for example -- then the fake spade finesse looks good. However, if rho persuades you she hasn't both clubs, then the best play for the hand is the best play in spades.

Please show me a few. I don't recall ever being discomfited by this old Acol rule, and have seen many times where it helped. I can well imagine that, if the partnership puts no price on a proliferation of detailed agreements, this rule like any simple rule will be slightly non-optimum on occasion. But you said "very obviously." 2/1:1♠ - 2♥ 2♠ - 3♠ 4♦ - 4♥ <--Natural, suggesting to play? I agree 4♥ sounds forcing, and certainly there is no awkwardness in it being forcing with 4♠ obviously reasonable. I don't understand what you are trying to say. How do you agree a suit unambiguously and cue in the suit? The rule I meant to quote probably should say "return to *partner's* major". I'm surprised others haven't heard of it. The main point is that 4M can't be a small singleton or void. Would you still disagree?