dburn

Don't mind 3D - would probably bid it at the table. Don't mind 3S either, but in general I need a rather better spade suit - partner is supposed to move towards slam with decent controls and a singleton spade. Of course, here I know he doesn't have decent controls, so if he does move, his spade support should be adequate. But it's hard to answer these questions without some knowledge of the context in which the partnership operates. How often will Rex or Jay bid 2S as opposed to 2H on hands with three spades and six bad hearts? If the answer to this is "frequently", then I strongly prefer 3NT to 3D. If the answer is "not often" or "never", then I prefer 3D to 3NT. Over partner's 3S, will bid 4C and pack up if he signs off. Over 4S, will bid Blackwood. Over 3NT, will pass.

Would open 1NT even if I had the nine of clubs as well as the nine of spades. However, recent research leads to the conclusion that (contrary to popular belief) 4-3-3-3 shapes actually play rather better in no trumps at the partscore or game level than 4-4-3-2 shapes with the same honour structure. The main reasons for this are: if partner has a five-card suit, you will have a three-card fit for it, making it easier to establish; even if partner does not have a five-card suit, then as long as he has a different four-card suit from yours, you will have (at least) two 4-3 fits either (or any) of which might break 3-3 and provide some extra tricks; if partner does not have a singleton (when you probably won't play in no trumps anyway), the opponents won't have a nine-card fit, so that even if they lead your weak suit, it might break 4-4. So maybe I should upgrade this hand because it's 4-3-3-3. I still won't, though, if it's all the same to you.

The trouble is, as I have mentioned elsewhere, that crossing to ♥A might constitute a danger play. If East does have a singleton club, he may have this hand: ♠? ♥KQx ♦AK? ♣x Then, he will ruff the second club, cash his hearts, and play a diamond. Of course, this enables you to pitch your remaining club loser, cash ♠K, lead ♠10 and... well, if East began with ♠Qxxx you had better finesse, while if he began with ♠xxx you had better play for the drop. The chances are that he started with 3=3=6=1 and not 4=3=5=1, because West with four diamonds, a singleton spade and six clubs might have taken some action in the bidding - but if the 1♦ opening could have been a three-card suit, he might not. Moreover, if East began with this hand: ♠xx ♥KQxx ♦AKxxxx ♣x you cannot make the contract by crossing to the ace of hearts and playing a club. East will win and play three rounds of hearts, and you cannot shut out West's ♠Q. Of course, West could have beaten you on that layout by leading his singleton heart, and maybe he would have done. But maybe he would not, and it would be a shame not to make your contract when your team-mate found the singleton lead in the other room. Suppose East ruffs the king of clubs at trick three. Then you can still make the contract whatever hand he started with, provided you can guess what it is. Since he is somewhat endplayed at this point, your chances of doing this are very good. The decision is a close one, and I don't claim to have analysed the position exhaustively. I would say only that crossing to the ace of hearts "feels wrong", an evaluation that I realise won't help beginners and intermediate players very much. They might like to consider how they would proceed if after ruffing ♣K, East were to exit with a spade. As a hint, assume that East played a low club on the first round - what does that imply about the location of heart honors, given that East seems to have only ♦AK without the jack and no club honor, yet opened the bidding?

Not sure about this crossing to dummy business. The only card you can do that with is the ace of hearts. If East has a singleton club (the only reason for crossing to dummy in the first place), then he may ruff the second club anyway and play three more hearts from an original 2=4=6=1 distribution, leaving you unable to make the contract if West began with three spades to the queen. Of course, this implies that West did not lead his low singleton heart at trick one, which is unlikely. But so is a 6-1 club break. Moreover, if East began with ♥KQx and a singleton club, he may ruff the second club, cash two hearts, and exit with any diamond, leaving you to guess whether he began with 4=3=5=1 or 3=3=6=1. It seems better on the whole to cash the second club at trick three - even if East ruffs, he is somewhat endplayed at that point, and your chances of making the contract are still very good. Now, does crossing to the ace of hearts constitute an error? I think I had better leave that to the experts.

The most likely West spade holding consistent with my making the contract is three to the queen. I also require him to have at least three diamonds. It is obviously foolish to play the ace of spades before running the jack, and to play diamonds before spades (both of these lines will go down when the distribution is as I hope, because I cannot cope with a second round of hearts). Therefore, jack of spades, spade to the king, diamond. Of course, this will fail miserably when East turns up with ♠Q and I could have made the hand trivially by ruffing a heart, drawing trumps via a finesse against East, and knocking out West's ♦A. But Roland did say that this was a difficult slam, so I'm not going simply to draw trumps, take finesses and cash winners.

It might be plain sailing, but then again it might not. Presumably if the jack of diamonds holds, you will draw trumps and repeat the diamond finesse - but if East is a strong player, the second diamond finesse might lose, whereupon you will go down at least one. Leading a middle diamond at trick two and simply playing for 3-2 breaks in both red suits seems the most promising approach. If I have understood aright, the line chosen at the table - heart to the ace, club ruff, middle diamond - makes the contract on almost no distribution of the outstanding cards assuming half-way competent defence, so can safely be dismissed. An alternative line - heart to the ace, club ruff, and three rounds of diamonds - appears to require a later successful guess in spades even if the queen of diamonds falls on the first two rounds of the suit. It is therefore indeed a "close second", but only to the original line in terms of futility, not to any sensible line in terms of probability of success.

Not that he needs me to defend him, but you are completely wrong. I mean you are right about what he has to do, but wrong when you say he didn't do it. His calculation is accurate to the degree it was rounded. You don't need a complex statistical formula to solve this, a basic understanding is plenty good enough. If hearts are 7-2 then west has 6 empty spaces (13-7), east has 11. The odds of west having singleton king are (6/17)*(11/16)*(10/15), in other words (empty spaces in west / total EW empty spaces) * (east spaces / total remaining spaces) * (east spaces / total remaining spaces). This equals about 16.18%. You can follow this process to find, given that west has 7 hearts and east has 2, the odds of west having a diamond holding of... void = (11/17)*(10/16)*(9/15) = 24.26% 5 = (6/17)*(11/16)*(10/15) = 16.18% Q = (6/17)*(11/16)*(10/15) = 16.18% K = (6/17)*(11/16)*(10/15) = 16.18% Q5 = (6/17)*(5/16)*(11/15) = 8.09% K5 = (6/17)*(5/16)*(11/15) = 8.09% KQ = (6/17)*(5/16)*(11/15) = 8.09% KQ5 = (6/17)*(5/16)*(4/15) = 2.94% As a check the total is ..... 100%! Ok, 100.01%, stupid rounding error. So as I suspected all along, David was completely correct. The odds of west having a singleton diamond honor, GIVEN that west has exactly 7 hearts, are 16.18*2 = 32.35% (more rounding error). Your criticism of his calculation is entirely unfounded. More relevant may be waiting to see what east follows with when you lead off dummy. If the assumption is still west has 7 hearts, and east follows with the 5 of diamonds, the odds he has KQ5 are 24.26/(24.26+16.18+16.18+8.09) = 37.5%, whereas the odds he has either K5 or Q5 are 50%. So if you knew hearts were 7-2 (which of course you don't) then you should go up ace by a 4 to 3 margin. This, combined with all appropriate bridge inferences (which are truly the interesting part of this problem IMO, and are probably David's greatest strength over the rest of us here) is how the problem should be solved. I understood most of that, because it agrees with what I think, so I was a heavy favourite to understand it. But I am not sure about the last part - in fact, I don't understand it at all. If East follows with a diamond other than the five when you lead from dummy (or does not follow with any diamond) you can forget about computing probabilities and concentrate on not revoking. But if East does follow with ♦5, you need to compute the probabilities as we (or at any rate some of us, cherdano being primus inter pares) have already done. The only relevant cases are those in which East has three diamonds (you should finesse) or West has one diamond honour and seven hearts (you should play the ace). Since it is about nine times more likely that the first case holds than the second, you should finesse by a 9 to 1 margin, not go up ace by any margin at all, let alone 4 to 3. It is worth remarking that East, with three or more hearts and ♦KQx, might follow upwards in hearts (to pretend to have a doubleton playing udca). I gather that in fact he followed downwards, to represent three or more. Now, should I play him to have been false-carding? The original problem invited me to pretend that West was an expert, but who is this East guy?

They aren't "close to the actual probabilities". They are the actual probabilities. This ought to have been apparent from my use of the phrase "the chance that West has a singleton diamond honour given that he has seven hearts". The a priori probability that a given West hand about which nothing else is known has a singleton diamond honour, for example, is exactly 26% (when North-South have ten diamonds). West will have one diamond exactly 39% of the time; it will be an honour in exactly two thirds of those cases. But the probability that the West hand has a singleton diamond honour given that it has seven of East-West's nine hearts rises to 32.35%, which is the figure I quoted in my post. As I have already explained to Hannie, I am not a mathematician. But - or therefore - I know how to count.

2NT forcing is actually a very good idea, which I would commend to the attention of all BBO "experts" - many BBO experts doubtless use it already. No guarantees, of course, but it simplifies a great many auctions in these troubled times where the opponents seem to bid before you do whenever one of them is the dealer. As it is, I don't see much of an alternative to 3♦. It's not that I have a plan, but when you can't make some nebulous double, the best you can do is make some nebulous cue bid and see if partner can think of a plan.

I think your odds are wrong, the first case is around 1.3%. How do you play if LHO shifts to a club at trick two? I agree with you; I was calculating in my head and forgot to factor in the extent to which West's holding seven hearts to East's two affected the probability that he would hold a singleton diamond honour. I think I also divided by two once more often than necessary. But it was early in the morning, or if it wasn't, it felt as though it was. To illustrate what I ought to have done: The chance that West has seven hearts and East two is about 4.28%. The chance that West has a singleton diamond honour given that he has seven hearts is about 32.35%. The chance that West has both danger holdings is thus, as cherdano rightly says, the product of those two numbers - about 1.39%. The chance that West has a diamond void, regardless of what he has in hearts, is exactly 11%. On ace and another heart, I would still be inclined to take the safety play in diamonds. For the case where West cashes ♥A and shifts to a club, we need the chance that West began with four clubs - about 14.13% - multiplied by the chance that he has a singleton diamond honour given that he has four clubs - about 29.77%. The product of these two numbers is about 4.21%; still significantly less than the chance that West has no diamonds, and the safety play in diamonds is still better in a vacuum. Of course, as always we are not operating in a vacuum but at a bridge table. An interesting question is this: how should West (having led ♥A) defend with five clubs and the singleton king of diamonds?

Relevant cases appear to be: West began with seven hearts and a singleton diamond honour; West began with a diamond void. In the first case I should play ace and another diamond; in the second I should take a first-round finesse in diamonds. Since the first case has an a priori probability of around 0.5% and the second an a priori probability of around 11%, I will take a first-round finesse in diamonds.

I would suggest that the term "beginner" might more aptly be applied to to someone who suggests bidding 2♥ over 2♠ than to a Gold Cup semi-finalist. If the notion is that this is a 3♥ bid, the same considerations hold.

Would be inclined to lead a heart, unless we had a specific agreement that the double called for a spade. It seems to me that partner may have doubled on a spade guard (probably the ace) and a side suit that is solid missing the ace or king (probably only five cards in length, since he did not overcall). A priori that suit figures to be diamonds, since I have fewer of those than hearts, but RHO can hear the bidding as well as I can, and he might have elected to remove 3NT doubled to a major-suit game if he had that option. Could be very wrong, though. Still, so can any opening lead, especially one of mine.

Could work to bid, but most of the time it will end up helping declarer in the play of the hand, and some of the rest of the time it will induce partner to do the wrong thing either in the auction or in the defence.

Indeed - I seem to have been guilty of keeping up with the d'Alemberts. Sorry about that. We fix the North cards as 8765 and the West cards as K1094. Then, from West's point of view there are indeed five possible equally likely layouts (since everyone knows the distribution and everyone knows South has the ace). East's holding is QJ, Q3, Q2, J3 or J2. South is about to play ace and a low card, whatever his holding and whatever the defenders do. Assume that the position recurs 60 times, and assume that East will choose randomly from QJ and South will choose randomly from 32. Then: West will see Q-3 (East plays the queen on the first round, South wins the ace and plays the three on the second round) three times when East has QJ and twelve times when East has Q2. Similarly, he will see Q-2 three times when East has QJ and twelve times when East has Q3, and so on for J-3 and J-2. With everyone playing at random, then, the defence will beat the contract four times out of five (48 winning cases to 12 losing ones) if West plays the nine on the second round, and not two times out of three as I foolishly stated earlier. Now suppose that East always plays the jack from QJ. Then: West will see Q-3 only when East began with Q2, and Q-2 only when East began with Q3. The defence will prevail in all 24 of those cases. West will see J-3 six times when East has QJ and twelve times when East has J2. Similarly, he will see J-2 six times when East has QJ and twelve times when East has J3. Unless the clues from the bidding and play make it more than twice as likely that the jack really is from QJ than from Jx, West is still better off playing the nine on the second round. The same applies, of course, if East always plays the queen from QJ. I am not sure whether this justifies the assertion that West will be able to make an "educated" play of the king "much more often" than he could otherwise have done. Still, it only has to work once to show a profit (provided that it doesn't then fail).

As the prominent poster mentioned by ArtK78, I should like to apologise for my discourteous assertion that he was writing nonsense. On the question of agreements, there is this to be said: East must play an honour from Qx, Jx and QJ. If a partnership has no agreement, then West should never play the king on the second round of the suit. The defenders will get the position right every time East holds Q2 or J2, and get it wrong every time East holds QJ - that is, they will succeed in 66.67% of cases and cannot do better with any agreement in place. Of course, they might not do worse. Suppose that you have an agreement in place that East will always play the queen from QJ. And suppose that we replay the scenario of the original problem (with no inferences available to the defenders) 300 times. Then: On 100 occasions East will play the jack from J2, and West will win the next two tricks when declarer leads low from his hand. On 100 occasions East will play the queen from Q2, and on 100 occasions he will play it from QJ. Since West must guess which holding East has, and since he will guess correctly half the time, the defenders will prevail in 100 of those 200 cases. This means that defenders who have an agreement will succeed exactly as often as defenders who have none: two times out of three. If one is to rely (as of course one always does at the table) on inferences from the bidding, it is likely to be superior always to play the jack from QJ. It is more likely that West will be able to infer from the bidding which of East and South has a missing queen than a missing jack. However, players who have recently learned that they should play randomly from QJ when declarer leads the suit are not likely to welcome the news that after all, they shouldn't.

I don't understand this part. What does West gain by ducking the Q? Doesn't declarer then make 2 tricks anyway? He does, but the stated problem was how to play the suit for three tricks. If you have to play for two tricks only, it is better to start with the ace, then lead to the queen.

I can't imagine doing anything more complicated than winning the spade, ruffing a club and playing a diamond. I can't make the hand if spades are 4-1. I won't commit myself in hearts just yet. Probably, I will win the queen of diamonds at trick four and lead my last club towards dummy. If LHO has three clubs, I will ruff and play a low diamond from the table. If LHO has only two clubs, I will take my chances - maybe he also has ♠Qxx, in which case I'm not dead. I am aware that this isn't the detailed analysis for which Frances was hoping. But as someone who may have been Skid Simon once remarked, I play hands quickly because I have a genius for recognising in half a minute that I won't know what to do if I think for half an hour. And I really would rather that East didn't win the first round of diamonds and play another trump. But if he's that good, he deserves to beat me, and I hope has has the queen of hearts so that he gets his deserts (because, when push comes to shove, I am going to play West for that queen).

The thread deals with the meaning of a double of 2S. I thought Dburn was discussing the bidding problem of what to do with this hand after a 2S call. Discussing what to after a 2D balance is somewhat off-topic. I am a bit lost here. True, the original post asked for the "standard" meaning of double after 1x - pass - pass - 1y; 2x. In the example I gave, the auction was of the form 1x - pass - pass - 2y; 2x. I guess that might make a difference, but not so much of a difference as to be "off-topic". We can modify my original example easily enough: ♠76 ♥AQ32 ♦J4 ♣A7632 RHO opens 1♦ and you pass (if you would double or overcall 1♥ or 2♣, you need read no further - as Bobby Wolff remarked, I admire you but I don't want your results). This is passed round to partner who bids 1♠, whereat RHO bids 2♦. What call do you make? Frances may have had a discussion on the topic similar to one I had with members of what was then (and may still be) the cool school; I can recall someone (Jonathan Cooke, perhaps?) explaining to me that you should double bad players for penalty but good players for takeout. That may be theoretically best, but I can see one or two problems arising in the context of "full disclosure"; it would be a trifle awkward to have to ask LHO how bad a player RHO is before doubling. Don't get me wrong - I cast my vote for "penalty" because as ArtK78 correctly says, that is the standard meaning insofar as there is a "standard". But the original poster was quite right to include an option that "it depends on x and y". People who play five-card majors and rebid their major at the two level in this kind of sequence will not have a hand consistent with being doubled for a huge penalty. Even the bad players are getting better these days, and you don't come by 1100 penalties nearly as often as you used to. But people who play systems where a 1m opening may be 2, 1 or even 0 cards (prepared 1♣, Precision 1♦ and the like) might well take a chance on rebidding their minor with a ropey six-card suit. I know this for a fact - I used to do it myself, but I made sure I had garnered several master points before doing it against Jonathan Cooke.

Suppose you have: ♠76 ♥AQ32 ♦J4 ♣A7632 You would not double 1♠ for takeout, would you? Nor would you overcall (if you would, then you should probably defer lessons in bidding theory until you have learned something about bidding judgement). When the auction proceeds 1♠ - pass - pass - 2♦; 2♠ to you, what call do you make? You would like double to be for takeout, but you cannot seriously see the use of such an agreement. There are many things you cannot see, but this does not mean that they are not there.

I haven't read the answers to this particularly closely; apologies for any old ground I may be covering. jdonn appeared to me to be writing sense, ArtK78 to be writing nonsense, but rather than look at their arguments in detail I thought I would offer my own explanation. Since East must play an honour if the defence is to have any chance of beating the contract, nothing can be inferred about his holding when he does - in particular, no agreement as to whether one plays the queen or the jack from QJ doubleton can avail. West should simply defend as if his partner had Hx, since he will have this considerably more often than he will have QJ. Restricted choice is not an issue here; nobody has any choice (unless you wish to argue that one can always choose to misdefend).

At the risk of continuing off-topic, I completely agree with Fred's assessment of Roy Hughes's book. It and Sabine Auken's "I Love This Game" are the two best new bridge books to appear for quite some time.

That is certainly the best line for three tricks with A1072 Q86 or at any rate it is best to start that combination by leading the queen - if it is covered by the king, win the ace and run the six; if it loses to the king, lead to the ten next. With A1072 Q83 it is best to lead low to the queen. Whether that holds or loses to the king, lead to the ten next unless you believe that West will not duck the queen from KJxx. As I remarked, though, this A1072 Q85 is a particularly difficult combination to analyse. It breaks Suitplay, the program written by Jeroen Warmerdam of the Netherlands, which runs out of memory before completing its analysis. You may like to consider how you would play as East with J9 doubleton when declarer leads low from the dummy at trick one.

There is a story that Sami Kehela and Eric Murray had to fill out a form indicating how many master points they had. Kehela wrote "Not many", but Murray wrote "Plenty".

That's not the normal policy. Instead, you should play small to the ten if the queen holds. I'm surprised David. Doesn't finessing lose two tricks to Kx on the right? It does, but standard operating procedure for an East with Kx is to put up the king. You will - or at least you should - next cash the queen and the ace, thus losing two tricks anyway (East is slightly more likely to have started with KJx than with Kx - the a priori probabilities are about 5.33% for KJx and 4.84% for Kx). The reason you should play to the ten when the queen holds is that West with KJxx should duck the queen. You will doubtless tell me that you never play against opponents who defend like that, and it is certainly true that you should take into account the standard of your opponents and the likely state of their knowledge of your holding when playing any suit combination. When we are asked "what is the correct play with a particular combination?" we assume that the defenders are playing optimally with full knowledge of declarer's holding. At the table, of course, this is often not the case.