dburn

They do, and I have a copy of them. Is there anything in particular you would like to know?

Def double now. I mean partner should have xxx - AKQxxxxx AK or something and could easily be worse. No need to get greedy, maybe our teammates are in 5♥X. 7♦ isn't so bad opposite that hand, is it? A spade lead would be worst for us, but hard to find, and on any other lead I would fancy my chances. And it's hard to imagine partner offering a forcing pass with a worse hand. Not that I would do anything other than double at the table - bidding grand slams on murky auctions in Hubert Phillips matches is, to put it mildly, unsound. Still, if it turned out that partner had the hand above, and if it turned out that we lost the match because I didn't bid 7♦, my attitude would be apologetic rather than expostulatory.

Well, on this occasion if he doesn't lead a diamond he will probably lead a spade, and that might not be so good for your side either. Only on rare occasions will he try a club from such as ♣Jx - "my LHO has the majors, my RHO has diamonds stopped, but what these fools do not know is that sometimes my partner opens 1♦ with a long club suit." Not that this means I would not bid 1NT with the North hand - I would. After all, you can scarcely expect me of all people to violate the Law of Total Trumps by risking 2♣ on a possible 4-2 fit.

Wouldn't blame anyone. If the North hand were given to the Master Solvers' Club, I'd imagine you would find a 50-50 split between 1NT and 2♣. Some might even bid 1♥, and I would not call them fools.

Some consideration might be given to East's apparent competence. With four spades to the jack and the king of clubs, he could have beaten you by ducking the first club trick - you would play a spade to the ace and repeat the club finesse, would you not? Since he did not follow this line of defence, he should not have that hand, wherefore you should not play him for it. Of course, as other contributors have suggested, you should not play him for it anyway - even though West has five hearts and East two, West will have Jx or Jxx of spades much more often than a small singleton. Curiously, with this particular layout West will have Jx and Jxx equally often - that is, about 15.9% of the time for each combination and 31.8% of the time in all. He will have a small singleton only about 18.2% of the time, making it clear to play for the drop.

I imagine most of us would consider that after (1♥) 3♥ (4♥), 4NT would be an attempt to play there, showing a heart guard and a trick to go with partner's eight winners. I don't imagine the sequence (1♥) 3♥ (5♥) has occurred often enough for any one of us to know what any other one of us would intend by 5NT. But one possible way to think about it is this: the 5♥ bid is presumably sacrificial in intent, so that at least one of our opponents believes than we can take eleven tricks in a minor. That being so, why - if we have a heart guard - should we not be able to take eleven tricks in notrump, without being able to take twelve tricks in the minor? Of course, there is also some danger in bidding 6♣ without discussion - partner might think "he could have bid 5NT to ask me to bid my suit, so he must be bidding his own suit and I will pass despite having solid diamonds". My view is, though, that a pragmatic partner would tend to assume that the likelihood of making 6♣ and not 6♦ was not all that high, and that 5NT might therefore be more useful as an attempt to play in 5NT.

You may not make it. And if I were your partner, I can tell you right now that I would pass it.

Without the eight, it is correct (as others have said) to lead to the king and then to the nine. With the eight, however: [hv=n=sj9732&w=s&e=s&s=sk84]399|300|[/hv] it is better to lead low to the eight first, then if this loses to the ten, to run the jack. Leading low towards dummy is inferior by some margin.

If your methods encompass the notion that a pass in the pass-out seat is forcing, they should probably be revised. If on the other hand you are asking whether opener's pass to 4♠ is forcing, the answer is no. Would pass at IMPs - why should we make game, or lose points on the board if 4♠ goes down? Doubling or bidding could easily result in a three-digit score starting with 5, 6 or 8 being entered in the minus column. Might double at matchpoints just in case we get 300, but probably would not. 5♦ might work, but is ridiculous. Of course, I would not have doubled 1♠. Instead I would have bid 2♠ to show a sound diamond raise. That might have left partner better placed over 4♠ to his right, but so strong is the tendency to show four hearts in this kind of auction that I do not expect to convince others of the soundness of this approach. But it is pretty stupid, when the opponents have started bidding spades, to conceal excellent support for partner's diamonds just in case we can fight spades with the hearts that we may or may not have. Supporting diamonds does not deny holding four hearts, nor preclude reaching a heart game if that is where we belong.

Because she does not need to. If you are going to play for the drop on the second and third rounds of the suit, then she should play an honour on the first round so that you make two tricks rather than three. As to the actual case, you should play for the drop in clubs (especially at matchpoints, where making no tricks at all from this combination will score a bottom and render you the subject of much justified ridicule). Moreover, you should not have played the queen of hearts from dummy to the first trick.

This hand must have come up in that game Andy and I had at the Young Chelsea in the 1990s. Only thus could it be the case that: [a] I have no recollection of ever having seen it before; and Andy is confident that I lacked the ability to play it correctly. However, if this is to be considered a collaborative effort, I think that partial credit should be given to Ken Rexford for having the foresight to play a spade after drawing trumps. This seemingly pointless manoeuvre is actually an important element in the eventual fulfilment of the contract, and should be duly recognised. If declarer plays a low diamond without first playing a spade. West wins and plays a spade to East, whose return of the jack of diamonds disrupts communications for the squeeze. It is also worthy of note that West could have broken the contract in one of two ways, by leading either a spade or his singleton ♦K. Although it seems at first that the requirements for a squeeze on East are still present, both of these leads render declarer's task impossible. The reasons for this are left as an exercise for the reader.

If West has the singleton king of diamonds (and he might well have led some other singleton) then it ought to be possible to squeeze East in the pointed suits. Ruff the second spade, play a low diamond to West's king, ruff the forced spade return and run trumps, reducing to ♦Qx and a spade in dummy, ♦Axx in hand with East still to discard from his spade winner and ♦J10x. Of course, this doesn't need the nine or the eight of diamonds, or the nine and the eight of spades, or anything except for West to have started with 3=7=1=2 shape and ♦K. But the line does not seem to cost when he in fact began with any of the other favourable diamond holdings, so should be adopted.

You could, of course, play both. After, say, 1D-1H-1S, 2C is a transfer to 2D, which opener bids if he would have passed simple preference. After opener does this, responder's continuations are invitational. After 1D-1H-1S, 2D is artificial and forcing to game; continuations are more or less natural. Peter Crouch, an English bidding theorist all of whose ideas are mad, is as far as I know the originator of this idea, his only sane contribution. It is a beautiful idea, and it works very well indeed.

Not really possible to answer this, because there may be a restricted-choice element that has not yet been taken into account (Frances, I'm surprised at you :) .) All I know is that one of the opponents led one of the (minor) suits in which I was solid. But if that opponent were South and led from some random collection of low cards in a minor, he might equally have led from some random collection of low cards in hearts if he had one. The fact that he led a minor increases the chance that he has the king of hearts by a factor of... well, who knows? The same sort of reasoning, of course, applies to North. It is a capital mistake, as someone once observed (no *****), to theorise without data. Who was declarer? What was the actual opening lead?

Very much so. The exercise in futility above was an attempt to show how distributional probabilities are calculated in terms of vacant places. Or to put it another way, I was bored, and I didn't see why I should be the only one.

Of course it is. The chance that a suit will be 1-1 as opposed to 2-0 or 0-2 is exactly 52 to 48, because the chance that East will be dealt the second card after West has been dealt the first is exactly 13 (the number of vacant spaces East has) to 12 (the number of vacant spaces West has). The chance that West will have two cards of four missing cards is somewhat harder to calculate in this way, because it can happen in a number of different ways (six, to be precise). West can receive cards 1 and 2, East cards 3 and 4; or West can receive 1 and 3, East 2 and 4; and so forth. If we look at the likelihood of each of these in terms of vacant spaces, we soon see that each is equally likely: West gets card 1 happens with probability 13/26 West gets card 2 then happens with probability 12/25 East gets card 3 then happens with probability 13/24 East gets card 4 then happens with probability 12/23 West gets card 1 happens with probability 13/26 East gets card 2 then happens with probability 13/25 West gets card 3 then happens with probability 12/24 East gets card 4 then happens with probability 12/23. In short, each of the six ways in which West can receive exactly two of the missing cards happens with probability (13*13*12*12)/(26*25*24*23), or 6.7826087%. Multiplying this by six gives the actual probability of a 2-2 break, which is 40.69565217% (give or take a pip or two). The same sort of calculation can of course be performed to arrive at the probability that West has three cards and East one: each case has a probability of (13*12*11*13)/(26*25*24*23), or 6.217391304%, which we multiply by four to give 24.86956522%. Not surprisingly after all this, the ratio of the chance that West has two cards to the chance that he has three is the ratio of: 13*13*12*12 to 13*13*12*11, or exactly 12/11. This is not 52 to 48, but nobody ever said it was - or if he did, he erred.

Did it matter what the opening bid was? If it worked out well to open 1♣, or 2♣, or 6♣ on this particular hand, what conclusions are we supposed to draw that will improve our bridge in the future? I mean, I would open 2♣ and hope for the best, although I am dismayed to find that Andy Bowles, Fred Gitelman and Eric Kokish would never play with me again if I did this. Not that they've ever played with me before, but a man can dream.

Well, that is not quite the best way to play this particular combination (you should in fact run the eight if it is not covered). But I cannot tell from your post whether you are offering advice or asking for it.

[hv=d=s&v=b&n=sk3hqj4d64ca97432&s=sajha108763da102ckq]133|200|You, South, open 1♥ and West overcalls 2♥, spades and a minor. North bids 3♣, natural and forcing, East passes, you bid 3♦ and your side then reaches 6♥ (apologies for not knowing how the rest of the auction went). The lead is ♠7. Plan the play [a] at IMPs and at board-a-match, assuming in both cases a competent NS and EW pair at the other table.[/hv]

Why are spades almost certainly 4441 around the table? You are assuming responder would respond with 5+ spades always? Against most opponents I don't think that's true. I don't assume that anyone would do anything "always", which is why I said that spades are "almost certainly" 4-4-4-1 round the table. If this problem had occurred in an English context, where many people open 1♣ with 5-5 in the black suits, I would have modified "almost certainly" to "fairly likely to be" (and I might have passed). My experience is (and other people's mileage may well vary) that many part-score and even game swings are lost because players are afraid to balance for fear that the opponents might find a better fit. That could well be the case here of course, but the questions are: how likely are they to find that fit, and how likely are they to do well in it? It seems to me that most of the time when I bid 1♥, opener will pass, partner (with his 4=1=4=4 shape) will bid 1NT, I will bid 2♦ and everyone will pass. We will score 110 in 2♦ as against -70 or -90 defending 1♣ (maybe we could have beaten it, but I am an old man with better things to do in my few remaining days than sweat out the best defence to 1♣ after partner has made his usual clueless opening lead). Some of the rest of the time, partner's massive penalty double of 1♣ will produce a game in hearts or diamonds or notrump facing my hand. Some of the rest of the rest of the time, my opponents will bid to seven spades and make it. But so what? I've been there before.

Would be inclined to bid 1♥ - after all, if the opponents bid game in spades they don't have to make it, since partner will have clubs and spades over the opening bidder (spades are almost certainly 4-4-4-1 round the table). But as a man who once protected against a Precision 1♦ opening passed around, only to find that his opponents could make 7♣, my view may not be worth very much.

No, it isn't. With J1065 facing A432, you have two equally plausible lines for one loser: lead the jack, hoping that North has a doubleton honour; or lead low towards the J10, hoping that South has a doubleton honour. When you lead the jack you are indeed hoping that North has Kx (or Qx), but you're not "hoping to induce a cover" - you don't care whether he covers or not. Cashing the ace first is hopeless - that gains only when North has a singleton honour or either opponent has KQ doubleton, a worse chance than to find Hx in the "right" hand. A case where one should perhaps not select randomly from equals is this one: [hv=n=s987&w=sj1043&e=sa652&s=skq]399|300|[/hv] Declarer leads low from dummy (East). South should always play the king, never the queen (because declarer will not believe that South would play the queen from Qx). However, benlessard is right about one thing: these are complex positions. Roudinesco's Dictionary of Suit Combinations and Warmdeman's program Suitplay are, as far as I know, the best attempts so far to address the question of how to handle certain common (and uncommon) combinations. As far as I can see, though, they both operate on the premise that the defenders know what declarer's holding is, and will false-card and give other losing options where necessary. In real life, of course, this is almost never the case. The actual position in Pau was: [hv=n=s987&w=sj1043&e=sa652&s=skq]399|300|[/hv] or the like, and what interested me was what North's strategy ought to be. At more than one table (with East as dummy) North did not cover the queen; declarer led the jack next (playing for North to have been forced to play low from Kxx, rather than to have chosen to play low from Kx) and went down - an interesting application of the Principle of Restricted Choice. At more than one table North did cover the queen; declarer led to the nine next (playing for North to have refused to risk letting a no-play slam through if declarer did not hold the nine) and made the contract. Since it is exactly 50-50 whether declarer holds the nine or not, were the Norths who did not cover the queen defending rationally?

I don't recall mentioning what the contract was, so I am not sure whence this talk of "three other sure losers" comes. You may assume for the purposes of the exercise that declarer is in a grand slam (this was not actually the case - he was in a small slam with this suit as a side suit, but it was evident that he could not afford a loser in it since he had already lost a trick).

How would you suggest that declarer (West) play the suit for no loser holding QJxx in his hand? Of course, legitimately he cannot, but we do not always arrive in the best contract, and at least against you he has a chance...

A deal from the European Championships in Pau revolved around the play of this suit for no loser: ♥QJ93 ♥A642 North actually held ♥K8, and both defenders knew that East-West had a 4-4 fit. It seemed to me that if West were declarer the contract ought to make, while if East were declarer the contract ought to fail. How does it seem to you?