dburn

Would play a spade at matchpoints, a diamond at any other form of scoring.

As to a player's obligations: As to the ruling that should be given:

[hv=d=w&v=b&n=sq10732hq4da972c103&w=sk984haj532d43c95&e=s6hk876dj1086cqj42&s=saj5h109dkq5cak876]399|300|Scoring: IMP[/hv] South opened 1NT after three passes and played in 4♠ on a transfer auction. West led a club, and South played the first few tricks at a frantic pace: ace and king of clubs, club ruff (West pitching a diamond), spade to the jack and king. At this point West needed to shift to a heart to beat the contract, but he played his remaining diamond to the two, six and queen. South cashed the ace of spades and, with immortality in his grasp despite (or perhaps because of) the way he had played until now, bizarrely led a club - a hopeless play that guaranteed not making the contract. All he had to do, though, was draw trumps in this position: [hv=d=w&v=b&n=sq10732hq4da972c103&w=sk984haj532d43c95&e=s6hk876dj1086cqj42&s=saj5h109dkq5cak876]399|300|Scoring: IMP[/hv] to execute a play I have never seen before - a stepping-stone winkle. East must come down to the singleton ♥K to avoid immediate loss, but South pitches a heart and leads a heart from the dummy. West cannot overtake, so East remains on play with ♥K. If East plays a high diamond, South wins the king and exits with a club; if East plays ♦8, South runs it to the nine, crosses to ♦K, exits with a club and East must give the last trick to dummy. There are times when, browbeaten by half the world who think that as a committee member I am not imposing enough regulation on systems and the other half who think I am imposing too much, while all of them think that I am acting solely in my own interests, I wonder why anyone plays this stupid game at all. But then, thanks to Fred and to BBO, I can watch this gem of a hand live from China at half past two in the morning, and I know why I play bridge.

Sorry - the Encyclopedia is quite right. For some reason I thought that there were rather more 7-2-2-2 shapes than there actually are. I am abashed, though not especially surprised, to discover that when I set this as a problem in the bulletins for the 1988 Junior World Championships I had calculated the correct answer. Twenty years later, I managed the wrong one. Corpse evangelists nothing.

We have a winner - more than one, in fact, since that was also Nigel's suggestion (and perhaps cherdano's second suggestion, although the figures he gives do not accord with my own calculations). There are 3,812 hands in total on which one could open 7NT and claim before the lead. Of these, 1,512 have 9-2-1-1 distribution, since the nine-card suit must consist of AKQJ and five of the remaining nine cards. There are, as Nigel says, 126 ways of selecting five cards from nine, and there are 12 possible 9-2-1-1 patterns (here I use the Bridge World notation in which 9-2-1-1 means any nine-card suit, any doubleton and any two singletons; 9=2=1=1 would mean nine spades, two hearts and one card in each minor). 126 * 12 = 1,512. The next most common 7NT openers have 8-3-1-1 and 8-2-2-1 pattern (the eight-card suit must be AKQJ10 and three of the remaining eight small cards; there are 56 ways of choosing three cards from eight; twelve ways to hold each distribution; 56 * 12 = 672). Then comes 10-1-1-1 (480 of those), and 7-3-2-1 (168 of those). The chance of holding one of the 9-2-1-1 shapes is 1,512/635,013,559,600, or 0.00000024% (give or take). The total chance of being able to open 7NT and claim is a more encouraging 0.0000006%. Suggest not holding your breath while waiting for one.

I am quite sure you have both the decade and the form of scoring wrong. So am I. The new scoring (300 for each doubled non-vulnerable undertrick after the third) was introduced in 1987, not 1975.

This may have been asked before - apologies for not reading through all the comments. Is it envisaged that commentators will be able to use the Flash client?

I am not quite sure what is meant by "one of those questions" - four questions have so far been asked in this thread: [1] What is the chance of holding a hand with 30 hcp? [2] What is the chance that a player will bid and make 7NT on two consecutive deals? [3] What is the chance that a player will bid and make 7NT three times in nine deals? [4] What is the most likely distribution of a player who opens 7NT and claims before seeing the opening lead? Of these, [1] and [4] can be calculated precisely. [2] and [3] can neither be calculated nor simulated at all, since we do not know who this player is. Perhaps one should restate them as "what is the chance that a player who always bids to the optimum contract and plays double-dummy will bid and make 7NT...". In that case, precise calculation would be possible in principle but exceptionally tedious in practice; a simulation would certainly be a better approach.

6332 Not this either, since although hands with 14 cards are quite likely on BBO, in real life they are less probable. Neither is 6-3-2-2 the answer, but feel free to try again.

Nice! Must be (hidden). If it must be, then it would be. But it mustn't, so it isn't.

Quick quiz: a player opens 7NT as dealer and claims before seeing the opening lead. What is his most likely distribution?

It's not really a question of the odds in individual suits, more a question of what distributions consistent with the bidding will allow us to make the contract. Of course, we don't have nearly enough information to allow us to determine this, since we don't know for example: whether 3♣ denies a four-card major; whether 3♣, described as "inverted", can be purely pre-emptive, or whether East is expected to bid 3NT with a balanced 18 or so opposite; what range 1NT opening East-West play (Nigel quotes an East hand of ♠Qx ♥Axxx ♦Ax ♣KQJxx, but many Easts would open 1NT with that playing 15-17). At the table one would just get on with things: win the lead in dummy and play a spade to the ten; ruff the club return and play a second spade, requiring the suit to come in for no more losers; play on hearts next, with one's later play being determined by what has happened in spades. I expect that it will prove convenient in most circumstances to play West for the jack of hearts, but since I have no idea what will happen in spades I cannot conjecture further.

1♦-2♣-2♦ - what now? 2♠, perhaps? One is almost tempted to splinter with 3♥ on the first round, when one contemplates sequences such as this.

If playing 3♣ as Stayman, I imagine that one could bid 3♣ followed by 3NT even over 3♥ to offer a choice of games - what else would that sequence mean? Playing 3♠ as Stayman one does not have this option, and on the given hand I would certainly bid 3NT. If partner has four hearts and one spade stopper, he will sometimes double 2♠ for takeout rather than overcalling 2NT; when he overcalls 2NT, either his spades are robust or he is not particularly interested in playing in 4♥ facing four cards. I should add that there is a considerable difference between a 1NT overcall of a one-level opening bid and a 2NT overcall of a weak two bid. In the former case, a stopper such as Axx or Kxx will often not be adequate, because a one-level opener will have an entry to his long suit. In the latter case, such a stopper will often be adequate because there will be no entry to the long suit. One is in general more fearful of a bad trump break in 4♥ than the opener being able to establish and cash his spades.

I am not quite sure why I have been cited as someone who does not care about the survival of bridge, but it is not true. As to my views on forcing pass and other highly unusual systems, I believe that they should be permitted at national championship level and above, but not below that unless there is local demand. My first assignment as coach to the national team was in the 1987 Bermuda Bowl in Ocho Rios, Jamaica. Great Britain had two pairs playing some form of strong pass system: Forrester and Armstrong used TRS, which had other unusual features; Flint and Sheehan used a kind of geriatric strong pass which involved opening 1♣ when you had a pass and pass when you had clubs. New Zealand also had two strong pass pairs, one of whom used a system in which 1♠ was a fert at favourable, 1♥ at equal and 1♦ at unfavourable vulnerability. Brazil had a pair who, non-vulnerable, played a kind of "one under Precision" in which pass showed 16+ hcp, 1♣ was a catch-all, 1♦ showed hearts, 1♥ showed spades and 1♠ was a fert. Vulnerable, they played standard Precision. Was this a problem? No, not really - there were no seating rights, so everybody just got on with it. Occasionally, the HUMs would gain an advantage simply because the auction "looked" different from what it was, and this led to concentration lapses. For example, Mike Lawrence and Hugh Ross had an accident when one of them bid 2♣ over a 1♦ opening that showed a pass; he thought he was opening an artificial game force, but his agreed defence was that 2♣ showed a club suit in a limited opening bid. Lew Stansby bid 1♠ over a pass that showed an opening bid; Chip Martel raised him to 2♠ and he bid 2NT, which would have been an artificial force if he had opened the bidding, but was natural and non-forcing if he had overcalled (as in effect he had). Both of these mishaps led to ridiculous results that cost the USA several IMPs. I felt then, as I feel now, that such occurrences are an undesirable effect of highly unusual systems. But the way to eliminate them is not to abolish these systems at the highest level - it is to ensure that your team has done enough preparation against them to negate as much as possible the aspect of unfamiliarity. Before the British team left for Jamaica, each of its pairs played more than a hundred boards against all manner of unusual methods (there was no shortage of volunteers prepared to give the team some practice) so that we were equipped to deal with Brazil, New Zealand, Sweden and the other countries we encountered who were using strange systems. And we were not all professional players with vast amounts of time and energy to devote to such practice - Kirby, Armstrong and Brock all had full-time jobs. In these days, when most top players devote all or most of their time to bridge, I can see no real reason why such methods should be prohibited or greatly circumscribed. It irks me somewhat to read, for example, Larry Cohen describing some misfortune that befell a pair when a dastardly opponent responded 1♥ to 1♣ to show a spade suit. Surely, the world's leading players do not need molly-coddling to the extent that they never have to cope with anything other than the totally familiar.

Jeff Rubens occasionally referred to a parabolic utility function when talking about the value of playing for overtricks in teams matches (and, what is more or less the same thing, defending for extra undertricks at the risk of letting a no-play contract make). By this he meant (I think) that in very short or very long matches, it was worth playing for overtricks because, other things being equal, there was enough chance that they would be a decisive factor in the outcome. In matches that were neither sufficiently short nor sufficiently long, it was a better idea just to make the contracts you were in. Whereas this is obviously true of very short matches, it is not clear to me how long a match needs to be before the utility factor dictates that you should play for overtricks during it. Hugh Kelsey wrote of safety plays that if you give up a trick to guard against a low-probability distribution that will jeopardize your contract, you may for various meta-reasons be doing the right thing even though as a purely pragmatic matter you are doing the wrong one. For example, needing five tricks from a suit of AKQ1043 facing 65, you might duck the first trick completely in both hands if there is no entry to the long suit, to guard against 5-0 onside. This is theoretically losing bridge - if you spend your life doing that, you will lose more IMPs than you will gain, and some of those lost IMPs may lose matches for you. But Kelsey said (I am paraphrasing here because I don't have the relevant book with me) that "partner will not care about the overtricks you expect to make on 99 other deals out of 100 - all he will see is that you have put a cold game on the floor". Not upsetting partner may be worth many more IMPs than a dozen overtricks. Some of these safety plays are not necessarily as safe as all that. You, South, play in 6♠ with: [hv=d=s&v=n&n=sk942h432d432ca32&s=saj53hakqjdakqjc4]133|200|Scoring: IMP[/hv] and West leads a diamond. You can of course play the trumps safely for one loser against a 4-1 break by cashing the ace and leading to the nine, but if East wins his doubleton queen or ten and gives West a diamond ruff, how unlucky were you? The a priori chance that West has ♠Q10xx is significantly greater than the chance that he has one diamond and three spades to the ten or the queen - but what is that chance now given that he led a diamond? Does this answer your question? No, I thought not. Still, if bridge were an easy game, how many of us would play it?

If East has seven diamonds and five clubs, then he has a major-suit void and the final contract would have been doubled. Not that it would necessarily have been defeated, of course - if East has a heart void, West will probably lead a spade anyway (unless North has indicated his heart length during the bidding). However, the chance that East has five clubs to go with his seven diamonds, a priori a far from negligible 0.096961862%, drops to 0.000000000% given the actual circumstances. Still, the point about East's possibly having eight diamonds is a good one, and in any case the problem appears to have been not to play the hand accurately down to the last percentage pip, but merely not to play it awfully. In that resepct, awm's analysis is very sound.

Is that right? If West has two diamonds and East seven, the chance that West has five clubs and East none is roughly 7.466063348%. This is a little less than one in 13, not one in nine.

Having been through many hundreds of convention cards at major international events, but not having kept a careful count while so doing, the most popular defence seems to be: Against a weak no trump, double is penalty. Against a strong no trump, double shows a four-card major and a longer minor. Against any kind of no trump, 2♣ is majors, 2♦ is one major, 2M is the bid suit and a minor. Having oberved many major international events at close quarters, I can say this: what you play over an opening 1NT never seems to make a blind bit of difference. I cannot recall a significant swing generated by a difference in method (as opposed to style) when overcalling an opening 1NT. I did, while commentating today, observe a small swing on this deal from a tournament in Portugal: [hv=d=n&v=b&n=sq752hqjdakqj8c84&w=sak94ha76d6cj9653&e=sjhk8543d752ckq72&s=s10863h1092d10943ca10]399|300|Scoring: IMP[/hv] At both tables, North opened a strong no trump. I make no observation on the wisdom or otherwise of so doing - I reside at Table Mountain and my name is Truthful James. At one table this was passed out, and the contract was made when the defenders foolishly put their faith in hearts rather than clubs, for 90 to North-South. At the other West was able to protect with 2♣, showing clubs and a higher-ranking suit (DONT, I believe the method is called). This became the final contract, and made a couple of overtricks. How should East-West have bid their cold game in hearts? When you can tell me that, perhaps it will be worth discussing defences to 1NT with you.

Would certainly not double at IMPs. Might double at matchpoints, but would not be surprised to concede 730 - the opponents also know that they are vulnerable. Would probably just bid 4♣ - perhaps it will make anyway, or perhaps my RHO will have ♠A and lead it, allowing partner to pitch a heart. If partner bids five, I expect him to make it. 3NT is absurd - partner would have bid 3♠ if we could make that. 3♦ was not forcing, even if it showed a full reverse (which is questionable).

Law 9B says in part: If a defender exposed a card, there would be no question that it should be left exposed until the Director had been summoned - the defender would not be allowed to pick it up temporarily (in order, for example, to prevent declarer from remembering what it was). Why, then, should declarer's cards be treated differently? Perhaps because: The question arises: is it illegal for declarer to show all her cards to the defenders? It is certainly irregular behaviour, but that is not what an "irregularity" means in the context of the Laws. I cannot find anything in the Laws that makes it illegal (and thus "irregular" in context) for declarer to show as many cards as she wants to as many defenders as she wants for as long as she wants; if that helps them, well and good, but having exercised such generosity she is not compelled to perpetuate it. In short, declarer has (in effect) accidentally dropped all her cards face up on the table. This is not illegal, and there are no restrictions on a declarer who has so acted. In particular, there is no onus on declarer to leave the accidentally dropped cards on the table for a moment longer than she wishes. Suppose a declarer dropped a card face up on the floor. Do you suppose that a defender has the legal right to insist that it remain there until he has seen and committed to memory its face? If not, why do some of you (blackshoe in particular) differentiate in this respect between the floor and the table?

Was mildly amused the other day to overhear someone saying to her companion in a restaurant: "Courgette is the English word, zucchini is the American word".

[hv=d=s&v=n&n=sk1084had973ca10543&s=saqj97hj2da104cq87]133|200|[/hv] You, South, reach 4♠ with no opposition bidding. The opening lead is a spade, to which East follows. How should you play [a] at IMPs or money bridge; at matchpoints?

Not quite sure what this is about. Certainly if spades are 3-2 one can play two top trumps and claim (if no one ruffs any round of diamonds, declarer pitches a heart, ruffs a heart and ruffs a club). At matchpoints, one might be tempted to ruff a club, cash ♠K, cross to a diamond, ruff another club, cross to a diamond and cash ♠A, making an overtrick if all goes well. But if South has, say: ♠Q98 ♥ KJ109 ♦8765 ♣75 he will overruff the third club and play a heart to North, who will cash a club and play another, ruffed by South to promote a trump for North. How one would play would thus depend on how likely one considered it that North would have six or seven clubs for his overcall. The size of South's card on the first round of the suit might assist with that decision, but this datum is not vouchsafed by the original poster.

Nor is playing them, of course. Whereas it seems only natural caution for declarer to play a club to the king before establishing East's long diamond, this is actually a mistake. Details left as an exercise for the reader, but commendation to the original poster for finding an example of a triple squeeze without the count - possibly one of the rarest positions in bridge.