dburn

Technically, of course, "forward-going" cannot be applied to any non-forcing call, since if partner passes it we have not gone forward, which contradicts the original description. "Forward-looking" would be better, but it is far too late to expect bridge players (who have already espoused such terms as "semi-forcing") to start speaking English. One might, I suppose, claim that any bid other than pass is "forward-going", since it has in and of itself moved the auction forward. One would hesitate, for aesthetic reasons only, to apply the description "forward-going" to the last bid in the uncontested auction 1NT-2♥ (transfer)-2♠, but if you are going to use meaningless terminology, you must accustom yourself to thinking meaningless thoughts. The whimsical notion has also been introduced that in the contested auction Pass-4♦-4♠-Pass, 5♣ should show "five-level safety". Given that ♠AJ109xxx ♥x ♦Qx ♣Kxx is a 4♠ overcall of a 4♦ opening, it is not easy to construct a passed hand that will be safe at the five level.

No, no. Han is a mathematician, and will say that two is the correct answer (for sufficiently large values of two).

It is as if one were to post a message asking what one would bid with: ♠AQx ♥xxx ♦KJxx ♣10xx after partner opens a 15-17 1NT. To those who naively raise to 3NT, one then says: "Well, on this occasion partner had ♠KJxx ♥Ax ♦AQxx ♣Qxx and the defence took the first five club tricks when the opening leader turned up with ♣KJxxx. I of course passed 1NT, because one must, must, must pass in these positions with balanced ten counts including two unguarded suits, and look how clever I was." I am in Poland at the moment for the Champions Cup, which begins tomorrow. Of the champions to whom I have spoken thus far, I have collected one passer, two 5♠ bidders and one 5♣ bidder. Oh, and no 4♠ overcallers on the actual East hand, though I have learned the word for "ridiculous" in two languages in which I did not already know it.

Such as? It is no wonder that pre-empts work, if people are going to bid over them every time they need four trumps to an honour, an ace and a king opposite to esacpe for down only one.

Mostly West, partly bad luck - it's hard to see what East was supposed to do other than what he did. One can imagine West, who knew that he and East had not discussed the position before, wanting to bid 5♣ as a control bid for spades, but not particularly wanting to play there if East did not share this view. He might also have wanted to bid 5♦, which certainly agrees spades, but did not particularly want to have East do something foolish on the assumption that West had a diamond control. If West could bid 5♣ and know that East would understand it, then obviously he should have done. Perhaps the partnership will know next time - when, of course, West will be dealt ♠None ♥Axx ♦xx ♣KQJ10xxxx. But that's life.

Having said all of that, it remains to wonder what declarer's best line may be with ♠AQJ ♥Axxx ♦AQJ10 ♣xx (on the assumption that hearts are 4-4). Technically, it seems to me that he should use his first club entry to dummy to finesse in spades. If West has ♠K, declarer has three spade tricks, one heart, three diamonds and two clubs; the defenders get only a diamond and three hearts. If the first spade finesse loses, declarer can still succeed if West has ♦K or ♦Kx. If the first spade finesse wins, there is of course no guarantee that the second one will; a strong East will usually duck the first round holding the king. Even so, declarer's best line is probably to drive out ♦K and hope that ♠K is right after all; he makes the contract whenever West has ♠K or either defender the singleton ♦K. Of course, if declarer is going to follow that line it does not matter what the defenders do - the contract will fail on the actual lie of cards.

If declarer has that, you can't beat the contract. He wins the club, finesses in diamonds (dropping East's 10) and plays ace and queen of spades. East can win and return a club, preventing declarer from making a third spade trick - but declarer doesn't need one, since he has two spades, four diamonds, two clubs and a heart. If, as another poster mentioned, declarer's diamonds are AQJ10, then shifting to a club will indeed beat the contract - but declarer has misplayed; if he had won the first heart (he can tell from the lead that the suit is 4-4) and played on spades, he would take three spades, a heart, three diamonds and two clubs. Still, the original post said that declarer was not the strongest player at the table. Perhaps, then, a club return is best. It's not easy to construct a layout on which a club fails while other defences succeed against 3=4=4=2.

Close between 3♥ and "abstain, this system is sick", which it is if I can't bid 3♥ with this hand now having not supported hearts on the previous round. Since I can't abstain at the table, will bid 3♥, but I can see trouble ahead.

Ernst Eduard Kummer (1810-1893), a German algebraist, was rather poor at arithmetic. Whenever he had occasion to do simple arithmetic in class, he would get his students to help him. Once he had to find 7 x 9. "Seven times nine" he began. "Seven times nine is er... ah... ah... seven times nine is..." "Sixty-one", a student suggested. Kummer wrote 61 on the board. "Sir," said another student, "it should be sixty-nine." "Come, come, gentlemen, it can't be both!" Kummer exclaimed. "It must be one or the other." Another great mathematician, Paul Erdos, suggested that Kummer in fact solved the problem himself as follows: 7 x 9 can't be 61 because 61 is prime; it can't be 65 because that is a multiple of 5; 67 is prime; 69 is clearly too large; so that leaves 63. But if it's poetry you want, here is an indication of how to pronounce the Hungarian name of Erdos: A conjecture both deep and profound Is whether a circle is round. In a paper by Erdos That's written in Kurdish, A counter-example is found.

It should also be said (before I go to bed, which I should have done some hours ago) that: If you are in 7NT in a pairs tournament with this combination, you should follow the Higgins pin-drop strategy, for it will not matter whether you go down one or down two - the field will not be in your contract. If you are in a 27-point 3NT in a pairs tournament with this combination, you should (for the reasons I have given above) follow the drop-finesse strategy. If you are in the real world, you can do what you like, for it won't make all that much difference in the grand scheme of things. Well it was said by the bard: To some people a squirrel's a squirrel, To others a squirrel's a squrl. Since freedom of speech is the birthright of each, I can only this fable unfurl: A virile young squirrel named Cyril, In an argument over a girl, Was lambasted from here to the Tyrol By a churl of a squrl named Earl. Ogden Nash

I observe that I have just subtracted 108 from 924 and arrived at an answer of 906. This might foster in some minds the notion that I am a mathematician, because it is well known that mathematicians cannot do simple arithmetic to save their lives. I assure you that I am no mathematician of any kind, but I am typing this post (and the one that preceded it) after a friend's birthday party. I see, however, that Halo has invited Stephen (who clearly is a mathematician, and an excellent one at that) to "consider the real world". Mathematicians should not be invited to do that. Nor, at times, should I.

How are we supposed to explain a false statement. Are you claiming that declarer will for some reason adopt an inferior line of play at MP scoring. Perhaps he does not recognize that the defender is "optimal" and hopes for typical MP foolishness? Declarer only deviates from drop-pin when he is seeking to exploit foolishness on his right. This does not vary by scoring! What do you mean by "an inferior line of play at MP scoring"? It is well known that in a great number of positions at MP scoring, declarer should not adopt his best line of play for the contract; instead, he should seek to combine a good chance of making the contract with a good chance to minimise the number of tricks he goes down, if go down he must. Indeed, there are some easily exhibitable positions in which declarer should not even try to make the contract at all. But for the most part, what declarer seeks is a line of play that makes the maximum number of tricks per deal. In this case, the line we have described as pin-drop makes four tricks (against optimal defence) roughly 16.4% of the time. But it makes two tricks roughly 8.5% of the time (when an optimal West ducks the queen from K10xx, as he always will). It makes three tricks the rest of the time, and it makes 3.04 tricks per deal. The line we have described as drop-finesse makes four tricks about 15.8% of the time. But it never makes only two tricks, and it makes 3.13 tricks per deal. Assume that in the 11-table 1,000-board final of the World Open Pairs Championship, I sit South at one table and Bill Higgins sits South at the other ten tables. By a statistical miracle, every board is the same - all Souths arrive in a 27-point 3NT that needs four tricks from QJ98 facing A432. I will play drop-finesse throughout (if the queen is not covered, lead the eight from dummy and run it unless the king appears; if the queen is covered, win with the ace and play to the eight). The Higginses will play pin-drop throughout (if the queen is not covered, run the jack; if the queen is covered, play to the jack). East will almost never cover from Kx, and West will never win the first round from K10xx. I am English, so I will assume English matchpointing - two for a win, one for a tie, none for a loss. The East holdings are small enough in number to tabulate here. When East has: K10xxx it does not matter; we will all go down one. K10xx it does not matter; we will all go down one (for different reasons, though). Kxxx it does not matter; we will all make three. K10x it does not matter; we will all go down one. Kxx it does matter; I will get 0 match points for down one and the Higginses 11 match points apiece for making three. This will happen on 102 of the boards, so Bill is ahead of me by 1,122 matchpoints at this stage. K10 it does matter; I will get 0 match points for down one and the Higginses 11 match points apiece for making three. This will happen on 34 of the boards, so Bill is ahead of me by 1,496 matchpoints at this stage. Kx it does matter; I will get 20 match points for making three and the Higginses 9 match points apiece for down one. This will happen on 102 of the boards, so Bill is ahead of me by 374 matchpoints at this stage. K it does matter; I will get 20 match points for making three and the Higginses 9 match points apiece for down one. This will happen on 23 of the boards, so Bill is ahead of me by 108 matchpoints at this stage. So much for the cases where East has the king. There is only one relevant case where West has the king (we have not explicitly discussed singleton king, but both Bill and I will cash the jack next and go down one because of what Halo does not yet think of as "classical" restricted choice, even though it really is). However: When West has K10xx, I will get 20 matchpoints for down one and the Higginses 9 matchpoints each for down two. This will happen on 84 of the boards, so I am ahead of Bill by 906 matchpoints at this stage. And there aren't any more stages. Really, Bill, there aren't. An inferior line of play at IMP or rubber bridge or total-point scoring may nevertheless be the correct line of play at MP scoring. You knew that all the time, though. Maybe you just didn't know why.

I suppose that after all, the well-known combination we are discussing here may have something in common with Fred Gitleman's new combination that inspired the original post in this thread: the capacity to astound. Fred's offering was: North (dummy) J108 South (declarer) K65432 Declarer runs the jack if East plays the seven, but plays the king if East plays the nine. Fred and others were surprised that declarer's strategy should vary with the low card that East plays. Here, with North (dummy) QJ98 South (declarer) A432 an optimal defender sitting East against an optimal declarer will never make a trick with Kx at matchpoints, but will always make one at IMPs. Now is not this ridiculous, and is not this preposterous? - a thorough-paced absurdity; explain it if you can.

Of course, if I were playing for a billion dollars in the final of the World Pairs Championship and not the Bermuda Bowl, I would play low from dummy on the second round if the queen were not covered, and finesse against West's ten if the queen were covered (the strategy I have described as drop-finesse). Bridge is not an easy game. But then, the only person who said that it is was a Conservative politician.

Cryptic writing due to cryptic reading - that is, I had scanned the first few posts under the misapprehension that the deal had been properly analysed in the first place (5H makes, 5S goes down because of H ruff, et cetera). It was only when some cryptologist said that 5S had play and 5H did not that I investigated the (possible) play of the hand further. It seemed to me that the analysis advanced of the former contract was rubbish, but I had been taken in to the extent of suggesting that maybe South ought to have bid 5H and not 5S. South should not have done half as much bidding as he did. Neither should North. As usual, someone ought to have doubled someone else, but no one could.

Let us examine this in the context of the more familiar "restricted choice" position: North (dummy) A10876 South (declarer) K954 I, South with a few hundred thousand dollars on the line, play the six from dummy. East plays the queen, I win with the king on which West plays low. Then I lead a low card, on which West plays low... Halo will argue that East "must as a matter of fact" have started with either QJ or Q. Since QJ is a priori more likely than Q, why should I (who will finesse against the jack every time, and win almost two times out of three) "propose to lose" to an original holding of QJ with East? Even if QJ were not a priori more likely than Q but exactly as likely as Q, isn't it "just a guess"? No, it isn't. I'm sure Halo knows this as well as I do, and that he will now know what was wrong with drawing the conclusions he drew from "must as a matter of fact" in his earlier statement. If not... well, this conditional probability is perhaps counter-intuitive stuff.

The foregoing assumes that South had the queen of diamonds, otherwise the whole thing is an April fool. Whether too late for this year or too early for next is left as an exercise for the reader.

I am not entirely certain why South should bid 5S instead of 5H. Maybe South should not bid at all, but that is a separate issue. But I confess that if North were to raise spades, I would disagree with skaeran's assessment that this was "not close to bidding at the five level". I might, however, have bid the suit in which we were more likely to make a five-level contract; it would be hard for me to construct a hand opposite which 5S would make and 5H would not.

Not much of one, for the prize money seems to be dropping by a factor of ten every time I play a card. But in your scenario: the best card player in the world, who knows my game inside out to boot, will not cover from Kx because he knows that I will run the jack on the next round. If he does cover, therefore, I will (of course) play him for K10, because that is more likely than singleton king, the only other holding from which he must cover. It might help if you were to imagine not how humans would play, but how to program robots to play. If you program your East robot to cover the queen with the king from Kx less than one time in nine, but more than not at all, you should not implement any strategy in your South robot other than pin-drop. Nor should you implement any such strategy in yourself, of course. But you did say that this was a bidding forum, and I have no advice to proffer in that context other than that you should use whatever knowledge you glean from others here to avoid contracts that depend on this suit combination for no losers.

Si la jeunesse savait, si la vieillesse pouvait... et si la loi permettait. If only old has beens were not so oblivious to very obvious typos (don't know how to say that in french). Nor in English, it seems, for it should be obvious to all but the obnoxious that if I had been "oblivious" to the obtuse typo, I would not have obtruded my objection thereto. Should you remain obdurate, I can only refer obliquely to the obscure observation that "Ob-la-di, ob-la-da, life goes on..."

Si la jeunesse savait, si la vieillesse pouvait... et si la loi permettait.

Most of the time, partner will know from an inspection of his or her heart holding what I have for this delayed double. But quite a lot of that time, partner will be faced with working out whether we are more likely to concede 1100 if she bids or 990 if she passes. Of course, if partner has three small hearts and enough shape that we have a profitable sacrifice, I will be a lion. If not, I will be a goat. Though I was born under the sign of Leo, I am old enough by now to realise that Capricorn would have been more appropriate, wherefore I would double in the given auction only if my clubs were interchanged with my hearts - and sometimes not even then.

It seems to me that there will be no views to take in the play of whatever contract you reach - it will either make or it won't, regardless of who is at the helm. Try to construct a hand with which partner will face a guess at any point during the play of any contract, and then get back to me. Still, you can overdo the kind of thinking Justin exhibits here. Only yesterday I had: K106432 3 AJ654 Q and opened 1S in first seat at game all (four-card majors, strong no trump). Partner bid 2C (Acol style, not game-forcing, could be a balanced 11-count with four clubs). RHO (Tony Forrester) doubled. There didn't seem to be much point in bidding diamonds now, so I bid 2S. Partner raised to 3S. I, thinking that diamonds or spades or both might break badly, passed. Partner had: A5 A1042 1082 K982 They led the nine of diamonds (from 9x). Spades were 3-2. I made a shame-faced eleven tricks (yes, I know, but I didn't lose a club), and vowed never again to accept the premise that one should not do the normal thing because of "inferences from the bidding". Most of the time these days, no one has their bidding anyway. Mind you, 1S was a bit silly on the hand Justin gives. How would redouble (followed by penalty doubles from both sides thereafter) have done?

Suit combination repeated for convenience: North (dummy) QJ92 South (declarer) A873 Now that Halo seems to be convinced of the main point at issue, it is time to dot some i's and cross some t's. We have said that an optimal defender should never cover from Kx. This is true if the only relevant question is whether or not declarer will make four tricks in the suit - we do not care whether he makes two tricks or three. But at the table, this is not the only relevant question: declarer has as a secondary goal to minimise undertricks, and the defenders have as a secondary goal to maximise them. Against an East who never covers from Kx, declarer has a pure guess on the second round for four tricks. In that context, he will lead low from dummy and, if the king does not drop, finesse as a safety play to go down only one when East began with K10xx (declarer can no longer make the contract once East does not play the king at trick two). Why not lead the jack from dummy, per the original pin-drop strategy? Because that concedes a second undertrick when West has (as he very well should) refused to win the first round holding K10xx. An optimal East will therefore cover from Kx often enough to prevent declarer playing drop-drop - which is the correct strategy against an East who never covers - but not often enough to enable declarer to switch beneficially to either of the strategies that involve finessing against West's ten on the second round. How often is that? Others here have provided the information - seek, and ye shall find.

It's an example of the General Principle of Restricted Choice: assume that someone did something because he had to, not because he chose to. RHO must cover with K10; he may choose to cover with Kx, but he may not - indeed, he should not (or at least, not often enough to unbalance John Forbes Nash). We adopt the shorthand notation: pin-finesse for this strategy: if the queen is not covered, try to pin the ten; if the queen is covered, finesse against the ten drop-finesse for this strategy: if the queen is not covered, try to drop the king; if the queen is covered, finesse against the ten. drop-drop for this strategy: if the queen is not covered, try to drop the king; if the queen is covered, try to drop the ten. and now be very quiet, for you are about to hear a pin-drop for this strategy: if the queen is not covered, try to pin the ten; if the queen is covered, try to drop the ten. An optimal defender should follow this strategy: never ("What - never?" "Well, hardly ever") cover except with K10 or K. Trust me on this for the moment - I will clarify later, when you can give one cheer more for the hardy captain of the Pinafore. Now, in the relevant cases: pin-finesse succeeds against an East holding of Kxx (three 3-2 breaks) and singleton K (one 4-1 break). drop-finesse succeeds against an East holding of Kx (three 3-2 breaks) and singleton K (one 4-1 break). drop-drop succeeds against an East holding of Kx (three 3-2 breaks) and K10 (one 3-2 break). pin-drop succeeds against an East holding of Kxx (three 3-2 breaks) and K10 (one 3-2 break). Since a 3-2 break is more likely than a 4-1 break, it is clear that drop-drop and pin-drop are better than the other two strategies, and that they are equivalent for present purposes. At the table, you should follow drop-drop because this minimises undertricks against K10xx in either hand, but here we are not concerned with such trivia - we are used to being in grand slams with this trump suit by now. I hope that Halo has been following this, because I can sense this question lurking in the back or even the front of his mind: "if declarer is going to follow X-drop, I can beat him by covering from Kx (or K), so isn't that optimal defence? What does dburn mean by saying that an optimal defender should cover only from K10 or K?" Welcome back to my table, Halo my sub-optimal friend. Was it only last week that you covered from Kx? Did you beat me then? I guess you did. And yesterday - well, I had my suspicions, but I lost a coin-flip. Today, though, you have no chance at all unless you happen to have been dealt K10, because against you I have switched to pin-finesse, so I'm going to beat you now and for evermore when you have Kx. And Kxx too (six of the 3-2 breaks in total) - oh, and singleton king. Though "bother it" you may occasionally say, never - never - use a big big D.