Fighting chance. by Jos van Kan After a couple of weeks of radio silence another lesson in the series "Thinking Bridge". You are playing a team of four (Imps) match against good opposition and a couple of hands have passed without excitement. Then you get, vulnerable against not, in third seat as S S J932 H AKJ D AJ752 C 3 and after two passes you open a normal 1D. LHO overcalls 2C and partner doubles (negative). 4C says RHO, putting you in a nasty spot. The thing you can't do here is think and pass (well, you have your 10 compulsory seconds, but after that you have to have made up your mind whether you are going to bid or pass), because that puts partner in an impossible position. Since your points appear to be working well, the balance tips in favor of bidding and though you may not make it, you bid 4S. LHO passes, but partner converts to 5D and all pass. LHO leads CK and partner shows: S A65 H QT63 D KQ43 C 72 Yes, that's about what that bidding suggested. Not that this contract is laydown. Superficially there are three losers: a Club and two Spades. LHO continues with CA and you ruff. 1. How can you avoid two S losers if the Spades are 3-3? 2. How can you avoid two S losers if the Spades are 4-2? 3. How can you avoid two S losers if the Spades are 2-4? 1. If S are 3-3 you can avoid a S loser by drawing trumps, that split hopefully no worse than 3-1. After that you cash all your hearts, ending in dummy and lead a small spade to the 9. This works if LHO holds KQx and RHO Txx. Estimate the probability of winning, given that the suit is 3-3. (Hint: how many tripletons can you draw from 6 cards?) 2. If S are 2-4, you must hope that the doubleton contains either the K, Q or both. You draw trumps, strip the Hearts, cash SA and get off lead with a Spade. Since the S suit is blocked defenders either drop KQ in one trick, or are forced to give a ruff sluff. Estimate the probability of winning given that the S suit is didvided 2-4. 3. If S are 4-2, your technical chance is that it is divided KQxx vs Tx, in which case the line in 1 wins. A good practical chance is that the suit is divided KTxx vs Qx or QTxx vs Kx. To defeat the contract RHO holding honor doubleton must *unblock* his honor when you cash SA. If he doesn't, the same ending develops as under 2. If you cash SA early on, you will catch most defenders napping. As an extra this wins you your contract also when RHO holds KT or QT. Given that RHO holds a doubleton, estimate the likelyhood that it is Tx vs that is Kx, Qx, QT or KT. 1. You can draw 20 different 3 card combinations from 6 cards. (For your first card you have 6 possibilities, for your second 5, for your third 4, giving you 6x5x4 = 120 possibilities. However, you could get the same three card in 6 different orders, so you have to divide 120 by 6.) Obviously there are exactly 3 combinations giving you KQx, since there are three different x'es. So your chances of winning are 3/20 or 15%, given that S are 3-3. 2. You can draw 15 doubletons from 6 cards. 8 of those are favorable (Kx (3), Qx (3), KT and QT), hence your chances of winning are 8/15 or 53.3% 3. There are 8 favorable doubletons (Kx, Qx, KT and QT) in which your practical chance must be played for and only 3 unfavorable in which your technical chance will come off. (The remaining 4 possible doubletons don't offer winning possibilities). Who (if any) opponent is most likely to hold a 4c S suit? How are you going to play? If anyone holds a 4-card suit that is RHO most likely, because LHO is marked with the clublength. If C are 5-5, both opponents are equally likely to hold 4c S, but if the overcaller holds a 6 card Clubs, his partner is somewhat morelikely to hold long Spades. Since everything points to playing somone for a doubleton Spades that is what we do, but we play directly toward SA in trick 3, just in case. RHO looks at that card for awhile, but finally plays a small one. Next we draw trumps, everyone contributing two and after LHO throws a club and a spade on the third and fourth round of Hearts, we exit with a Spade. RHO says "I should've unblocked" and gives up. This was the ending: S 65 H -- D Q4 C -- S QT S K H -- H -- D -- D -- C J9 C QT8 S J9 H -- D J7 C -- On the actual layout it was nearly impossible to see for RHO in trick 3 that he must throw his SK or else. Should declarer postpone the play of SA, then it would be much easier for the defenders to read his motives. Without a shadow of a doubt the fact that LHO possesed S Kx and not S Qx was a big help to declarer. Most defenders would have unblocked that SQ from Qx right away, even in trick 3. Copyright (c) 1997 by Jos van Kan. All rights reserved.