MIT/DL Session Note, May 2 Jun 97 ------------------- Paul Wendt "ISOLATED WORSE" BUT "BETTER, IN CONTEXT" East-West enjoyed several slam opportunities during our 20 May session. --As Walter Lee and I noted on the email discussion list next day. His partnership bid and made three bad slams and missed two better ones that would also be made. The third bad slam is interesting (#11, none vul.): Kx AJ872 AKT64 982 632 AJ QT7 AK2 This represents a type of bad slam that is easy to reach, even with clear "keycard" agreements and no interference: 8-card fit, extra values, rich in Aces and Kings. If West shows 5+ hearts with delayed spade support, East might estimate that slam will be "at least a finesse" opposite two keycards and that the 5-level will be "safe enough" opposite one; hence might bid six hearts via RKC. To me, that debacle seems likely if East opens 1S, or if West passes and responds P-1S-2H in a style where that might be Kx/ AKxxxx/ xx/ xx; unlikely if West opens 1H. But an old-fashioned strong jump shift, 1H-2S (which modernly shows 4+ or 2- hearts, not 3), might cause trouble for a pair "on different wavelengths" about 3C, 3H, and 3S rebids. At my table, the auction began 1H-1S-1N. Responder set hearts, used RKC, and passed 5H. Apparently, he judged that slam would be a good contract, on average, opposite a minimum balanced hand with hAKQxx --and good enough to pay for the occasional 5H, down one. But there *you* are, in a bad slam, with Walter Lee watching as dummy. PLAYING TRUMPS IN CONTEXT The main point of play is that declarer should not play trumps AKT64 982 in isolation, where the best play for four or five tricks is to run the 9 (double finesse); run the 8 if it wins or is covered but first cash an honor if it loses. (__The Encyclopedia of Bridge__ includes a large directory of suit combinations. My old edition includes one combination that is equivalent to this one in isolation, AKT9x:xxx .) On a diamond lead, the "isolated best" double finesse might be wrong because of the fast diamond loser, which places value on avoiding a fast trump loser. The principle is obvious but I have not examined the details here. (Does cashing two high trumps earn enough pitches of two diamonds to pay for that "isolated worse" play in trumps?). On any lead, the "isolated best" double finesse might be wrong because of the need for spade tricks, which places value on drawing trumps in three rounds and on preserving entries to dummy. For example, suppose a club lead. For simplicity, suppose no club ruff is possible and the defense switches to diamonds if in with a trump. After no trump loser, declarer will need three spades with no more than one loser; after one trump loser, declarer will need four spades with no loser. Either way, declarer's chances will depend on the number of side entries that remain in dummy and trumps that remain in hand, since entries and leftover trumps will allow ruffing spades rather than finessing. Ignoring distributional inferences from the lie of trumps, declarer's chances in spades will be: PERCENT PROBABILITY OF SCORING SPADE TRICKS GIVEN SIDE ENTRIES AND LEFTOVER TRUMPS NUMBER OF SPADE TRICKS, NO LOSERS (one loser) 2 3 4 5 --------------------------- no entries or no trumps 100 51 18 18 1 entry & 1 trump 100 55(57) 52(55) 18 2 entries & 2 trumps 100 89(95) 52 18 where numbers in parentheses show those chances that improve given the luxury of one spade loser. ("89" and the parenthetical chances do use the 8-7 spots. Other entries are the finesse/drop chances for Kx:AJxxx .) The first and last columns show that entries and leftover trumps are irrelevant when declarer needs two spade tricks or five. The middle columns show the key to the "perverse" features of this deal. The first entry and leftover trump --compare the first two rows-- are worthless needing three tricks but valuable needing four; the second entry and leftover trump --compare the last two rows-- are valuable needing three tricks and worthless needing four. So much so, that the chances for three and four tricks are nearly identical, given one entry and one leftover trump. (Ruff once, making three tricks if sQ drops stiff, doub, or trip; four tricks is she drops doub or trip; the only differences occur against stiff Queen and righty void.) What is it worth here, to pick up trumps without a loser? To make the slam, declarer will need three spade tricks (with the luxury of one loser) --and so face column two (in parentheses)-- after picking up trumps without a loser and will need four spades (without a loser) --and so face column three-- after one trump loser. Thus the difference between the middle columns of the table represents the bottom-line gain from picking up trumps (ignoring the rare overtrick in this shaky contract). On this deal, picking up trumps without a loser will never burn all three entries or all five trumps (in contrast to AKT9x:xxx). So the relevant portion of the chart is this: NEED: 3 SPADE TRICKS 4 SPADE TRICKS (maybe a loser) (no loser) WHICH PRESUMES: 5 HEART TRICKS 4 HEART TRICKS ---------------------------------- LEFTOVERS FROM HEART PLAYS CHANCE OF GETTING NEED: -------------------------- no entries (or no hearts) -- (DNA) 18% 1 entry & 1 trump 57% 52% 2 entries & 2 trumps 95% 52% So, picking up trumps without a loser is valuable --compare the columns-- only when accomplished with two entries and two trumps leftover (hence needing a 3-2 break and more), not when accomplished with only one entry or one trump. And presuming one trump loser, the key is to avoid burning all three dummy entries. So, what trump play is "best, in context"? Intuitively, there are three strikes against the "isolated best" firstround finesse: it costs one entry at trick one; if it loses, it costs a second entry, on the diamond switch, before you are ready (you wish to cash one trump honor and repeat the finesse only against H:Hxxx only); and you cannot afford to repeat it if righty covers! Why not? Unless righty often covers with QJx(x) (which is dangerous) and rarely covers with honor doub (which is safe), you will not gain enough by picking up both honors onside --a big gain only when righty splits QJx-- to make up for burning all three entries when righty covers with honors split --a big loss that is certain against honor stiff and cheap for righty with Hx. So win the first club in hand and cash the trump ace: "isolated worse" but "better, in context". If righty drops an honor under the ace, cash the king, of course. If lefty drops an honor under the ace, cash the king anyway: another "isolated worse" that is "better, in context". Against a true card, from QJ doub or honor stiff, the secondround finesse is isolated best, better by roughly 2-1 odds ("restricted choice"). But the reward for picking up honor stiff is only a 57% versus 52% chance to make the contract, since only one trump remains after the 4-1 break, whereas the reward for picking up QJ doub is 95% versus 52% (or less than 52 if clubs might be 5=2). The latter is much more attractive even at 2-1 odds against. Against a falsecard from QJx your trump play doesn't matter; you will need 4 spade tricks by aid of one ruff, either way. Against a falsecard from xxxx/ Jx/ KJxxxx/ x , cashing the king saves the contract, so you offer your compliments rather than your congratulations! If both defenders follow low under the ace, cross in clubs and run the 9 (or maybe not, if clubs might be 5=2). This secondround finesse is a play to avoid two trump losers against x:HHxx . It burns two entries when defenders make the diamond switch, but that is no cost at all because you will need four spade tricks and you preserved the one entry that matters at trick one. Intuitively, this line of play combines good plays for four spades and four hearts. The "isolated best" play for five hearts too often leaves four spades unlikely and three uncertain --as do some "isolated second bests" like cashing the ace and finessing if an honor drops left. When defenders do not lead a diamond, this line achieves a 48.5% slam --less if the opening lead is consistent with a black ruff at right (spade void or stiff; club void, stiff, or doub). ----Paul