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Playing the Percentages
It's not always possible, in the middle of the play of the hand, to calculate the precise percentages of alternative lines of play, and sometimes intuition is required to make the right choice. Check out your own intuition in the following examples.
Related Play Problems Play Problem 6
Related Extracts from Past Wednesday Games
In the play of 2♠, South makes 8 or 9 tricks, depending on her ability to guess the Q♦. The Q♣ is the most likely lead, covered by the King and the Ace. Say that East shifts to the K♠, in an attempt to stop the Club ruff on the board (he doesn't know that the ruff is no longer needed, thanks to Declarer's Club spots) ... then a Spade to Ace, and a third Spade ... then the Heart finesse, lose a Club, win the Heart return, ruff a Heart (West showing out), cash a Club. At this point, Clubs could be 4-4 or 5-3 either way, which means that West started with 3 or 4 or 5 of the missing 6 Diamonds. That should be enough to play West for the Q♦, which turns out to be the winner.
Suppose that South leads a fourth-best Spade. Now, East will show us whether he’s a Mouse or a Pig: - If East is a Mouse he’ll settle for a safe 11 tricks … he’ll play a low Spade from Dummy, winning the Ace … then he runs the Q♥, even if it loses it will be into the hand which cannot attack Spades profitably … but the Queen is covered by the King and Ace, and Declarer has his 11 tricks (he cannot risk the finesse against the T♥ because if it loses and a Club is returned his communications will be ruined and he’ll end up with only 10 tricks). - If East is a Pig, he’ll play the Q♠ at Trick One … if this loses to the King, it’ll be 9 or 11 depending on whether the Heart finesse works. However, the Q♠ holds the trick, Declarer crosses to the A♦, then the Q♥ is covered by the King and Ace. Declarer is up to 12 tricks already, and runs the Diamonds and cashes the A♠, in the process squeezing North in Hearts and Clubs. 13 tricks, no less! Oink, oink!
Actually, the odds clearly favor being greedy on this one. The safe line (low Spade from the board at Trick One) renders exactly 11 tricks pretty much all the time, whereas the greedy line gives the following (ignoring the surprising additional squeeze trick): 25% of the time (both major Kings with North) it’s 9 tricks 25% of the time (K♠ with North, K♥ with South) it’s 11 tricks 50% of the time (K♠ with South, K♥ anywhere) it’s 12 tricks.
Against 4♠, South can bring the proceedings to a swift close by cashing the A♣ and continuing the suit, at which point a disgruntled Declarer will claim 11 tricks. But that’s an unlikely defense, perhaps a Heart opening lead would be more likely (not that this lead looks like such a great bargain either, by the way). Anyway, a Heart is led, trumps are drawn, and the Hearts are cashed (Declarer is looking for distributional clues before he tackles the crucial Diamond suit). Now the KQ♦ are cashed, both defenders following, and it’s decision time! Here are Declarer’s choices: - Lead a Diamond to the Ace, scoring 11 tricks if the Diamonds are not 3-3, and 12 when they are. - Finesse the T♦, scoring 10 or 12 tricks.
It might seem that “11 or 12” is better than “10 or 12”, and if the relative odds were even money then of course it would be. But there’s no even money here, North showed up with all four trumps, and also followed to all 3 Hearts. As the trumps were being drawn, South had some pitches to make, probably 3 Hearts and a Club. If that was the case, North will be known to have started with 8 major cards, and South with just 5. We’d say that makes South a clear favorite to hold both remaining Diamonds. Making 6 if Declarer trusts his judgment, for a positively gruntled +480.
Against 3NT, East does not have an attractive lead, and may well start out with a top-of-nothing Club. Declarer has three ways to play this hand: - Line 1: Declarer wins the A♣, takes the Spade finesse, cashes the A♠ dropping West’s King, and now (thanks to the onside A♦) crosses to Dummy to enjoy the Spades, racking up an astonishing 11 tricks! Of course, if East has the K♠ and at least two others he will duck that first Spade, in order to lock out Dummy’s Spades. Any Declarers who found that line of play will get a top board, but we’d suggest that they don’t brag about it too much, as that line of play is inferior in the extreme. We calculate that it brings in 11 tricks no more than 4% of the time, 10 tricks another 4% of the time (when East has doubleton King so cannot duck the first Spade) and the other 92% of the time it will result in defeat. Not very good odds! - Line 2: Win the Club lead in hand, cash A♠, then overtake the J♠ with the Queen. This line makes 10 tricks whenever Spades are 3-3 (36% of the time) or when East has doubleton King (another 8%). Even if Spades are 4-2, then the contract still has chances given some luck in the red suits. - Line 3: Win the Club lead in hand, cash A♠, then play the J♠ and low from Dummy (the defense should duck this if they can). Now, if the A♦ is with East, the Spades can be established and enjoyed. That will be 10 tricks 50% of the time, and there is the additional chance of a doubleton K♠ in either hand which takes the chances for 10 tricks up to 58%. And there are additional red suit chances if the Spades don’t come in. Yes, Line 3 looks like the winner, but Line 2 is certainly a vast improvement on that all-or-nothing Line 1.
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