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

                                                     Play Problem 36

                                                     Play Problem 161

 

 

Related Extracts from Past Wednesday Games

 

 

21	♠ 973 ♥ AQ63 ♦ AJT3 ♣ K5	From 5th July, 2006
♠ A84 ♥ K4 ♦ Q976 ♣ QJ76	North West             East           South	♠ K2 ♥ JT875 ♦ 84 ♣ A432	Dlr     North   Vul     N-S
© BES, Inc All Rights Reserved	♠ QJT65 ♥ 92 ♦ K52 ♣ T98	West    North   East     South              1♦        Pass     1♠  Pass    1NT     Pass     2♠  Pass    Pass     Pass

 

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.

 

 

3	♠ JT84 ♥ T42 ♦ 93 ♣ KQ32	From 20th December, 2006
♠ Q93 ♥ AJ86 ♦ J7 ♣ JT76	North West             East           South	♠ A6 ♥ Q9 ♦ AKQT842 ♣ A9	Dlr     South Vul     E-W
© BES, Inc  All Rights Reserved	♠ K752 ♥ K753 ♦ 65 ♣ 854	South   West    North   East  Pass    Pass    Pass    1♦ Pass    1♥        Pass    3NT Pass    Pass    Pass

 

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.

 

 

32	♠ 8643 ♥ 8764 ♦ 53 ♣ K75	From 31st January, 2007
♠ AQJ9 ♥ 2 ♦ AT86 ♣ Q963	North West             East           South	♠ KT752 ♥ AKQ ♦ KQ4 ♣ 82	Dlr     West Vul     E-W
© BES, Inc  All Rights Reserved	♠ ♥ JT953 ♦ J972 ♣ AJT4	West    North   East     South 1♦        Pass    1♠        Pass 2♠        Pass    2NT     Pass 4♥        Pass    4♠    All Pass

 

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.

 

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