Declarer Play

Combining Your Chances As Declarer (Mark Oettinger)

You are playing at Honors Bridge Club, in New York City. It’s the biggest club in the ACBL, having hosted more than 21,000 tables in 2016. You’ve paid $25 for the privilege of playing a single session against a field that includes a dozen world champions. Of course, for the price, you also get an all-you-can-eat session-long buffet, and occasionally, a pre-game lecture from a luminary like Barry Rigel

It’s first board of the night, and you’re in first seat, sitting South. You’re feeling like you shouldn’t have eaten quite as much as you did...but there’s no time for regrets, as you begin the evening with the following robust collection:

South Deals

Both Vulnerable

Matchpoints

AJT94

Q96

AQ9

With the opponents passing throughout, the auction goes as follows:

S N

1N 2D

2H 3C

3H 4C

4D 4H

4S 4N

5S 6H

Yes, it’s aggressive, but the hands do fit well, and we appear to have all of the Aces (although if so, not the King of hearts). Let’s not dwell on the merits of the contract, however, as this is an article about declarer play.

West leads the King of spades, and here’s what you see:

AJT542

AQ74

AJT94

Q96

AQ9

How do you like your chances? Make your plan before you read on.

At first glance, success appears to turn only on the heart finesse. If it succeeds, you have 6 heart tricks, three club tricks, two outside Aces, and the last trick in spades after you concede a trick to the Queen of spades. 50%. Is there more to the analysis?

Yes, there’s another option. You can finesse the Queen of diamonds at Trick 2, and if it holds, you can pitch the board’s second spade on the Ace of diamonds, thereby making the contract even if the heart finesse subsequently loses. Of course, you will feel pretty sheepish if you lose to the King of diamonds at Trick 2, and lose a spade trick at Trick 3...only to find out that heart finesse would have worked. And if you adopt the diamond finesse line and both the diamond and heart finesses lose, you will be down 2 instead of down 1. A glance at the round clock discloses 10 minutes left in the two-board round, and you haven’t even starting the play of the first hand. You quickly decide that down 1 versus down 2 is unlikely to matter, as the contract is non-standard. You either make it and get a top, or you go down and get a bottom.

Do you take the heart finesse or diamond finesse?

Is it really a guess?

Sort of, but before you embark on the finesse of your choice, you can increase your odds by playing the Ace of the other suit first...in the hope of dropping the stiff King! Clearly, the chance of a stiff King of hearts is far greater than a stiff King of diamonds, so the correct line to to finesse the diamond, AFTER cashing the Ace of hearts.

My reading of the mathematical tables in the Official Encyclopedia of Bridge (the 1984 Edition, but these things don’t change) is that the odds of dropping a particular card singleton when there are 4 cards outstanding is almost 10%. (Frank, are you listening? This is what Letters to the Editor is for). Therefore, the correct line gives you a combined likelihood of success of almost 60%. Sure enough, this was the actual layout:

AJT542

AQ74

KQ 8752

873 K

T765 KJ432

J832 T65

AJT94

Q96

AQ9

Note that if you are fortunate enough to drop the singleton King of hearts, you should abandon the idea of finessing the Queen of diamonds, and simply knock out the outstanding Queen of spades for your 12th trick. The contract is an aggressive one, and few pairs will reach it. Having dropped the stiff King of hearts gives you a guaranteed path to this hard-to-reach slam, and especially if the King of hearts was offside, chancing the diamond finesse risks snatching defeat from the jaws of victory. Take your likely 90+% matchpoint result, and don’t take a 50% chance of turning it into a “zero.”