Puzzle 8Q69 Main

Best Contract

by Richard Pavlicek

My cat recently signed a contract for a rent increase, but now she refuses to pay!

She purrs it’s the “best contract” she ever had, as I have no legal right to collect because it was signed “Mabel” and not “Mabel Jr.” When I told her I saw her sign it, she purr-purred that away by offering to settle it in court… I can say whatever I want, but she’ll just claim my vision has deteriorated.

No problem, kitto! I reminded her there’s more than one way to skin a cat, and she forked over the rent.

Meanwhile, back to bridge. Choosing the best contract on a bridge deal is straightforward: Determine the number of tricks won by each plausible contract with logical play (not double-dummy) then choose the one producing the highest score.

Looking at only two hands, however, this is more difficult. You don’t know the location of the missing high cards, or the distribution of the unseen hands. Therefore, determining the best contract must be done by probability, or the average expected score if the situation were to occur many times. Further, if duplicate, you may need to consider what might happen at the other table or tables.

This will be your task on the following six problems. You are shown the West and East hands, the form of scoring, and the vulnerability. Assume all players* are experts. Contracts must be at the two level or higher and not doubled or redoubled. West or East must be declarer (you do not need to stipulate which) lest any wiseguys claim the best contract for East-West is 7 NT by North down about nine.

*including those at the other table if IMPs or board-a-match, and all tables if matchpoints.

North and South will pass throughout. For the sake of analysis, the beginning of each auction is shown to clarify the opportunities North and South had to bid, as their silence may affect the chance of a contract’s success.

Problem 1

IMPs, None vul, North deals

4 3
A 8 7 6 5
Q 8 4
A Q 7 Table A 2
Q J 10 9
A K J 3
K 8 2

West North East South

… Pass ? Pass

Best contract

Problem 2

Cavendish*, N-S vul, East deals

*same as Chicago (four-deal bridge) except dealer is nonvulnerable on Deals 2 and 3

A K Q
A 6 4 2
A K 5 3
A 9 Table J 6 2
K
7 6 2
8 7 6 5 4 2

West North East South

?
Pass ?
… Pass

Best contract

Problem 3

Matchpoints, E-W vul, South deals

J 6
A Q 10 9 7 5
A 2
7 5 3 Table 5 3 2
K J 8
7 6 4 3
A K 2

West North East South

?
Pass
… Pass

Best contract

Puzzle 8Q69 Main Top Best Contract

Problem 4

Board-a-match, Both vul, West deals

Q J 5 4
A K J 10
A K 2
Q J Table A K 9 3 2
Q 4
3
A 10 9 8 3

West North East South
?
… Pass ? Pass

Best contract

Problem 5

Chicago, None vul, North deals

K Q 4
—
A K Q J 10
9 8 6 5 3 Table A 2
7 6 4 3 2
7 3 2
A 7 2

West North East South

… Pass ? Pass

Best contract

Problem 6

Matchpoints, N-S vul, East deals

Q J 9 7
K Q 3
Q J 10
A 8 2 Table A 10 8 6
4 2
A 9 3
K 9 4 3

West North East South

?
Pass ?
… Pass

Best contract

Puzzle 8Q69 Main Top Best Contract

Enter the contest

Join the fun and participate! You won’t win anything, other than the satisfaction of making my Winners List if you’re clever, or just lucky. Contest ends December 31, 2024 (midnight GMT). Winners and solutions will be published January 2, 2025.

To enter, provide your name, location and e-mail address, then click Submit. A copy of your entry will be sent to you automatically, so be sure your address is correct. Multiple entries by the same person are allowed, but only the latest one counts.

First name Last name

E-mail address

Puzzle 8Q69 Main Top Best Contract