# Playing the Odds

Dlr:
South
Vul
N-S
North
♠ Q J 2
A 3
A 8 4
♣ K J 9 6 2
South
♠ A K 3
K J 9 8 7 2
5
♣ A Q 10
 West North East South 1NT 3♦ 3♥ Pass 3NT Pass 6♥ All Pass

In a teams event, you reach a fair contract of 6. West leads the 9, suggesting that the suit is split 7-2 (West would have led low with three). How will you get to 12 tricks on this deal?

## Solution

Both South players in a team game reached 6 and received the opening lead of the 9. The first declarer was a good, if somewhat unimaginative, player. After winning the first trick with the A, he cashed the A and led a second one. When East threw a diamond, declarer had to concede two trump tricks to West, finishing down one. The other declarer was both more experienced and a student of the odds. After winning the first trick with the A, , he crossed to hand with a spade to the ace and led the J, running it when West followed with a low card.

After playing a low trump to dummy’s ace, declarer came back to hand with the ♣A and cashed the K, claiming 12 tricks after conceding a trump to West’s queen.

What are the odds, given the diamonds are breaking 7-2 and there is no defensive ruff? The first declarer succeeds when trumps are 3-2 (about 58%) and also when East has a singleton 10 or queen, about a 70% chance. The second declarer makes his contract when trumps are 3-2 or when West has four trumps including the queen, about an 83% chance. The full deal:

Dlr:
South
Vul
N-S
North
♠ Q J 2
A 3
A 8 4
♣ K J 9 6 2
West
♠ 10 9 7 5
Q 10 6 5
9 2
♣ 7 4 3
East
♠ 8 6 4
4
K Q J 10 7 6 3
♣ 8 5
South
♠ A K 3
K J 9 8 7 2
5
♣ A Q 10

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