Percentage play in Bermuda Bowl (Quarter finals round 4, board 25)
(Page of 3)

West
K74
83
9874
AQ94
North
Q108
KJ742
J32
J7
East
AJ92
A5
AK106
1032
South
653
Q1096
Q5
K865
W
N
E
S
P
1NT
P
3
P
3
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

On the BB VuGraph, six declarers played 3NT on this hand on a Heart lead. Each one chose a different line:

Katz finesses the 9 immediately [Edit: Turns out Katz played the A first. I'll leave this line just for the discussion, and note that in fact the line was identical to Wooldridge's].

Wooldridge played the A, then finessed the 9

Sun started by running the T

Bessis finessed the Q, then played K, K, and finessed the J.

Justin Hackett started with A, then played K, and finessed the J.

Mazurkiewi started with K and finessed the J

Which is the correct line?

[Edit: Ralph Katz made a great point that when your line loses, the 9 line is often a trick or more ahead of the Spades line. Therefore, on a IMP expectation basis, there is a strong case for the 9 line. The following analysis only refers to the chances of making the contract.]

West
K74
83
9874
AQ94
North
Q108
KJ742
J32
J7
East
AJ92
A5
AK106
1032
South
653
Q1096
Q5
K865
W
N
E
S
P
1NT
P
3
P
3
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

Declarer has six top tricks, and needs to establish three more tricks, either from Clubs, or combination of two or more suits. It is very hard to calculate the percentage play at the table. However, there are two principles that are almost always correct to follow:

1. If you are giving up a finesse in a suit, cash its top honors before finessing the other suit(s).

2. Out of two or more suits with some extra tricks potential through finesses, choose the finesse that is most likely to influence the way you play the other suits.

A quick analysis would suggest:

A. The diamond suit can't be the best one to take a deep finesse: It is as likely to produce 2 extra tricks as Clubs, but can't produce three extra tricks. It it slightly less likely to produce two extra tricks than Spades, but offers much higher chance to fail immediately. Therefore, we can give up finessing that suit, and should therefore cash its top honor(s).

B. If we play Spades we have ~25% of getting four tricks, thereby informing our play of the Club suit (finesse to the Q rather than the T). Clubs are much less likely to inform our play in Spades (only if there is KJ onside, with only one more card at most, we can avoid the Spade finesse). Therefore, Spades should be played before Clubs.

This suggests that Justin Hacket's line is the best, which seems to be correct.

The next page contains a detailed analysis.

West
K74
83
9874
AQ94
North
Q108
KJ742
J32
J7
East
AJ92
A5
AK106
1032
South
653
Q1096
Q5
K865
W
N
E
S
P
1NT
P
3
P
3
P
3NT
P
P
P
D
3NT East
NS: 0 EW: 0

What are the chances to play Spades for 4 tricks? You will need either Spades 3-3 with Q onside (36% * 50% = 18%), or Spades 4-2 with Tx offside or QT onside (24% * 5/15 = 8%), for a total of 26%. There is also 25% chance of making three tricks in the suit but not four.

What are the chances of playing Clubs for 4 tricks? You will need KJ onside, with either 3-3 distribution (36% * 3/6 * 2/5) or the KJ doubleton (24% * 2/6 * 1/5) = ~9%. There is also ~15% of making three tricks in the suit but not four. You can also play for 2 tricks in the suit for 50% chance, but you need to decide in advance whether you play the suit for 2 tricks or more.

What about the Diamonds? A double finesse will produce 4 tricks in 24% of cases. Playing the honors from the top will make four tricks whenever QJ drop doubleton (68% * 2/5 * 1/4) = 7%. If an honor drops on your left and you decide to finesse it's hard to calculate the odds, since they depend on your LHO falsecarding with QJx. Even though LHO risks blowing a trick if declarer has AKxxx, it is not a real risk since he probably knows Hearts are running. For simplification, let's assume declarer plays the other top honor in any case.

Let's rank the plays that declarers have chosen:

Katz's line is superior to Sun's line, since it also wins in case of KJ doubleton. It wins whenever Clubs produce 4 tricks (9%), and in case Clubs produce three tricks, if QJ drop (7%) or the Spade finesse is on (50%), for a total of (9% +15% * (7% + 93% * 50%)) = 17%.

Wooldridge's line is superior to both, since if he finds QJ, he can play AK, and if the Q doesn't drop, finesse the Q. 7% * 58% + 93% * ( 9% + 15%*50%) = 19.5%.

Bessis tried to combine the chances, but did so in the wrong order. Finessing the Q removes the option of playing the suit for 3 or 4 tricks, which is needed almost half of the times when the contract is makeable. In addition, he might not need this finesse at all, if QJ and the Q drop. Bessis' line is therefore the most inferior line - he had 50% of winning the Club finesse, and then needed the Spade finesse (50%), and either QJ dropping (7%) or the Spades producing 4 tricks (50%). 50% * 50% * (7% + 93%*50%) = 13.5%.

Only Hackett and Mazurkiewi pursued the correct suit, with Hackett's line dominating thanks to the extra chance of QJ. Depending on how Diamonds and Spades behave, they would know how to play the Clubs. Hackett's had the highest odds to make: 7% * 58% + 93% * (26% * 50% + 25% * 24%) = 22%.