Playing the Odds

From Wednesday (31/08/2016). Board 21 produced a straightforward lesson in declarer play. None of the declarers managed to make 4S though, so the lesson bears repeating.

Board 21 Dealer N NS Vul

K65
J96
Q632
T52
92
A73
95
AK9764
AJT873
KQ42
J7
3
Q4
T85
AKT84
QJ8

The bidding might have taken different turns, so I won't talk about that too much, suffice to say that East should open 1S, South might overcall 2D and then East might end up in 4S. After South leads off the two top diamonds and switches to a heart, the play should be automatic for any declarer who knows the odds: for ONE of the defenders to have both of two missing honour cards, the odds are 25% (half of 50% for each of the missing cards).

After losing two diamonds, the only suit that matters is trumps. How best to avoid TWO losers, to the king and queen? Playing off the ace and another will surely leave a trick for the king and queen separately. Declarer must do better than that, and there is a straightforward FINESSE position. Declarer should win the heart in dummy and lead the nine of trumps. If North plays low, declarer should finesse and let the nine run, quite expecting to lose to South. It does just that, but when South leads another heart, declarer wins with the queen in hand and, intent on pursuing the finesse option, leads the three of clubs to dummy. In case the hearts don't break, declarer then cashes the second top club, discarding a heart from hand. Being in dummy, declarer can now take a second trump finesse, leading the two to the ten.

Playing this way, declarer has increased the chances considerably. As a rough guide, in most cases, taking two finesses missing the king and queen will lose you only ONE trick, whereas playing the ace will ONLY succeed in losing only one trick if either opponent has the singleton king or queen or KQ doubleton.

P.S. While cashing a second club may add a slight risk in case a defender is able to ruff the second club, it is a sensible and necessary play because you should not rely on the hearts to fall 3-3 or for the defender with four of them to toss one on the run of the trumps. All good declarers work on the odds and minimising risks, and adding to their chances by carefully thought-out play.