By the Percentages (by Brad Carmichael)

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BY THE PERCENTAGES

By Brad Carmichael

Sometimes in this game it can be quite difficult to successfully analyze minor details, particularly given the time constraints. Consider this hand from the regional knockouts:

S: xxxx   H: A9   D: Axx   C: AKQx

You open 1NT, partner raises to 3NT. LHO leads the 6 of hearts, and you see the following:

                                                            S: Kxx

                                                            H: QT

                                                            D: KJxx

                                                            C: JTxx

The first decision is what to play from dummy. All in all, it is mostly a pure guess, given that LHO is likely just leading their best suit, or longest major against this kind of auction. All things being equal, an expert IMP player is more likely to lead aggressively from a king than a jack, so you try the queen and it holds.

Time to take inventory. You have now 2 hearts, 2 diamonds and 4 club tricks. Obviously if the spade king or diamond queen is onside or diamonds are 3-3, there is a play for a ninth trick. What is the best way to maximize these chances?

The simple play is to lead a spade to the king. If it fails, undoubtedly another heart will be played, dislodging your last stopper. In that case, you must fall back on the diamond finesse. This will give you roughly a 75% chance of success – not bad. But is there a better way?

You could focus solely on the diamond suit and try to make 3 tricks there. In this situation, the best way to play this combination to make 3 tricks is to play low to the king and low to the ace, followed by leading to the Jack. This will pick up all 3-3 splits, all 4-2 splits when the queen is with LHO, and 4-2 splits where RHO holds Qx. 5-1 and 6-0 splits will reveal themselves in time for a fall back play of a spade to the king. This play will only fail when diamonds are specifically 4-2 with the queen on your right. The odds of a 4-2 break are 49%, so 24.5% specifically 4-2 on your right.  On these 24.5%, 2/3 of the time the queen will be with length, so the odds of failure are about 16% for this line. When the freak 5-1s and 6-0s are offside coupled with the spade king offside, the failure percentage gets to a little over 20%, so a success rate of about 78%.

I actually took this line and I would like to say that it worked, but diamonds were QTxx with RHO and the spade ace was onside. Oh well, sometimes it happens, but maximizing your chances for success on all hands will make you a more successful player in the long run.

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