Voltaire said, “Chance is a word void of sense; nothing can exist without a cause.”

That is a tad melodramatic. One can often calculate the chance that a contract will make, but it does sometimes need an “approximately” attached. For example, a six-spade contract that seems to rely totally on the trump finesse is not exactly 50 percent, because an opponent might be able to get a trick-one ruff. But the chance of that will be very low.

In today’s deal, what is the chance that six spades will make? How should declarer plan the play after West leads the club queen?

In the auction, after North raises spades, South shouldn’t use Blackwood, because when North shows one ace, South will not know if it is the valuable diamond ace or the less useful heart ace. Instead, South should continue with four clubs, a control-bid showing a first-round control (ace or void) in that suit. Here, North control-bids four hearts, denying the diamond ace and showing the heart ace. South ends the auction with a plunge into six spades.

South has three possible losers: two diamonds and one club. The club six will disappear on dummy’s heart ace, but to hold the diamond losers to one, declarer must find East with the diamond ace – a 50-50 chance.

After winning with his club ace, South plays a trump to dummy, pitches his low club on the heart ace, then leads a diamond to his king. When it wins, declarer returns to dummy with a trump, and plays another diamond through East to get home.