Odd Odds

		North
		-
		109xx
West		xx		East
KQxx		KJ10xxxx		AJxxx
Jxx				xx
Qxxxxx		South		J10x
-		10xxx		Qxx
		AKQx
		AK
		A9x

Against 6 West led the K, which declarer (a good friend of mine) ruffed before falling into a meditation. The spade losers could not all be ruffed in dummy without losing control in the end, so dummy's clubs would have to be used for discards. There was no problem if hearts and clubs both split favorably, but what about a 4-1 trump break? If either opponent held H Jxxx, the defense could always score a heart trick and multiple spade tricks if the AK were cashed.

The odds of a 4-1 break? About 25%, which is not peanuts to a vulnerable slam at rubber bridge. Declarer therefore led a heart to the king and continued with a LOW heart to the 10. If the hearts were 4-1, the opponents could win this, of course, but a spade continuation could be handled by dummy and there was a strong probability (over 80%) the clubs could then be run.

If instead the hearts were 3-2 and someone won the HJ, the contract was only in danger if the jack was doubleton and a club ruff was found by the defense, OR if the Qxx was offside (since declarer's play in clubs would always be to cash the ace first). But the odds of a 3-0 club break? About 20%, and even then the club tripleton would have to be in the wrong hand to set the contract. So make it about 10%.

A strange thing happened, though, when declarer led a heart to the 10. It held the trick! West had ducked, hoping his partner started life with Ax and could give him a club ruff. This left declarer in control. Leaving the J outstanding, he next led a club to the 9. Since West was marked with the J after East failed to cover the T, this play catered to all possible club distributions. West could win the queen or ruff, but declarer could then win any return, draw the last trump if necessary, and run six club tricks.

In practice West ruffed and declarer claimed his entertaining +1430.