Source: Lack King, Jack? Play The Odds By OSWALD JACOBY And ALAN SONTAG
The classic case here is A Q 10 9 6 opposite 8 7 x x. If you want the maximum, finesse the queen. This gives you a 27 percent chance for five tricks and just over an 81.5 percent chance for four.
On the other hand, if you want to be as sure of four tricks as can be, you should play the ace and then lead toward the queen. It only gives you a 12.5 percent chance for five tricks, but it gets you four any time you don’t find K J x or K J x x in back of the ace. This is an 83 percent chance. Not much better than 81.5 percent. but definitely better.
FURTHERMORE, IF YOU do play the queen and it loses to the king, your best play is to lead the ace next. Now, if it turns out that the king was singleton you lose two tricks in the suit while the ace lead would get you all five.
Let’s shift the queen. You hold A 10 9 x x opposite Q 8 x x. If you need all five tricks, you can lead the queen and hope for K x x opposite J or lay down the ace and hope for J x x opposite K. Either play is a 6 percent chance for all the tricks. If you need four you should lay down the ace and lead toward the queen — an 83 percent chance.
THE PRECEDING ASSUMES perfect defense. Against human defenders, you should lead the queen when playing for five. Sometimes an opponent will duck with K x.
If playing for just four and you lead from the ace toward Q 8 x x. there are lots of players who will never play low from K x. Hence, if they do play low, you play the eight. If it loses to the jack, finesse for the king on the way back. This play insures four tricks unless the first player held K x x in which case you would lose to a singleton jack. This play wins 94 percent of the time.