Two reactions then an answer:
1) the context of the entire hand is always important - so is the bidding.
2) the "x's" matter - holding 9's or 8's have an impact on the odds.
Try
http://www.rpbridge....cgi-bin/xcc1.pl
Richard's site is highly manual but helps anyone visualize the reasons why a given line of play is best.
Taking three strategies:
- Play AK:------------------53.13% - catches 2-2(40.7%) and q-xxx (12.44%)
- Play A then finesse: 51.43% (loses to qxxx-void (4.78) but gains xxx-Q (6.22%)).
- Finesse:------------------45.22% (50%? - only if West does not cover from Q987). Since we assume they hold 9 and 8, the Q987 - void case loses one trick that you were never going to win).
The fourth strategy (Play A then lead small toward KJxxx) allows for the case where LHO plays xx. Now going up with the K is better (original probability Qxx-x 18.65% and xx-xQ as 20.35%). Notice that 20.35%/(18.65+20.35) = 52.17% - exactly what vacant spaces would predict (after LHO plays the second x, the odds are 12/23 that the Q is with RHO. You know 2 of LHO's cards leaving 11 spaces - and 1 of RHO's cards leaving 12 spaces. 12/23 = 0.5217).