[cherdanno]

MFA, on Aug 14 2010, 09:57 AM, said:

Cherdanno came to rescue, but I would like to answer your questions anyway.

Actually I think of it as coming to mgoetze's rescue (who is a friend from another world^H^H^Hgame), without having the time to write a full explanation.

[jdeegan]

The ten is better than the queen by 54-46. East has 8 vacant spaces - 4♠ and one trump . West has 6 vacant spaces - 7 ♠ are known. There are two missing cards - K & J of trump. The odds are 52 to 31 that RHO has a trump, but you will guess correctly only half the time - so you win only 26 times while the ten wins 31 times.

Curiously, if you assume that RHO would NEVER preempt with a stiff K of ♠, the odds are the same. Now, LHO has 6 known cards - 4♠ and Kx of trump, or 7 vacant spaces. RHO has the same 6 vacant spaces. Now there is only ONE missing card, the trump J. The odds are the same as before: 54 to 46 in favor of the ten.

If you assume that RHO will TEND not to preempt with the stiff K of trump, it favors playing the Q rather than the ace, BUT the ten is still the right play based on a Baysian-type analysis that imposes fractional vacant spaces on East and West.

Drs. Friedman and Savage (who posited that humans as a group inuitively select the choice with the best odds (from two choices) as long as the true odds are between 90-10 and 10-90) would be gratified with the results of your poll in which real human beings intuitively reject the worst case (trump ace) and favor the slightly better choice of the ten by 2 to 1. By comparison with their research, your problem is complex with three choices and unstated conditional probabilities (the stiff K issue).

James F. Deegan, Ph.D. Econometrician