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some clarifications

Posted By: Steve Mellen
Date: Friday, 16 December 2011, at 2:46 p.m.

In Response To: some clarifications (Chuck Bower)

You said this is a probability question and not a bridge question, so I assume this isn't about whether we can infer the location of the ace from the opening lead or anything like that.

I think Casper had a point that deserves further deliberation. Alder's logic seems to be: "there is a 52% chance aces will be split rather than together; RH has already shown up with an ace; so LH is a slight favorite to hold the remaining ace."

As Casper points out, one could equally well reason, "there is a 52% chance the ace of diamonds and 4 of hearts will be split rather than together; LF has already shown up with the 4H; so RH is a slight favorite to hold the remaining ace."

To look at it another way, after the first trick LH and RH each have the same number of cards (of course) and yet by Alder's logic LH is a slight favorite to hold each and every one of the missing cards.

Alder's statement is still quite right as an a priori statement of probabilities. If you were charting out a course of play with two aces missing, you would be correct to assume they are split if no other clues are available. But if Casper's argument is correct, you can't simply jump from "the aces are probably split" to "the guy who didn't play the first ace probably has the second one" because you're no longer looking at it from an a priori perspective.

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