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bridge probability question (OT)

Posted By: Chuck Bower
Date: Thursday, 15 December 2011, at 7:06 p.m.

OK, this is long. You can skip the preliminaries if you like:

Intro: My newspaper has a daily bridge column by a national columnist, Phillip Alder. Recognizing the audience, his columns tend to be for the intermediate players. ~75% are declarer (offensive) play and the rest defensive. He usually makes a comment about the OtB bidding.

Bridge background: Of course there are many considerations for making a play at the bridge table: were there clues from the auction (bidding)? Were there clues from the cards already played? What do I know about my opponents and what kind of plays/misplays are they capable of? Etc.

Premise: I'm putting forth a specific sentence from today's column for discussion. It's fine if someone wants to discuss the other inputs but my probability question is just that -- a probability question sans other factors.

Declarer has 7 spades and 2 in each of the other suits.

(spades): KQJTxxx

(hearts): xx

(diamonds): Kx

(clubs): xx

He must win 10 tricks and can count exactly 9 winners outside of Diamonds. (BTW, for the curious who understand the game, declarer was dealer and opened 3 Spades. LH opp passed and partner raised to 4 Spades. All passed from there.) LH opp leads the Heart 4. Dummy (declarers partner's now exposed hand) contains three hearts to the J. RH opp wins with K and cashes A (his partner plays the deuce). RH opp then leads the diamond 2. Dummy has Jxx of diamonds. Declarer will either make his contract or go down (unless of course the opps completely fall asleep) with his play to this trick.

(Finally) the probability question: Author Alder begins his analysis with the statement: "The odds slightly favor two aces being split between the defenders, not both in the same hand." Is this statement correct/accurate for the situation at hand? If not, explain why, optionally correcting the statement so that it is both accurate and relevant (if possible). If his statement is correct, is there a better way to say it -- i.e. was his justification misleading?

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