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Bridge 5/1
What are the odds against an ace?
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    What is the chance that you will get a hole in one — an ace — on a golf course? What is the chance that your bridge hand will contain at least one ace?
    When you take a trick with an ace can be critical to a contract's outcome. This is an example.
    You are South, the declarer in three no-trump. West leads a fourth-highest heart four, and East puts up the queen. What would be your plan?
    Remember that South's rebid of two no-trump is theoretically forcing. Responder may pass only if he "miscounted" his points on the first round, bidding with fewer than six high-card points.
    You have seven top tricks: four spades, one heart, one diamond and one club. There are three more tricks available in diamonds (four if the finesse wins). However, there is a danger that if the diamond finesse loses, the opponents might cash too many heart tricks.
    If you win the first heart trick, you go down, losing four hearts and one diamond.
    If you win the second heart trick, you make the contract. When the diamond finesse loses, if East has a heart left, that suit must be splitting 4-3.
    If you duck the first two tricks, you put your contract in jeopardy with this layout. West, with no entry, might shift to the club 10. Now your contract goes down two (if you cash out) or down four (if you take the diamond finesse).
    Your chance for a hole in one is about 1 in 31,000. The chance that your hand will contain at least one ace is approximately 7 in 10.
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