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Bridge 10/10

One is better, two is best

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    When you are the declarer, you will sometimes see that there are two chances to make your contract — let's imaginatively call them line A and line B. Most often you will have to choose between them. Then you would usually select the mathematically superior one. But occasionally you can start on line A, and if it does not pan out, you can give line B a try.
    Which applies in this six-spade contract? West leads a club.
    South's immediate use of Blackwood would not please some scientific purists (if that is not an oxymoron), but it has the advantage of simplicity. And with this layout, South did well to insist on making his solid suit trumps, even though he knew of at least a nine-card heart fit. (This will almost always be the right thing to do.)
    There are two chances to make the contract. Line A: the four missing hearts divide 2-2. Line B: the seven missing diamonds split 4-3. Which is mathematically superior?
    A 2-2 break has an a priori probability of 40 percent; a 4-3 break, 62 percent. So, start by adopting line B.
    Win trick one with your club king, take dummy's two top diamonds (discarding a heart from your hand), and ruff a diamond in your hand. Are they 4-3? If not, draw trumps and hope for 2-2 hearts. But when they are 4-3, enter dummy by trumping the club ace — what fun! — and ruff another diamond. Draw trumps, play a heart to dummy's ace, and discard your penultimate heart on the high diamond seven.
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