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A word about probabilities

The subject of probabilities in bridge poses a mental hurdle for many players. Like it or not, though, bridge is essentially a game of percentages, which gives those who familiarize themselves with basic probabilities a decided edge over those who don’t.

Take this case where you get to three notrump and West leads a spade. To make the contract, you must score at least four diamond tricks, so you take the first spade in your hand in order to preserve the ace as a later entry to dummy. If you now cash the A-Q of diamonds and lead a spade to the ace, in effect hoping to score all five diamond tricks, you eventually go down one.

This is unlucky — but by no means surprising — because the probability of finding a diamond division that will allow you to score four tricks on this approach is only about 54 percent. This includes the 36 percent chance of a 3-3 division in the suit, plus an additional 18 percent if either defender has the singleton or doubleton jack.

But if instead you start by cashing the ace of diamonds and then overtake the queen with the king (planning to concede a diamond on the third round of the suit), your chances of making the contract rise to nearly 70 percent.

This is because you retain not only the 36 percent chance of succeeding against a 3-3 break, but also because you make four tricks in the suit whenever either opponent was dealt the J-x, the singleton jack or the 9-x — which will happen about 33 percent of the time.

In the actual case, after East’s nine falls on the king, you next play dummy’s ten to force out the jack. This establishes dummy’s 8-6, and you finish with nine tricks.

It is true that if East had the doubleton jack of diamonds, or if the suit proved to be divided 3-3, the recommended method of play would cost you a trick. However, you should be happy to risk a 30-point loss for the sake of elevating your chance to make the contract from slightly better than 50-50 to one that makes you more than a 2-to-1 favorite.

Bridge club results

The Northampton Bridge Club welcomes anyone who wishes to play duplicate bridge. Open pairs game: 7 p.m. every Tuesday at the Clarion Hotel and Conference Center, 1 Atwood Drive, Northampton. The club manager is available at 253-3508 to assist players in need of partners. The club’s website is www.northamptonbridgeclub.com.

There were 11 tables in play Feb. 12.

Overall winners: Paul Bacon-Philippe Galaski-John Sedgwick-James Hastings, 61.00; Roger Webb-Leo Sartori-Sonja Smith-David Rock, 54.00; Evie Glickman-Roger Miller-Edward Hougen-Arthur Franz, 51.00; H.Dan Williams-Michael Ramella-Israel Koren-Alan Peterfreund, 43.00; Strata B: H. Dan Williams-Michael Ramella-Israel Koren-Alan Peterfreund, 43.00

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