Backgammon

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In the early stages of tournament games, doubling decisions are normally the same as they would be for money. The key differences come in one of two situations: either when one player has a very large lead, for example leading 10-1 in a match to 13, or the match is very close and one or both players are within four points of winning the match.

As an example let's study the position above where Black has opened with a 64, playing 24/14 and White has rolled 55, playing 8/3(2), 6/1(2)*. Black now rolls 63 and stays on the bar. Should White double, should Black accept? It all depends on the match score.

Firstly as a benchmark let's consider the cube action in a money game. This is a well-known position where the correct action is double/take. Now suppose the score is 3-3 in a match to 7. In this instance White should double and Black should drop. Why drop? Because White is offering an optimally efficient double. If he wins a gammon - and a lot of his wins in this position will be gammons - then he will win 4 points - precisely what he needs to win the match. Black does better to decline and play from 3-4 down.

What if White leads 10-1 to 13? Then he should not double but should play on for an undoubled gammon - note that the Jacoby Rule does not apply in tournament play. (The Jacoby Rule states that a gammon cannot be won if the cube is still in the centre). If he does double, Black will accept with alacrity and on the merest excuse redouble to 4. If Black then gets lucky he could win a gammon making the match score 10-8.

How can we prove that these answers are correct? The answer lies in the concept of match equity tables, a topic we shall broach next week.

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