To double or not ?

The Jacoby Rule which is named after the backgammon and bridge master Oswald Jacoby states that you cannot win a gammon unless the doubling cube has been offered and accepted during the course of a game. This rule was designed to speed up the pace of games by stopping players who gain an overwhelming early advantage from playing on for a gammon and forcing them to cash a point.

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The Jacoby Rule is nearly always applied in money games It is never used in tournament matches. However, once the cube has been turned it is a different matter altogether. Then the holder of the cube may suddenly turn the game round and develop an advantage that will be big enough to be able to redouble his opponent out.

Can he get too good to redouble? By this we mean will he do better to play on for a gammon rather than cash his sure two points? The mathematics involved are straightforward.

  • By playing on for the gammon he is trying to gain an extra 2 points.
  • If he plays on and loses he will lose the two points he would have won by redoubling his opponent out and he loses a further two points because he loses the game. In other words he will lose 4 points.
  • Therefore he is risking 2 points to gain 4. Simply put if he wins at least twice as many gammons as he loses games then it is correct to play on for the gammon.

The difficult part of course is estimating how many gammons and losses might arrive from a particular position. This week’s position is a case in point. White is stuck on the bar against a four-point board and is a whopping 74 pips behind before the roll. When he loses he will lose a lot of gammons because of all those checkers located in black’s home board.

On the other hand if he does hit a shot his own home board is strong and may enable him to win quickly. The key is how often will hit that shot? It turns out that he will win the game about 20% of the time which is not nearly enough to take a redouble because of all his gammon losses.

When black wins he wins a gammon more than half the time and so it is correct to play on for the gammon at this stage. Remember every roll will make for a new doubling decision and you should re-evaluate the position again next turn.

Estimating these gammon/loss chances is difficult when playing and you can only succeed at this by playing a lot and developing your library of reference positions.

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In the game from which this position was taken black redoubled (which was a small error) but white took (which was a major mistake !). But as we all know sometimes in backgammon you get rewarded for your mistakes.