Take a look at the backgammon position below:
The Jacoby Rule states that you cannot win a gammon unless the doubling cube has been offered and accepted during the course of a game. This excellent rule, originated by the great bridge and backgammon master Oswald Jacoby, was designed to speed up the game. It stops players who gain an overwhelming early advantage from playing on for a gammon and it forces them to cash a point (unless of course the opponent erroneously takes – it happens!).
The Jacoby Rule is nearly universally played in money games. It is never played 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 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 arithmetic is simple:
• By playing on for the gammon he seeks 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 loses 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.
Of course the difficult bit 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 staggering 74 pips behind before the roll. When he loses he will lose a lot of gammons because of all those checkers 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 wins the game about 20% of the time which of course is not anywhere near 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 least for this turn. Remember every roll is a new doubling decision and he should re-evaluate the position again next turn.
Estimating these gammon/loss chances is difficult over the board and can only be done through experience when you have built a library of reference positions.
In the game from which this position was taken black redoubled (small error) but white took (mega-blunder!). Sometimes in backgammon you get rewarded for your mistakes.