Model Backgammon and the Jacoby Rule

by Douglas Zare
15 May 2012

Douglas Zare

Since backgammon bots play quite well, it is easy to assume that the theory of backgammon is almost complete. In fact, there are many fundamental questions which are still not settled. While the bots help, they are often not the most convenient tool.

In a recent discussion Rick Janowski and I had, we realized that we don't know what the gammon price should be with the Jacoby rule (that gammons don't count on a 1-cube). The gammon price in cubeless backgammon would be 0.5, meaning that promoting a normal win to a gammon is 0.5 times as valuable as changing a loss to a win. Because wins give you more ability to use the doubling cube, the cubeful gammon price is lower than 0.5. With perfect doubling efficiency, the gammon price would be 0.4. In real backgammon, it seems that the gammon price is somewhere between the two, about 0.43. However, Rick Janowski suggested that it should be lower with the Jacoby rule.

The take point, double point, and gammon price all follow the pattern that the value in real backgammon falls somewhere between the values with perfect cube efficiency and the values with no future cube use possible. This would suggest that the gammon price on a centered cube with the Jacoby rule would be between 0.4 and 0. If the cube were nailed to the center of the board with the Jacoby rule, then gammons wouldn't matter. However, is it plausible that the value of gammons is so low with a centered cube?

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