Equity in Backgammon - Part 3

A computer evaluation of the position will usually appears as follows:

Backgammon wins

Gammon and backgammon wins

Total wins

Total losses

Gammon and backgammon losses

Backgammon losses

The above position would therefore appear as:

2.0% 32.0% 70.0% 30.0% 10.0% 1.0%

You can achieve the same results by adding the numbers on each side:

(2 + 32 + 70) – ( 30 + 10 + 1) = 63

III. Why Equity Matters

There are a number of reasons as to the importance of equity.
One reason for the importance of equity is that it governs cube decisions. In a money game, if you cannot use the cube later on, you should take if your equity is better than –0.50 points, and drop if your equity is worse than –0.50 points. Allowing for the cube, the threshold equity is around –0.55 to –0.56 points. But if you don’t know the equity, you can not determine whether to take the double or pass.

Another reason for the importance of equity is that equity is the way decisions are evaluated. If one checker play gives you equity of +0.25 points and checker play gives you equity of +0.23, then the first play is the better one. The same is true in equity calculations for cube decisions. If your equity before doubling is +0.65 points, and your equity after doubling (allowing for giving up ownership of the cube) is +0.55 points, you have forfeited 0.10 points per game by doubling.

IV. Cubeless vs. Cubeful equity
The example we gave above is an example of cubeless equity. But let’s consider cubeful equity.
Take this position:

Black will win this position by about 70% of the time. It is not quite a double. Black’s equity would be 0.70 – 0.30, or 0.40 points per game if the cube were not in play.

Because of the cube, however, black’s equity is in fact about 0.60 points. Black is more likely to use the cube than White. You can consider the following when examining this position: If black’s winning chances get up to 78%, White will have a tough call whether to take or to pass. He only needs to increase his pure win chances by 8%, to a cubeless equity of 0.56 points, to have a cubeful equity of a full point.

Obviously, your cubeful equity in a position:

a) If the cube is dead for any reason then it equals the cubeless equity.

b) If you own the cube than the cubeless equity will be equal to or greater.

c) If your opponent owns the cube your cubeless equity will be equal to or less than.

d) When you are the favorite in the game your cubeless equity is usually greater than, and when you are the underdog in the game your cubeless equity is less than.



These equity concepts are more of stepping stones that we will use in later articles to absorb important backgammon concepts.

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