What is Equity?
In backgammon, equity is the point value of a game at a given position. A positive equity means you are ahead in the game while a negative equity means you are behind. The value is computed based on the summation of your winning, gammon, and backgammon probabilities minus the same probabilities for your opponent. In match play, the match score is also a major factor.
In the old days before respectable computer programs existed, circa 1970 to 1980, equity was important for position “settlements” at the very end of a game rather then having “pure luck” from 1 or 2 dice rolls determine the payoff. Today, computer programs such as Snowie or eXtreme Gammon can determine equities to three decimal places and beyond.
So, when you look at an equity table generated by the Bots (affectionate term used to describe the computer roBOTS), you might see a move (or a double) with the value of say +0.750. That means the current position is worth ¾ point. If that is the best move, the remaining moves in the table are displayed relative to that move. For instance if the next best move is worth ½ point, it would be shown as +0.500 (-0.250) with the value in parenthesis indicating the loss in equity from not having played the best move. So, let's take a look at an equity table.
The position below has White to play double 3s. The analysis chart from eXtreme Gammon is shown below the position. The chart shows the results of a 1296 game rollout between three move choices.
The single most important statistic in the table is the Equity Loss computation shown in parenthesis below the equity computation, eq:, for moves 2 & 3.
Also, note that in the table, Move 1 has a lower winning percentage than either Move 2 or 3. However, when gammons and backgammons are taken into account, Move 1 prevails.
© 2011 Edward Rosenblum