Equity in Backgammon - Full Explanation

During Backgammon Lessons one might here saying such as "if pass I am 34% to win” or “My equity here is over 0.7, but I still don’t think it’s a double.” These concepts of “equity” are important building blocks for a complete understanding of backgammon and today not too many players understand them.

The following will explain the basic concepts of match equity and game equity.

I. Match Equity

a) Terminology

Match equity is also referred to as match-winning chances or MWC%. It is exactly what it means, your chances of winning the match at play.

We explained previously that the odds of winning a 5-point match at a score of 4-0 Crawford is 25%. All match equity is defined in terms of “points away.” After all, it doesn’t matter if the score is 4-0 to 5 or 18-16 in a 19pt match. Giving the score is free for interpretation. I will use the notation of –a/-b to mean “I need a points, and my opponent needs b.” “C” at the end will mean “This is the Crawford game” and “pC” will mean “The Crawford game has already passed.”

b) Frequency of Gammons

Match equity is affected by the frequency of Gammons. The frequency of gammons is still being disputed among experts. A study of match equities was done by Kit Woolsey and Hal Heinrich around 1990, and determined that the in a game played to conclusion without the doubling cube, the frequency of gammons was about 20%. More current studies suggest a higher gammon frequency. For the balance of this article, we will assume a 20% gammon frequency. Towards the end, we will talk about what would happen if a higher gammon frequency is assumed.

Obviously, you can say “But matches are played with the doubling cube!” and you would be correct. The cube action is known in some of the examples we will give, such as Crawford and post-Crawford games. In other games, players will prefer not to lose a doubled gammon and will often lead them to drop a double with win chances well over 25%.

c) Match equity and Gammons

Consider the fairly simple score of –2/-1C. Let’s assume that the gammon frequency for a cubeless game is 20%. The following outcomes are possible:
i) Win a gammon this game, and the match, 10% of the time.
ii) Win this game without a gammon 40% of the time, and win the next game 50% of the time.
Calculating the above, I will win the match 10% + (40% * 50%), or 30% of the time. So my match equity at –2/-1C is 30%.