In October 1996 someone posted a common question to rec.games.backgammon:

"Can someone please explain equity to me and how it is calculated? I have looked in a few places and what I have found has been a bit confusing."

As I'm far from expert myself, I kept to simple principles in my short reply.


There are two types of equity: game equity and match equity. Match equity describes, holistically, your relative position within an overall bg match for any number of points. I'll talk only about game equity, which describes your relative position within a single game, beit for money (single games) or within a match.

Very briefly (and simplistically), equity is simply a number describing the current value of a game to you and to your opponent. The equity number is expressed as a proportion of the game's stake.

Another way of describing it: it is the proportion of the game's stake that you would be willing your opponent to pay you (or vice versa) were you and your opponent to stop the game right now and settle your financial differences. Your opponent's equity is always the negative of your equity.

For example, if your game equity in a single money game is 0.43 (therefore your opponent's equity is -0.43), and you're playing for $1 a point, then you would accept $0.43 in direct payment were you both to agree to stop playing at that point.

To convert equity to money value, you not only take the stake into account but the cube value also. You multiply the equity by the stake *and* the cube value.

So if your equity is -0.12 and you're playing for $3 a point, and the cube is currently on 2, then you would pay your opponent $3 x 0.12 x 2 = $0.72 were you agreed to stop playing at that point. (In this example. your equity is negative, meaning that you are the underdog in the game, and you would pay your opponent, not vice versa).

Yet another way to describe equity is the average of all the equities that would apply for each position were you and your opponent to play the game out to the end. Please note that I don't understand this description! (I said I'm no boffin.)

At the start of a game, before both players have rolled to see who moves first, your game equity is 0. I.e., you would pay your opponent and he would pay you, nothing if you decided to stop playing at this point. That should make sense, as you haven't started playing yet.

Imagine you have only one man left to bear off and your opponent has already borne one man off, for example:

      1  2  3  4  5  6        7  8  9 10 11 12
    +------------------------------------------+ O:  - score: 0
O   | O  O  O  O  O  O |   |                   |
    | O  O  O  O  O  O |   |                   |
    |             O  O |   |                   |
    |                  |   |                   |
    |                  |   |                   |
    |                  |BAR|                   |v    1-point match
XX  |                  |   |                   |
XX  |                  |   |                   |
XX  |                  |   |                   |
XX  |                  |   |                   |
XXX |    X             |   |                   |
XXX +------------------------------------------+ X:   - score: 0
     24 23 22 21 20 19       18 17 16 15 14 13

X's equity is 1 (so O's equity is -1). X cannot lose the game, regardless of who's on roll or what either player rolls, and cannot win a gammon. O would do as well to pay X 1 x stake x cube-value as he would to play the game to completion. If the stake is $5 and the cube is on 4, O could pay X $20 at this point.

      1  2  3  4  5  6        7  8  9 10 11 12
    +------------------------------------------+ O:  - score: 0
    | O  O  O  O  O  O |   |                   |
    | O  O  O  O  O  O |   |                   |
    |             O  O |   |                   |
    |                  |   |                   |
    |                  |   |                   |
    |                  |BAR|                   |v    1-point match
XX  |                  |   |                   |
XX  |                  |   |                   |
XX  |                  |   |                   |
XX  |                  |   |                   |
XX  | X  X             |   |  O                |
XXX +------------------------------------------+ X:   - score: 0
     24 23 22 21 20 19       18 17 16 15 14 13

In this position, *if* X is on roll, X's equity is 2. That's because he will win a gammon whatever happens. So a stake of $2.50 and a cube of 8 means O would do as well to pay X $40 now as he would do to play the game out (it's over next roll, anyway)

Those were black and white positions - the result of the game is already decided and they're only to illustrate simple examples of equity.

Things are usually more complex. In mid-game positions of almost any type, it is nigh-on impossible to work out your exact equity.


I stopped there, but there are several resources on the Net that go further. When I get round to it I'll list them on this page.

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