Editing Backgammon (section)

==Equity==
A player's '''equity''' in a money or unlimited game is the average  [[expected value]] that will be won or lost as a result of that game.  For instance, if a player is certain to win but has no chance of a gammon or backgammon their equity is 1 and their opponent's equity is −1. If it is certain that the player will win a backgammon, their equity is 3 and their opponent's equity is −3. In Example 1 below, the player's winning chances are 75%, which corresponds to an equity of +0.5.<ref>{{cite book
| last = Lamford
| first = Paul
| title = Starting Out in Backgammon
| publisher = Everyman Publishers
| date = 2001
| location = London
| pages = 126
| language = English
| url = 
| doi = 
| id = 
| isbn = 
| mr = 
| zbl = 
| jfm =}}</ref><ref>{{Cite book
|last=Schiemann
|first=Dirk
|url=https://dirk-schiemann.de/the-theorie-of-backgammon.html#
|title=The Theory of Backgammon Mathematics, Logic, and Intuition
|publisher=Sciwie Verlag
| pages =18–23, 64–77
| language = English
}}</ref>
:''Example 1''
[[File:Bkgm61.jpg|thumb|upright=.7|right]]
:Suppose there are only two checkers left on the board and the player on-roll has a checker on their six point and the opponent has a checker on their one point. The player on-roll will bear off with 27/36 rolls or 75% of the time.  If the game was played from that position 100 times the on-roll player would win ~75 games and their opponent would win ~25 for a net win of ~50 points per 100 games.  The on-roll player's equity would be .5 and their opponent's would be −.5.
:If the doubling cube was accessible they could offer the cube and increase their equity to 1:  either their opponent passes the cube and the game is over, or their opponent takes the cube and loses 100 points per 100 games (instead of the 50 with the cube centered). This illustrates that the raw takepoint for money play is 25%.

[[File:Bkgm521.jpg|thumb|upright=.7|right]]

:''Example 2''

:Now, suppose the on-roll player has two checkers, one on the five point and one on the one point while their opponent still has one on the one point. 23 rolls bear off both checkers so the winning percentage is 64% instead of 75% and the equities are about +0.28 ((64−36)/100) and −0.28. If the on-roll player offers the cube, their equity doubles to 0.56 and their opponent should take the cube because −0.56 is better than −1.
[[File:Bkgm5ptHoldingGame.jpg|thumb|upright=.7|right]]
:''Example 3''

:This example is more complicated, since there are gammons and backgammons to be had by both players and it is not the last chance to offer the cube. Computer analysis estimates the player with the black pieces wins 72.1% of games, plus 2.0% gammons, and 0.1% backgammons. Their opponent wins 27.9% of games, 2.0% gammons, and no backgammons. This adds up to the following equities:

::No double 0.667

::Double, take 0.684

::Double, pass 1.000
:The on-roll player should offer a double since their equity increases, and their opponent should take since they retain more equity by taking than passing.<ref>https://www.bkgm.com/articles/GOL/May01/hold.htm</ref>