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GNU Backgammon's cube decisions are simple based on calculations of cubeful equities. For a double decision GNU Backgammon calculates the cubeful equity for no double and the cubeful equity for double, take. Combined with the equity for double, pass, it's possible to determine the correct cube action.
The figure below shows the relevant cubeful equities for White and black's cube decisions in sample position from earlier.
mgcd
Equity
2.5 ++------------+-------------+-------------+-------------+-----------$##
+ + + + centered cube$******#+
2 ++ O owns 2-cube#######++
| X owns 2-cube#$$$$$$ |
1.5 ++ $$$$ #### ++
| $$$$ #### *********
1 ++ $$$$ ###********** ++
| $$$$ ****** |
0.5 ++ $$$$ ****** ++
| $$$$ ******## |
0 ++ $$******### ++
-0.5 ++ ****** ### ++
| ***** #### |
-1 ++ ***********$$ ### ++
******** $$$ ### |
-1.5 ++ $$$ #### ++
| $$$$ #### |
-2 ++ $$$ ####### ++
+####### + + + + +
-2.5 #+------------+-------------+-------------+-------------+------------++
0 0.2 0.4 0.6 0.8 1
Wins
On 0-ply Black will double when the green curve (White owns 2-cube) is above the red curve (centered cube), and White will take as long as the green curve is below 1. Similarly, White will double when the blue curve (Black owns 2-cube) is below the red curve (centered cube), and Black takes as long as the blue curve is above -1.
Note that GNU Backgammon doesn't calculate the take point or double point explicitly. The cube decision is simply made by comparing equities from the figure.