Permalink Submitted by Rick Janowski on December 19, 2017

Keeler and Spencer in their 1975 paper (Optional Doubling in Backgammon) modelled a backgammon game in an abstract but useful way: the probability of winning the game was treated as a Brownian motion, starting at 50%, and eventually diffusing continuously either to 0% (a loss), 100% (a win), or to a point where a player offered the doubling cube to their opponent. This approach is remarkably similar to the article” Backgammon, doubling the stakes, and Brownian motion”. Moreover the conclusions are identical.
Both model backgammon as a continuous game which it isn’t. For a more realistic approaches you may wish to consider the following works: http://www.bkgm.com/articles/Janowski/cubeformulae.pdf https://arxiv.org/abs/1203.5692

## This is remarkably similar to 1975 paper and is too simplistic

Keeler and Spencer in their 1975 paper (Optional Doubling in Backgammon) modelled a backgammon game in an abstract but useful way: the probability of winning the game was treated as a Brownian motion, starting at 50%, and eventually diffusing continuously either to 0% (a loss), 100% (a win), or to a point where a player offered the doubling cube to their opponent. This approach is remarkably similar to the article” Backgammon, doubling the stakes, and Brownian motion”. Moreover the conclusions are identical.

Both model backgammon as a continuous game which it isn’t. For a more realistic approaches you may wish to consider the following works:

http://www.bkgm.com/articles/Janowski/cubeformulae.pdf

https://arxiv.org/abs/1203.5692