Are there undefined equities in backgammon?
Backgammon bots presuppose that every backgammon position
has a well-defined equity, which in the case of a money game
means the expected payoff if both sides employ “perfect play”
(or more accurately, Nash equilibrium play).
However, if the cube value is truly unlimited,
then it is not clear that the equity of an arbitrary position
in backgammon is always finite.
In October 2026, I wrote an article on this topic.
The bottom line is that very likely, the answer is no,
not every money-game position has an equity.
However, the above article, though it carries the analysis
further than ever before, falls slightly short of a rigorous
mathematical proof. Prior work on the topic includes:
Perpetual
Redouble? by Bill Kennedy, 1982.
Riding
the Tiger, by Bob Floyd, 1982.
Undefined
Equity, by Douglas Zare, 2004.
Post 1 and
Post 2 by me on BGOnline, 2017. These posts are
not quite correct, but the errors are corrected in my October 2026 article.
Undefined Equity, by Tom Keith, 2017.
Back to Fun Stuff