On Mar 25, 10:18 am, (Torben Ægidius Mogensen)
wrote:
samsloan writes:
One factor to be considered is that the number of possible moves in a
backgammon games is infinite. The players could easily just keeping
hitting each other to infinity.

That doesn't matter, as long as the number of possible board positions
is finite (which it is).

The main difference between Backgammon and, say, Checkers is not the
possibility of infinite play but the fact that Backgammon involves
random elements, so few positions are definitely winning or definitely
losing -- all you can say is the probability of winning with perfect
play (i.e., always picking the move that gives you the best winning
probability after moving).

You can solve Backgammon by for each possible position have edges to
every other position that it is possible to get to in one move, and
label each edge with the dice outcome that allow this move).

This can be translated into a set of equations that you can solve to
find the probability of each possible position being winning or
losing. The set of equations is huge, but finite.

Torben

Even that is not obvious. There are 21 possible rolls of the dice (6!
= 21) and three possible positions of the doubling cube plus 24
possible slots for each checker.

The average chess position has 27 moves and most chess games are over
in 50 moves.

I have written a chess playing computer program and a shogi playing
computer program. However, I once tried to write a backgammon playing
computer program and I quickly gave it up as hopeless. It is much
harder than it looks.

Although backgammon seems to be an easier game than chess, I am not
sure that this is really true.

Sam Sloan