David Richerby wrote:
I've played a bit of backgammon but mostly against the computer. I
can't see any circumstances under which one might agree a draw -- if
the game looks level, you'd just wait and not double, since it'll
surely unbalance itself after a while. Since the men can only move
forwards in Backgammon, progress of a sort must be made all the time
so I don't see a situation comparable to the sort of honest draw in
chess where neither player can make progress by any means other than a
gross blunder from the opponent. I've not played backgammon except
socially and against the computer -- am I missing something?
Yes. To address your last point first - OF COURSE backgammon checkers
can move backwards! But, the real point is - you often find yourself in
a position where the entire game will hinge on the next roll. This is
not unlike an "unclear" chess position where neither player can see
enough to be sure who is winning. Another analogy might be a "race" in
poker where the odds are about 50-50 with a large amount of money on the
line.
In chess, players may accept a draw rather than continue in an unclear
position. Note that this is DIFFERENT than agreeing to a draw in a
clearly drawn position, and even different than agreeing to a draw in a
LEVEL position.
In poker, players may "run it twice" (if allowed), or even "chop". In
both cases, the point is to reduce variance when the odds are even but
the result will be a win or a loss (and very rarely a draw).
In backgammon, I've *often* been in positions where the cube has
(legitimately) gone back and forth and the position on the board is now
dead even....except that one player or the other will win based on the
next roll of the dice. In that position, I'd much rather agree to a draw.
In summary - these are all cases where the EV is 0.5, the stakes are
(now) very high, and the result CANNOT be 0.5 but instead must be either
0.0 or 1.0. Both players may well rather accept the (well earned) 0.5
than gamble.
--
Kenneth Sloan
Computer and Information Sciences +1-205-932-2213
University of Alabama at Birmingham FAX +1-205-934-5473
Birmingham, AL 35294-1170 http://KennethRSloan.com/