1 research outputs found
Gambler's Ruin and the ICM
Consider gambler's ruin with three players, 1, 2, and 3, having initial
capitals , , and units. At each round a pair of players is chosen
(uniformly at random) and a fair coin flip is made resulting in the transfer of
one unit between these two players. Eventually, one of the players is
eliminated and play continues with the remaining two. Let be
the elimination order (e.g., means player 1 is eliminated first
and player 3 is eliminated second, leaving player 2 with units).
We seek approximations (and exact formulas) for the elimination order
probabilities . Exact, as well as arbitrarily precise,
computation of these probabilities is possible when is not too
large. Linear interpolation can then give reasonable approximations for large
. One frequently used approximation, the independent chip model (ICM), is
shown to be inadequate. A regression adjustment is proposed, which seems to
give good approximations to the elimination order probabilities.Comment: 32 pages, 5 figure file