  In this paper, we propose a model which simulates odds distributions of
pari-mutuel betting system under two hypotheses on the behavior of bettors: 1.
The amount of bets increases very rapidly as the deadline for betting comes
near. 2. Each bettor bets on a horse which gives the largest expectation value
of the benefit. The results can be interpreted as such efficient behaviors do
not serve to extinguish the FL bias but even produce stronger FL bias.
