In some experiments rational players who understand the structure of t
he game could improve their payoff. We bound the size of the observed
losses in several such experiments. To do this, we suppose that observ
ed play resembles an equilibrium because players learn about their opp
onents' play. Consequently, in an extensive-form game, some actions th
at are not optimal given the true distribution of opponents' play coul
d be optimal given available information. We find that average losses
are small: $0.03 to $0.64 per player with stakes between $2 and $30. I
n one of the three experiments we examine, this also implies a narrow
range of outcome.