In some experiments rational players who understand the structure of the game could improve their payoff. We bound the size of the observed losses in several such experiments. To do this, we suppose that observed play resembles an equilibrium because players learn about their opponents' play. Consequently, in an extensive form game, some actions that are not optimal given the true distribution of opponents' play could be optimal given available information. We find that average losses are

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... $0.03 to $0.64 per player with stakes between $2 and $30. In one of the three experiments we examine this also implies a narrow range of outcome. * We thank Eddie Dekel, Jack Hirshleifer, David Kreps, Tom Palfrey, Alvin Roth, Jeroen Swinkels, and Steve Tadelis for helpful comments and conversations. NSF Grants SBR-9223320 and SBR-9223175 provided financial support.