In many strategic situations such as military conflicts, market competition and insider trading, a player might be able to observe the other player's move before making his own. This possibility of spying, or observability of moves, creates uncertainty over the order of moves in games. I study a particular strategic tension observability creates in dynamic games: a spying player might have incentives to “play dumb”. That is, the spying player might not myopically best respond to the other player's observed action earlier in the game so that he can manipulate the other's suspicion or lack of it for higher future payoffs. I model this situation with 2-period dynamic games in which a 2´2 game is played in each period. First, I characterize the conditions under which the spying player might or might not want to raise the other player's suspicion. Then I find conditions under which the spying player plays dumb in the perfect Bayesian equilibrium. I design and conduct a laboratory experiment to test the theoretical predictions. The spying players rarely play dumb even when the theory predicts it. Data suggest that the lack of dumb playing might be because the other player's deviations from “playing dumb” equilibria make playing dumb unprofitable.