We study a dominance-solvable 'p-beauty contest' game in which a group of players simultaneously choose numbers from a closed interval. The winner is the player whose number is the closest top times the average, where p =/ 1. The numbers players choose can be taken as an indication of the number of steps of iterated reasoning about others they do. Choices in the first period show that the median number of steps of iterated reasoning is either one or two. Repeating the game produces reliable convergence to the unique Nash equilibrium. Choices in later periods are consistent with subjects' best-responding to previous choices, or iterating one step and best-responding to best responses. (Choices are not as consistent with 'learning direction theory' which embodies elements of belief-free reinforcement models). Variation in the values of p, the number of players, and whether subjects played a similar game before, all affect choices and learning.
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