We have played a classic Keynes' beauty contest with over 1000 professional investors. We find that on average professional investors are using between one and two steps of strategic thinking in forming their expectations. We also find that many investors suffer the curse of knowledge and end up either picking zero or severely underestimating the irrationality of other players. These results speak directly to the ability of investors to exit the market before the mass exodus. We find, unsurprisingly, that only a very small minority show the required level of strategic thinking to beat the gun.