There are some games widely played in the routine world of gambles, roulette, quiz show and the sports exercises. The object of the game is to get the highest score among all of the players, from one or two chances of sampling. A three-player game of ^^ ^^ Risky Exchange", which reduces to a three-player continuous game on the unit cube, having symmetry between players' roles, is investigated, and the optimal strategies for the three players and the winning probabilities they can get in the optimal play are derived.