A system for playing electronic games includes a game server and one or more player terminals. Game results are based on a random number generated in each of the game server and the player terminals. The game server and the player terminals cooperate to ensure that the random numbers are generated independently. As a result, game players and the game host, such as a casino, can be confident that play results are not fraudulent. In one embodiment, the random numbers are transmitted between the game server and the player terminals at substantially the same time. In other embodiments, the random numbers are encoded and exchanged between the game server and the player terminals. Then, keys to decode the random numbers are exchanged.