A finite keno system includes a game server with one or more player terminals. A game of finite and pari-mutual keno which combines the characteristics of traditional keno with the finite pool concept of scratch-off lottery and pull tab games is played thereon. This finite keno involves the house creating a pool of predetermined outcomes that are stored in the game server. These outcomes are indicative of the catch for that round. Each player chooses its desired numbers and then the game server randomly draws one of the outcomes which indicates the catch, that is the number of matched numbers. The game server then randomly selects a draw in two parts. First, the game server selects the winning numerals of the draw from the player's desired numbers equal in quantity to the outcome numeral, and then the game server randomly selects numbers from the non desired numbers of the player to fill in the remainder of the draw. The effect is that the game meets all of the gaming regulations of various states and countries which forbid banking games but allow for pari-mutual games as the game requires players compete against each other to win from a common pool and are not wagering against the house as the house instead has a predetermined share so long as all of the pool is played.