Some casinos will run multiple games to entice players to wager more. You mark your ticket and tell the dealer to enter it in the "red game", "green game" or both. Basically it's a way to increase action (wagering) without having to increase floorspace and staff correspondingly. There are two separate sets of balls and two keno boards, but only one keno lounge and set of dealers.

The casino figures you won't want to just play one of the games because you "know" if you play just the "red game" your numbers will come up only on the "green game". So players tend to bet on both games, increasing the house's take. Mathematically there's nothing special about playing both games, though sometimes casinos offer prizes for hitting on both games. You can calculate the odds of hitting on both games by multiplying combinations that pay off.

For example, the chance of catching 4 out of 6 is 0.02854, so the chance of catching 4 out of 6 in 2 simultaneous games is 0.02854 x 0.02854 ~= 0.0008 or 1 in 1228.