Keno is a popular electronic game that is being played in casinos and Online by a large number of players every day. In a typical Keno game, a player may choose between 2 to 10 numbers, ranging from 1 to 80. The computer will then draw 20 numbers, ranging from 1 to 80, and the player wins according to a pay table and according to how many of his/her chosen numbers are matched by the 20 numbers drawn by computer. In the majority of cases, game designers add more features such as additional bonuses to the base keno game described above, so that the game becomes more attractive. In a particular version of such keno games offered by the Online keno vender "wizzardofodds.com", called the Caveman Keno, the game has the following characteristics: 1. The player chooses from two to ten numbers, ranging from 1 to 80, as in regular keno. 2. The computer will draw three numbers at random among the numbers the player did not pick. These three numbers will be marked with dinosaur eggs. 3. The computer will then draw 20 numbers, ranging from 1 to 80, as in regular keno. 4. The player will win depending in part on the number of the player's picks that match the 20 numbers chosen by the computer, as in regular keno. 5. The player will get a multiplier according to the number of eggs that match the 20-ball draw. The usual multipliers are 1x for 0 or 1 match, 3x (3 times the player's win) for two matches, and 6x for three matches. 6. The player's win will be the sum of the wins of the regular keno pay table and the multiplier wins. In this game, suppose that each game costs the player $1 to play.