Keno Appendix 2 - The Wizard of Odds

Last update: May 16, 2001

1. The player chooses from 2 to 10 numbers, ranging from 1 to 80, as in regular keno.
2. The computer will draw three 3 numbers at random among the numbers the player did not pick. These three numbers will be marked with a dinosaur egg.
3. The computer will then draw 20 numbers, ranging from 1 to 80, as in regular keno.
4. The player will win depending on the number of the player's picks that match the 20 numbers chosen by the computer, as in regular keno.
5. If the player did win something from step 4 then that win will be multiplied by a factor depending on whether the egg numbers match the 20 numbers chosen by the machine. This factor is 1 if the number of egg matches is 1 or less, 4 if two eggs match, and 10 if all three eggs match.

At the Suncoast casino in Las Vegas the player could play for 5 cents, 10 cents, 25 cents, 50 cents, $1, or $2. There were two paytables, one for 5 and 10 cents, the other for 25 cents to $2. The following following two tables show the two different pay tables.

The expected return for x picks and y catches is (combin(x,y)*combin(80-x,20-y)/combin(80,20))*(1 + 3*combin(20-y,2)*(60-x+y)/combin(80-x,3) + 9*combin(20-y,3)/combin(80-x,3)). To deterermine the total expected return for x picks sum the return of y catches over all values of y that pay anything.

The following tables show the expected return according to the number of picks and catches. The total return is in the bottom row.

The second table adds about 2% to the expected return, depending on the number of marks chosen. The highest return on the 25 cents - $2 table is the pick 7 at 93.68%. The highest return on the 5 to 10 cents table is the pick 5 at 91.64%. These returns are about the same as the conventional Four Card Keno on the same machine.