Keno is a popular game in casinos. Balls numbered 1 through 80 are tumbled in a machine as the bets are placed, then 20 of the balls are chosen at random. Players select numbers by marking a sheet like the one on the right. There are many different bets one can make. We will look at two of the simpler Keno bets.
Bet 1: You bet on a single number, called "Mark one number". This bet costs $1, and if your number is one of the 20 chosen ones, you are paid $3. If not, then you have lost your dollar.
Bet 2: You bet on two numbers, called "Mark 2 numbers". This bet also costs $1, but now you get $12 if both of your numbers are among the 20 chosen. The probability for this is approximately 0.06.
Compute the expected values for each of these two bets and decide which one is the better bet to make. Fill out a table like the one below for each of the bets and then use the EMV formula to calculate it.
Net gain
Probability
Weighted net gain