EXAMPLE 2 The Tri-State Daily Numbers, continued

The Straight wager in Example 1 pays off if you match the three-digit winning number exactly. You can choose instead to make a $1 StraightBox (six-way) wager. You again choose a three-digit number, but you now have two ways to win. You win $292 if you exactly match the winning number, and you win $42 if your number has the same digits as the winning number, in any order. For example, if your number is 123, you win $292 if the winning number is 123 and $42 if the winning number is any of 132, 213, 231, 312, and 321. In the long run, you win $292 once every 1000 bets and $42 five times for every 1000 bets.

The probability model for the amount you win is

The expected value is

expected value = ($0)(0.994) + ($42)(0.005) + ($292)(0.001) = $0.502

We see that the StraightBox is a slightly better bet than the Straight bet because the state pays out slightly more than half the money bet.