If you really want to use dice, at least do it properly:

We have a guy who offers up a new game: rolling dice. Here's how it works:

Each person is able to roll dice. For one, the deal is that if they roll a 1, they get $1. For the other, the deal is that if they roll a 1 4x, they get $4. The stipulation is that every 10 rolls, the number they have to go for changes.

Roller 1 goes and gets:

1, 3, 6, 5, 2, 1, 4, 5, 6, 2

So he gets $2.

Roller 2 goes and gets:

1, 2, 3, 6, 1, 3, 1, 5, 2, 3

So he gets $0.

Now it's time for the next game!

We now start over again, with the requirement being a roll of 3:

Roller 1 goes and gets:

1, 3, 2, 6, 3, 5, 3, 2, 3, 1

He gets $4

Roller 2 goes and he gets:

1, 6, 5, 5, 3, 1, 2, 5, 6, 5

He gets $4


What's the difference here? The first guy got MORE because he could get PARTIAL amounts, rather than having to rely on the FULL amount. He has the SAME chance to get 4/4 as the other guy does to get 1/1, with the stipulation being that the first guy could also get 3/4 and be paid 3/4 the amount, while the second ONLY gets paid if he hits that 1/1. The second guy will therefore always come out behind.