Last week I posted a simple casino-style game called 9 Lives . I noticed some peculiar math behind the mechanics. I bet this is one of those things mathfolk already know intuitively, but coming at it in long-hand on my notebook over a cup of coffee is still worthwhile. To review, the game involves playing pairs of cards, each showing a digit, either 0 through 9. Added together, the highest pair is the winner for that turn. The winner earns points equal to the 'ones' digit of their play. So if you played a 12 and won, you'd win 2 points. (Tied players both score.) So I wrote out the different pairs of digits that would make each sum, from 0 through 18. I also compared that to the value of each sum. This produced the following chart. (Click to enlarge.) There is only one way to make 0, 1, 17, or 18. Two ways to make a 2, 3, 15, or 16. Three ways to make a 4, 5, 13, or 14. Four ways to make a 6, 7, 11, or 12. Five ways to make 8, 9, or 10. This makes scoring str...