Six Dice Betting Game

A quick puzzle this week.

Your friend offers you a bet: Roll six dice, and if you get exactly four distinct numbers you win.

Question: would you accept this deal at even odds?

For example a roll of 1,2,3,6,3,6 would win but a 1,6,3,4,2,6 would be a loss.

Give it a few minutes thought …

Solution

There are many ways to solve this. One of these is with brute force. There are only 46,656 possible combinations the dice can land on (6  ×  6  ×  6  ×  6  ×  6  ×  6), and it’s just a couple of lines of code to write some nested loops and perform the check.

Here is a table showing the frequency count of every distinct combination of the spots.