What are the odds of getting six-of-a-kind out of nine dice in one shake? This is the shake of the day at a tavern near me. I know the odds of six-of-a kind-in one shake given six dice; the three extra dice have me bumfuzzled. I have been unable to plug the numbers into the equations I have come across. This is probably trivial math, which adds greatly to the irritation :) Thank you.