Puzzling "roll X dice, choose Y highest" problem Hi folks, Over the past few days, a friend and I have been wracking our brains over a dice throw probability problem. As the post title describes, it's simply rolling X dice and picking the Y highest (we coined the notation 'xky' for 'roll x, keep y highest'), then pondering what the average value of the sum would be. The end goal is trying to develop a formula in terms of X dice throws of Z-sided die, keeping the highest Y, and then summing/averaging that. We initially sought to figure out xk1 (roll x dice, keep the highest) and came up with a solution, but the methodology didn't seem to fit with xk2 and up. Anyone have any pointers or guidance on how to mathematically represent the "choosing Y highest" step of this problem? That seems to be our biggest road block. Thanks!