Two players alternate throwing a six-sided die. The first player who fails to roll a higher number than the preceding roll loses. What is the probability that the first player wins?

What if the die is n-sided?

(i) For a six sided die, the required probability that the first player wins is 0.665102 (correct to six places of decimals).

(ii)For a n-sided die, the required probability that the first player wins is 1 - (1 - n^-1)^n.