If you have two choices, one with probability 0.9, then your chances of a correct guess are 90 percent using the optimal strategy. The perplexity is 2−0.9 log2 0.9 - 0.1 log2 0.1= 1.38. The inverse of the perplexity (which, in the case of the fair k-sided die, represents the probability of guessing correctly), is 1/1.38 = 0.72, not 0.9.