I wonder if the "Bitmask with Rejection" method would be more efficient if you sometimes made the mask one bit larger than strictly necessary. As it is, if you

I wonder if the "Bitmask with Rejection" method would be more efficient if you sometimes made the mask one bit larger than strictly necessary. As it is, if you want a number in the range 0..8, you take 4 bits of randomness, giving you a number in 0..15. This is great, but 7/16 (43.75%) of the time you have to try again. This not only means more loop iterations, it also means you discard 4 bits of randomness, which may have been costly to generate. If instead you took 5 bits of randomness, you'd be able to accept anything in 0..26 and would only have to reject 27..31, which means only rejecting 5/32 (15.625%) of the time. 0..8 is a particularly bad case, though. If you need numbers in the range 0..14, then it's not worth trying to use 5 bits.