Answer by bobobobo for Why do people say there is modulo bias when using a random number generator?

As the accepted answer indicates, "modulo bias" has its roots in the low value of RAND_MAX. He uses an extremely small value of RAND_MAX (10) to show that if RAND_MAX were 10, then you tried to generate a number between 0 and 2 using %, the following outcomes would result:

rand() % 3   // if RAND_MAX were only 10, givesoutput of rand()   |   rand()%30                  |   01                  |   12                  |   23                  |   04                  |   15                  |   26                  |   07                  |   18                  |   29                  |   0

So there are 4 outputs of 0's (4/10 chance) and only 3 outputs of 1 and 2 (3/10 chances each).

So it's biased. The lower numbers have a better chance of coming out.

But that only shows up so obviously when RAND_MAX is small. Or more specifically, when the number your are modding by is large compared to RAND_MAX.

A much better solution than looping (which is insanely inefficient and shouldn't even be suggested) is to use a PRNG with a much larger output range. The Mersenne Twister algorithm has a maximum output of 4,294,967,295. As such doing MersenneTwister::genrand_int32() % 10 for all intents and purposes, will be equally distributed and the modulo bias effect will all but disappear.