With a RAND_MAX value of 3 (in reality it should be much higher than that but the bias would still exist) it makes sense from these calculations that there is a bias:
1 % 2 = 12 % 2 = 03 % 2 = 1random_between(1, 3) % 2 = more likely a 1
In this case, the % 2 is what you shouldn't do when you want a random number between 0 and 1. You could get a random number between 0 and 2 by doing % 3 though, because in this case: RAND_MAX is a multiple of 3.
Another method
There is much simpler but to add to other answers, here is my solution to get a random number between 0 and n - 1, so n different possibilities, without bias.
- the number of bits (not bytes) needed to encode the number of possibilities is the number of bits of random data you'll need
- encode the number from random bits
- if this number is
>= n, restart (no modulo).
Really random data is not easy to obtain, so why use more bits than needed.
Below is an example in Smalltalk, using a cache of bits from a pseudo-random number generator. I'm no security expert so use at your own risk.
next: n | bitSize r from to | n < 0 ifTrue: [^0 - (self next: 0 - n)]. n = 0 ifTrue: [^nil]. n = 1 ifTrue: [^0]. cache isNil ifTrue: [cache := OrderedCollection new]. cache size < (self randmax highBit) ifTrue: [ Security.DSSRandom default next asByteArray do: [ :byte | (1 to: 8) do: [ :i | cache add: (byte bitAt: i)] ] ]. r := 0. bitSize := n highBit. to := cache size. from := to - bitSize + 1. (from to: to) do: [ :i | r := r bitAt: i - from + 1 put: (cache at: i) ]. cache removeFrom: from to: to. r >= n ifTrue: [^self next: n]. ^r