[brendano]

Once you've reached input number 10^8 or whatever, you've got all sorts of chances to have arithmetic overflow and/or the weirdness of that many pseudo-random operations screw you.

Why? Double floats don't overflow until 10^-300 or so, and RNG's give uniform numbers from 0 to 1 just fine...

[dbaupp]

Most RNGs that generate numbers from 0 to 1 actually just generate a random 64-bit value, and divide by 2^64; which means that they do underflow relatively easily. (This is relatively easily to overcome using a better (& more expensive) random bits -> double algorithm.)