Here’s what’s going on:
default_random_enginein libstdc++ (GCC’s standard library) is
minstd_rand0, which is a simple linear congruential engine:
typedef linear_congruential_engine<uint_fast32_t, 16807, 0, 2147483647> minstd_rand0;
The way this engine generates random numbers is xi+1 = (16807xi + 0) mod 2147483647.
Therefore, if the seeds are different by 1, then most of the time the first generated number will differ by 16807.
The range of this generator is [1, 2147483646]. The way libstdc++’s
uniform_int_distributionmaps it to an integer in the range [1, 100] is essentially this: generate a number
n. If the number is not greater than 2147483600, then return
(n - 1) / 21474836 + 1; otherwise, try again with a new number.
It should be easy to see that in the vast majority of cases, two
ns that differ by only 16807 will yield the same number in [1, 100] under this procedure. In fact, one would expect the generated number to increase by one about every 21474836 / 16807 = 1278 seconds or 21.3 minutes, which agrees pretty well with your observations.
mt19937, which doesn’t have this problem.