Random draws: chance you can repeat

One draw is unpredictable; many draws follow a pattern

A random draw is one value picked by chance from a set of possible values. Rolling a fair die is a draw from {1, 2, 3, 4, 5, 6}, and each face has the same chance, 1 in 6. The rule that says how likely each value is called the distribution of the draw. When every value is equally likely, the distribution is uniform.

Roll 60 times and you expect each face about 10 times, but rarely exactly 10. Roll 6000 times and each face's share lands close to one sixth, even though its count can miss 1000 by 30 or more. The more draws you make, the closer the shares come to the distribution's chances.

A computer's draws come from a recipe that starts at the seed

A computer follows instructions exactly, so it cannot roll a real die. It uses a pseudo-random number generator instead: a rule that turns one number into the next, chosen so the results look random. The first number is the seed. Same seed, same sequence, every time.

Real generators use much larger numbers and cleverer rules, so their sequences pass strict tests of randomness and take an astronomically long time to repeat. The seed still works the same way. Researchers record the seed so that someone else can rerun a computation and get the same numbers.

rand.py: NumPy's generator, with a seed

import numpy as np

rng = np.random.default_rng(seed=42)
print(rng.integers(1, 7, size=10))   # ten rolls of a die

rng = np.random.default_rng(seed=42)
print(rng.integers(1, 7, size=10))   # same seed, same rolls

rng = np.random.default_rng(seed=7)
print(rng.integers(1, 7, size=10))   # new seed, new rolls

rolls = np.random.default_rng(seed=0).integers(1, 7, size=6000)
# np.bincount counts each value from 0 up; [1:] drops the count for 0
print(np.bincount(rolls)[1:])        # how often each face came up

[1 5 4 3 3 6 1 5 2 1]
[1 5 4 3 3 6 1 5 2 1]
[6 4 5 6 4 5 6 2 1 2]
[1017  970 1006 1008  969 1030]

integers(1, 7) draws whole numbers from 1 up to but not including 7. The output above came from NumPy 2.5; another version may print different numbers.