Relative frequency and the law of large numbers

Relative frequency = the number of times an event occurred divided by the total number of trials.

If you roll a die 30 times and get four sixes: 4/30 ≈ 0.13. The probability is 1/6 ≈ 0.167. They are not the same — but they are close.

The law of large numbers: the more trials you run, the closer the relative frequency gets to the true probability.

Number of rolls	Sixes	Relative frequency
30	4	0.133
300	57	0.190
3,000	486	0.162
30,000	5,012	0.167

import random
random.seed(0)

for n in (30, 300, 3_000, 30_000):
    rolls = [random.randint(1, 6) for _ in range(n)]
    print(n, round(rolls.count(6) / n, 3))

Two common misconceptions:

1. «We have gotten four heads in a row, so tails must come next» — no. The coin has no memory. Each flip is still 50/50. This is known as the gambler's fallacy.
2. «After 1,000 flips, it must be exactly half» — no. The proportion approaches 0.5, but the difference in counts can easily grow.

This is exactly why we test models on many examples: with only 20 test cases, random variation is larger than the difference between the models.