There are n games, and each game has a state after the start.
Based on this state, the probability of the outcome of the game can be calculated.
For example, there are 3 type of results, and the probabilities are p1, p2, and p3 respectively.
But in the next game, the game state is different, and the probabilities change accordingly, becoming p4, p5, and p6.
Play n games, and then there are n results.
So how to judge whether these n results are in line with these probabilities as a whole?

Suppose I have a sample $X_1, dots, X_n$, drawn from some distribution $mathcal{P}$ with cdf $F_X(x)$. Empirical distribution function is calculated as
$$ hat{F}(x) = frac{1}{n} sum^n_{i=1} I(X_i < x).$$
From the probabilistic point of view, for each $x$, $hat{F}(x)$ is a random variable (since it is the sum of random variables, since sample is viewed as iid random variables).