Statistical Significance Through Dice Rolling

Here, notice that while the mean of the average number on the dice remains the same at 3.5, the standard deviation decreases (as the number of dice increases) as follows:

Correspondingly, the probability that the average number on the dice is 4 or beyond also decreases from 50% (in the case of 1 die) to ~2% (in the case of 50 dice) — as can be seen in the shaded area in the graph.

In other words, whereas getting an average of 4 or beyond is pretty normal when throwing one die, the same becomes an extreme rarity when 50 dice are involved (and thus is taken as a statistically significant evidence that the die is biased). For more on statistical significance, see https://mathvault.ca/statistical-significance