>From personal experience, it is really annoying how many repetitions of an experiment it can take to obtain the "theoretical" outcome even in a game as predictable as rolling a pair of dice.
Many years ago, I tried to demonstrate to my little brother that 7 is most likely outcome when rolling a pair of dice. Even after a 100 actual trials, however, 7 was still not the most frequent outcome. Not even after 200 trials. It had to simulate the game on his computer. Low and behold, after about 10 thousand automatic iterations... Aha! I told you so! He didn't look very convinced.