Games of Chance

Discrete Math · Axiom Academy

Discover how probability works through casino games. Watch what happens when you play the same game many times! Let's start with the simplest game of chance: flipping a coin. Click the coin to flip it and track the results! In roulette, you bet on red or black. The wheel has 18 red slots, 18 black slots, and 2 green slots (0 and 00). What do you think your chances are? Rolling two dice creates different probabilities for different sums. Some totals are more likely than others! In all three games, you observed the same phenomenon: with just a few trials, your results varied widely from the expected probability. But as you played more and more times, your experimental probability got closer to the theoretical probability . Theoretical probability is what mathematics predicts should happen (like 50% heads for a fair coin). Experimental probability is what actually happens when you run trials. The Law of Large Numbers says these converge as the number of trials increases! Just because you flip 5 heads in a row doesn't mean tails is "due." Each flip is independent! The Law of Large Numbers works over thousands of trials, not the next single trial. This is why casinos always win in the long run—they have the probabilities on their side.

This is the written version of the interactive lesson above. See the full Discrete Math course.