I liked this one:

If one were to flip a fair coin five times and get heads each time, it would not be any more likely for a sixth flip to come up tails. Phrased another way, after a long and/or unlikely streak of independently random events, the probability of the next event is not influenced by the preceding events. Humans often feel that the underrepresented outcome is more likely, as if it is due to happen. Such thinking may be attributed to the mistaken belief that gambling, or even chance itself, is a fair process that can correct itself in the event of streaks.