I recently went to gamble at a casino. First timer that I was, I decided to stick with the roulette table. In particular, I decided to only bet on black and red (ALMOST 50% chance of success, as one must also factor the number 0, which is neither red nor black). After a while observing the results board (and not betting), I noticed that what appered to be a chaotic pattern of results, became a pretty steady and predictable 3-reds-3-blacks type of pattern. So I began betting, and, lo and behold, I began winning. Naturally, every now and then I would lose some (sometimes there would be 4 blacks in a row instead of 3)--but, overall, I was winning. Then this magical pattern vanished, giving way to the same chaotic (that is: to my eyes) pattern which I had observed at the beginning. After, say, 1 hour, the 3b-3r pattern was back in place. Days later, I returned to the same casino, and didn't even place one bet: my magical pattern just never manifested itself!
I am no mathematician, but is it possible that that pattern really was a pattern and not mere chance? I mean, if I tossed a coin, for every toss there would be equal possibilities for the outcome to be heads or tails; nevertheless, after 100 tosses, more or less, we'll have a result split down the middle: a pattern!