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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!
Any explanations?
I am no mathematician, but...

I'm no expert on probability, but I think you have to consider different types of pattern differently. In the case of the coin, a pattern of 50 heads and 50 tails (in any order) is much more likely than 99 heads and 1 tail. But a pattern of first 50 heads and then 50 tails is no more or less likely than a pattern that alternates heads and tails, or one that alternatives pairs of heads and tails, etc. Similarly, if you deal out 13 cards from a well-shuffled deck, you are very unlikely to get all 13 hearts, but that outcome is no less likely than any other specified hand.

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