Topics Probability

Question 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 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! Any thoughts? Thanks, a

Accepted:
March 27, 2006

Comments

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.