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© Copyright 1996, Jim Loy
Test yourself: You are flipping a coin, and you are not cheating. You have just flipped 7 heads in a row. Is your next flip more likely to be:
The correct answer is #3, heads and tails are equally likely. Answer #1 is an example of one version of the Gambler's Fallacy (you think that your luck will continue). Answer #2 is an example of the opposite version of the Gambler's Fallacy (you think that your luck will change).
A popular way to explain why answer #3 is correct is the expression, "the coin (or dice or whatever) has no memory." It does not matter what the previous flips were. The coin always shows 50-50 odds.
Probability says that approximately 50% of your flips will be heads and approximately 50% will be tails. It does not say that exactly 50% will be heads. In fact it says that there will be streaks of several heads in a row and streaks of several tails in a row. You will have streaks. But probability gives no clue when your streak will end. And if you think that you do have such a clue, you are fooling yourself.
What I said above, about coins, applies to any winning or losing streak. The only difference is that the chance of a winning flip (or roll or spin or whatever) is probably less than 50% (so the "house" can actually stay in business). But the fact that you are in a streak does not affect your odds in any way.
But, now I have to back off somewhat. Cards do have a memory, until they are shuffled. Let's say that you just saw the dealer get an ace. The chances of your being dealt an ace just went down, because there are now fewer aces in the deck. Incidentally, in video poker, the cards are shuffled at the beginning of every hand, so the cards have essentially no memory.
Well, with cards, can you now rely on your hunches? Does the fact that you are in a streak now mean that you can predict the next card? No (mostly). In Blackjack, the fact that you've seen few 10s means that you should increase your bet. But, the fact that you just won several hands does not affect the odds of your winning the next hands, in any predictable way. Your hunches are still based on the Gambler's Fallacy.
If you find yourself saying, "I can't quit now, I'm on a winning streak," Gambler's Fallacy. If you find yourself saying, "I can't quit now, my luck's about to change," Gambler's Fallacy (the second version). "Gambler's Fallacy" is another way of saying "stupid."