When mathematician and blackjack expert Jonathan Adler saw my post about hedge fund manager Michael GeismarÂs antics at the Vegas blackjack tables, he offered to explain just how silly Geismar was being. I jumped at the chance. So enjoy:
Like most stories dealing with probability, this one starts with a coin flip. If you take a fair coin and flip it, you would expect it to have a 50/50 chance of landing heads. But letÂs say that you flipped the same coin ten times, and on a wild streak of luck each of those times it happened to end up being heads. What are the chances that the eleventh flip will also be heads? While it may feel like youÂre Âowed a tails, the odds of it being a heads are still 50/50, since the coin didnÂt change in any way. Each flip is what mathematicians call an independent event: the outcome of each flip has no impact on the outcome of any other flips. The idea that after seeing a bunch of one side of the coin on past flips you are more likely to see the other on future flips is called the gamblerÂs fallacy. The fallacy comes from the confusion between the long run outcome (with a large enough sample size, I expect half of my coin flips to be heads and half to be tails) and the outcome on any one flip (since I have seen a bunch of heads before, I need to start getting tails to balance things out in the long run).
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Cheers,
Scott.