More on the Gambler's Fallacy
Read this introduction to the gambler's fallacy and the example of how it works.
The gambler's fallacy occurs when one thinks that independent, random events
can be influenced by each other. For example, suppose I have a fair coin and I
have just flipped 4 heads in a row. Erik, on the other hand, has a fair coin that he
has flipped 4 times and gotten tails. We are each taking bets that the next coin
flipped is heads. Who should you bet flips the head? If you are inclined to say
that you should place the bet with Erik since he has been flipping all tails and
since the coin is fair, the flips must even out soon, then you have committed the
gambler's fallacy. The fact is, each flip is independent of the next, so the fact
that I have just flipped 4 heads in a row does not increase or decrease my
chances of flipping a head. Likewise for Erik. It is true that as long as the coin is
fair, then over a large number of flips we should expect that the proportion of
heads to tails will be about 50/50. But there is no reason to expect that a
particular flip will be more likely to be one or the other. Since the coin is fair,
each flip has the same probability of being heads and the same probability of
being tails - 50%.
Source: Matthew J. Van Cleave
This work is licensed under a Creative Commons Attribution 4.0 License.