The gambler’s fallacy arises when, even if people are aware of the ‘data-generating process’, they nevertheless tend to assign a higher likelihood to certain outcomes, if it has been some time since they occurred.
For example, in the case we are keeping track on the number of dots thrown using a fair dice, a streak of sixes might cause you to think that something other than 6 ‘is due’. However, the fair dice does not have a ‘memory’, so all outcomes are still equally likely. So it’s perfectly rational to expect another 6.
Probabilistically, the probability of throwing any number of dots is 1/6. The probability of a set of n consecutive sixes equals
if the outcome of the coin flips is independent. For example, the probability of observing 5 consecutive sixes is (1/6)5 or 0.013%. However, the probability that the next throw of the dice will yield a 6 remains 1/6. Similarly, in the case we are keeping track on heads and tails of a fair coin, a streak of heads might cause you to think that ‘tails are due’. But again, the same principles apply. The likelihood of heads with the next flip is 50%.
Examples in finance
Investors might be tempted to expect a reversal in stock prices when they have been declining for a considerable amount of time. While reversals do occur, investors expect reversals to occur more frequently than actually happens.
Similarly, investment strategists and economists that provide market outlooks are tempted to predict reversals when current market conditions have not changed for a considerable period of time. Although bull and bear markets occur, market participants forecast more of such instances than actually occur.