Gambler’s Fallacy Vs Hot Hand Belief

The gambler’s fallacy and the hot hand belief really are connected to one another in the same way yin is connected to yang. We could even go as far as to say that the gambler’s fallacy is the positive to the hot hand belief’s negative. Both have however been classified by popular gambling psychology as examples of flawed human misperception.

The interesting bit though, is that some mathematicians have started to argue that there may be some truth in the principle behind the gambler’s fallacy, even if not quite for the same reason as would believe the superstitious gambler.

But first, let’s focus on what each of these entail.

The Gambler’s Fallacy Explained

When a fair coin with equal probabilities of coming up head and tail is tossed repeatedly, the laws of science dictate that the expected outcome should be exactly that: equal probability. Players leaning toward the gambler’s fallacy however believe that once any one of the two results happen to experience a repeat-streak, the chance of the opposite result coming up becomes better and better with every following toss of the coin.

In simple language: if heads were to fall 7 times in a row, then a tails-result becomes more and more likely with every subsequent toss of the coin. The gambler’s fallacy then, relies on the theory that past events somehow have an influence on future outcomes – a theory very much debunked by the laws of equal probabilities whenever a ‘fair coin’ is in play.

Which brings us to the opposite side of our own coin: the hot hand belief.

Hot Hands And Winning Streaks

Those who lean more toward the hot hand belief, are convinced of the existence of what gamblers often refer to as ‘winning streaks’. The player convinced of the existence of hot hands will instead of expecting an opposite result, rather lean toward the belief in a hot hand or winning streak, i.e. a recurring result.

The debate over the validity of the hot hand belief from a statistical point of view has been raging on for more than 30 years. Mathematicians are divided over whether or not there may be more to the hot hand belief that what meets the eye. Unlike ‘hot streak’ superstitions however, mathematicians base their opinions on an evaluation of human performance. For e.g., a person tossing a coin would be likely to toss the coin in a consistent style and at a consistent velocity. Or in other words, since how high a coin is tossed may determine the number of rotations before coming back down to land and show a result may actually influence the head vs tails outcome, one person repeatedly tossing the coin may be more likely to hit a hot streak (i.e. a string of similar results), than if that person were to be intermittently relieved by a second flipper of the same coin.