What is Gambler’s Fallacy

To make the whole thing look really simple, let’s use the coin toss example. It is not a secret that the chances of getting tails or heads are equal. Bernoulli found that as the number of tosses gets bigger, the probability of getting either side come closer to 50%, moreover the difference between the number of tails and head gets bigger as well.

That is that last part that gets people confused. It got so popular and common among gamblers that it even got itself its own name - Gambler’s Fallacy. If, for example, it happened that the coin’s landed tails up 10 times in a row, the most common prediction would be that the heads will land next. Such a statement by default is incorrect, due to the fact that coin has no memory of its landings and the possibility of each side facing up is 50%.

The discovery showed that a really big sample (ex. a million occurrences) will lead to the distribution of heads and tails to even up to around 50%. Due to the size of the sample, the deviation from an equal 50/50 split should be as much as 500.

The following calculation can help you to understand the theory better:

0.5 × √ (1,000,000) = 500

You would wonder if the probability is still 50% and the deviation is 500 then how do you get 10 tails in a row. It is said that the sample of 10 occurrences is too small to even out like in case of the 1,000,000,000. It is all the pure chance, and such a small sample should be treated just like an extract from a bigger one.

The theory finds its application in betting quite often. The best example, though, would be the casino. That’s where the theory gets its second name, Monte Carlo fallacy, from. Gamblers who truly believe that the sequences of red & black or even & odd will even out during just one sitting usually end up with empty pockets.

Let’s use another exceptional example here. In 1913, the Monte Carlo casino table witnessed, probably the longest same colour steak in the history of gambling. The ball has landed in the black cell 26 times in a row. Bettors started getting crazy after the 15th attempt going all in due to the false expectation of the red cell having enormous chances of being next. This just shows irrational is the belief of spins having an influence on one another.

Most common errors committed by punters.

Another excellent gambling example is slot machines. These machines generate random numbers with a set RTP (Return to Player). It is not a surprise to see someone wasting tons of money in front of those, thinking they are about to hit the jackpot. Usually, such players would encourage the next people to go harder because of the high possibility of the RTP coming soon (to their mind). Again, for such a claim to be accurate, there has to be an unfeasibly large number of tries.  

Just keep that in mind and do not overthink the chances of something happening.