Exposing the Gambler’s Fallacy

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Emily Tan Tuesday, October 17, 2017

So you have flipped a coin six times and it has landed on heads each time, if you were to bet on either heads or tails for the next flip which would you choose? Tails of course! Or what if you are at the roulette table where you have witnessed black roll in seven times? What would you bet on next, red or black? Again, you would go with red right? You simply cannot believe that this run of results can continue as surely the odds would suggest otherwise.

That above, is the Gambler’s Fallacy in a nutshell!

The Gambler’s Fallacy is where a gambler is of the belief that if something occurs a lot more or a lot less frequently than usual, then the odds of the opposite occurring in the future are decreased.

Many gamblers are unable to understand the statistical independence of a fair game. They mistakenly believe that they can predict what will happen next based on what has happened in the past. This is not true and despite how amazing a sequence of events may be, there is still the same chance of heads or tails landing again on the very next flip of the coin.

An Example of the Gambler’s Fallacy

There is a well renowned true story of a freak run of results that in many people’s eyes are where the term ‘Gambler’s Fallacy’ came from.

It occurred in 1913 in a Monte Carlo casino with people initially rushing to a roulette table after the last fifteen numbers that rolled in had been black. This led to frantic bets on red as many believed that surely the odds of black continuing to fall were shortened. The black came in a further eight times amid many players doubling up their bets to cover losses.

It is fair to say that the casino made quite a bit of money that night and that many a gambler left with empty pockets and broken hearts!

In games of chance there are still many of us that believe they can predict an outcome from randomness. This is why people still try to use systems on Roulette believing that they can beat the game, or why people try to predict the lottery based on previous results.

The fallacy can also be related to those that believe they or a machine/table is running hot or cold. Many believe that if we go on a run of winning or losing that it has nothing to do with probability and that we are just hot or cold. This of course is just silly, as the sequences that probability throws up are just random and have nothing to do with luck or superstition.

Common Phrases

The Gambler’s Fallacy can be found everywhere and you will have probably heard or believed some of the most common phrases yourself.

  • “I flipped a coin five times and it was tails each time, this means that the next flip has to have more chance of landing heads next time around”

This is never the case as each flip will have the same 50/50 chance of landing either way despite how many flips have shown the same result in a sequence. You are just as likely to see another tails as you are a heads.

  • “Red 21 just rolled in last time around on roulette, so I will not be betting on that to come in a second time in a row!”

Again, just because a number already came in on the previous spin, it does not reduce the chances of it coming in again on the next one. The odds of each spin stay the same despite previous results. You might think that it is unlikely that the same number will come in twice but it has the same chance as any other number.

  • “I would never play the lottery with the numbers 1, 2, 3 , 4, 5, 6, 7 as that is just stupid as this combination has no chance of coming in”

Well actually, it does have a chance. In fact it has the very same chance as any other combination of numbers that you can choose from. We fool ourselves into believing that a sequence of numbers like this will have larger odds and are very unlikely to come in.

This fallacy can also be attributed away from gambling as well. How many times have you bemoaned waiting a long time for a bus to arrive only for two to come at the same time? How many times have you said to yourself “I knew I should not have had that last drink” after it has tipped you over the edge?

Things happen in life through randomness and there is no way that we can predict anything from past experiences. Life just happens! The two buses did not show up at the same time purposely and there was no way that you ‘knew’ you should not have had the last drink because if you did, you would not have had it!

Forget the Fallacy and Treat Chance For What it Is

If we can understand that games of chance are exactly that and nothing else, we will probably be able to accept defeat a lot easier and be more realistic in victory. We need to just accept that there are no systems, no methods to predict, and no shortcuts around games of chance and that we must simply hope that the randomness will come our way.

There is nothing wrong with being a bit superstitious but there is no evidence to suggest that superstition plays a part in anything at all. Until there is, we have to accept that a game of fair chance is always going to be random no matter how many freak sequences might occur.