The Gambler’s Fallacy

The words ‘Gamblers Fallacy’ or the ‘Monte Carlo fallacy’ as it’s also known, has been tied with myth for centuries. This term refers to the belief that previous results can somehow have an impact on the results to come. To break it down in simple terms, if the coin flip has landed on heads four times in a row, then it’s more likely to land on tales on the next flip. The Gamblers Fallacy has been something that has influenced bets across many casino games, but most notably, roulette. The idea of thinking is that the odds of the ball landing on black will be higher, as the ball has already landed on red on the last five spins. It’s a common belief, but It’s a belief that goes against the laws of probability.

The laws of probability

The idea behind the laws of probability in gambling is that anything can happen, at any time. So, a sequence of past outcomes cannot have an impact of future outcomes. This idea has been named as ‘the maturity of chances’ which assumes a play in the game is connected with other events and therefore can dictate play. But, for any action, the probability of all possible results is simply, one. This means of balancing nature is nothing but random results, completely independent of any previous results.

This comes down to the thinking of the human mind. It’s a thought that can come into action in many practical situations, but it’s most strongly associated with gambling, where luck is everything. In reality, there is no such thing as luck, but it’s a thought that strongly influences decisions made when gambling. Games like roulette and baccarat are common with the gambling fallacy, players will side with a hand, colour or whatever the gamble based on the previous results. The Gamblers Fallacy is engrained in the gambling psyche – because it seems counter-intuitive.

Is it a theory that has some truth?

Some sequences of results may be more likely to appear than other, but there are no guarantees and anything can happen. A coin toss is 50/50 but the chances of landing heads four time in a row is very possible, actually, the chances of that happening are not that low.

The odds for this are 1/2 x 1/2 x 1/2 x 1/2 = 1/16 (or 0.0625 or 6.25% or 15-1).

The odds against this are 15/16 (or 0.9375 or 93.75% or 1-15)

This 1 in 16 probability is what influences many gamblers into thinking that results can be influenced by previous results. Before the coin is even tossed, the odds against landing four heads in a row is 1/16. After three tosses of the coin, the human temptation is to think that because it’s landed three times that the next toss of landing on tails is 15/16.

Let’s put it in layman’s terms, the chances of landing twenty tails consecutively are 1,048,576, that’s over a million to one. If you toss nineteen tails and you need to place a wager of £1000 on the next toss being heads, would your gambling mind tell you that the odds are a million to one in your favour, or 1 in 2? It’s 1 in 2 because coin tosses, roulette spins and card hands don’t have any memory and the past does not influence the present. The Gamblers Fallacy can be a costly truth if you believe previous results can sway future ones.

The Monte Carlo fallacy

This theory is also known as the Monte Carlo fallacy, it’s named after the principality’s Le Grande Casino, on the night of August 18, 1913. The roulette ball landed on the colour black 29 times in a row, a probability that is close to 1 in 136,823,184. This series of play became iconic of the Gamblers Fallacy because a huge amount of money was lost, this is because so many players believed that red would surely land on the next spin of the wheel. More and more money went down on the table after the black landed ten times in a row and then even more after the fifteenth and even more after the twentieth because players believed the odds were no longer close to 50/50. In truth, the odds of red or black landing never changed. By the end of the night, Le Grande’s casino were over ten million francs richer and most gamblers at the roulette table that night were left with empty pockets.

The law of numbers, big numbers

The law of numbers shows that the more coin toss outcomes, the results, according to basic odds will even out. So, a million coin tosses, in theory would balance the number of heads and tales. If you toss a coin 100 times, there is no reason why the first 50 tosses can’t land on heads. Of course, this is unlikely but the point is each toss of the coin resets to 50/50. It’s random distribution that flaws the reasoning behind the Gambler’s Fallacy.

The fall of the fallacy

These are the fallacies that drive bad investments and strategies, believing in trends that are based on chance has no positive influence or any reasonable outcome. It simply comes down to, nobody knows anything. In gambling, chances are set by the laws of mathematics. But dice can be weighted, roulette wheels can be rigged and cards can be marked. Simply said, anything can happen.