Gambler's fallacy

13 Jan 2023

I could insert a dictionary definition here of what gambler's fallacy is to kick start this article but that would be no fun. Gambler's fallacy is the mistaken belief that if an event we're to happen more frequently prior to that moment in time, it will now become less frequent from that point on-wards and vice versa. Essentially, if you were to take a coin flip, the realistic outcomes are heads and tails, if it lands heads 5 times in a row then someone with gambler's fallacy would think it is more likely to land tails next. This is in fact untrue. It is the fact of the matter that the previous outcomes do not affect this roll.

It is common for people to assume something that is 50/50 will have an identical outcome when played a certain amount of times. The more cycles, the more accurate as the percentage difference becomes minimal. For instance if you repeat it 10 times and heads happened once more than tails then you will have 6 heads and 4 tails, whereas if you repeated it 1000 times and had one more head than tails, you will have 501 heads and 499 tails. As a ratio, doing it 1000 times over will give you a much closer representation of the 50% than only only doing it 10 times.

But if it's going to trend towards a 50/50 distribution shouldn't I keep going until it reaches that?

NO. If you were to start a game involving a coin toss and plan to play it 100 times, you can EXPECT that 50 will be heads and 50 will be tails. If the first 16 flips show 11 heads and 5 tails, you will have 16 rolls used and 84 to go. If you had favoured tails in your bet, you would be dissatisfied and will want to chase your loss with the mentality that it will even out to 50/50 if you play it out long enough. This is false thinking and I will show you why. If we are to go under the assumption of expected values as the most correct way to determine an outcome, if 16 coins have been flipped out of 100, we had 11 heads and 5 tails. The assumption might have been if we play 84 more times, we will even out to 50 heads and 50 tails. However in actuality, when you roll 84 more times, you will expect 42 heads and 42 tails which will become an end result of 53 heads and 47 tails. Thus, with the expected value of the next 84 flips, you are still in the same position of having lost 6 more flips than you won and still being down the same amount of money.

Gamble smart not hard!

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