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What is the probability of getting Heads?’ This question tells you the result of the first coin flip and asks you for the probability of the second coin flip being Heads. Now let’s say that I flipped another Unbiased Coin with Heads on one side and Tails on the other (directly after that one). My exact words were ‘Let’s say that, in this case, the result of this coin flip was Heads. But I didn’t ask you what the probability of getting Heads twice in a row were. If you got it wrong then I’m willing to bet that you asked yourself what the probability of getting Heads twice in a row is (to which the answer is 25%). The issue people tend to have is that they consider all the information they have and link it all together.
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Why you may have thought the answer was 25% Regardless of what result the first coin flip produced, there are only 2 possible outcomes for flipping a coin: Heads and Tails and, as we established earlier, the odds of getting either Heads or Tails on an Unbiased Coin with Heads on one side and Tails on the other are 50% both ways. If you didn’t think it was either of these answers… then I am sorry to say that you are not very good at Mathematics. If you thought it was 25% then you made the same common error that most people make. If you thought it was 50% then congratulations! You understand statistics or were able to guess the result by judging the direction this post was going (in which case you get a cookie). The odds of the second coin landing on Heads are: What is the probability of getting Heads? (If you are interested in taking part in this experiment then do not read the next paragraph before you choose your answer). Let’s say that, in this case, the result of this coin flip was Heads. The odds of you getting Heads are 50% and the odds of you getting Tails are also 50%. Let’s say, for example that you flip an Unbiased Coin that has Heads on one side and Tails on the other. I would like to point out that The Gambler’s Fallacy only applies to situations where the outcome is truly random. Regardless of what result was obtained prior, you are not any more likely to achieve a different result. The Gambler’s Fallacy is defined as the common misconception that if you achieve any one outcome more frequently than another, it makes the other outcome more likely as a result. I tried to explain that they were wrong but they wouldn’t listen (still won by some miracle).įirstly, I’d like to clarify that the above situation is mathematically ridiculous. The reason was because I had gone 4 games without being a Fascist. Now my friends were convinced that I was a Fascist in the 5 th game with no supporting evidence. In the games of Secret Hitler I have been playing with my friends, there was a streak of 5 games where I was a ‘Liberal’ and not a ‘Fascist’ (these are roles in the game). It’s a really cool game and I might cover it in a future post but for now I’d like to explain the trouble my friends seem to be having with The Gambler’s Fallacy. This is a short post that I decided to make because I have been playing a game called ‘Secret Hitler’ by the makers of Cards Against Humanity with my friends recently.