Kind of a weird question to phrase… I understand the probability of winning each game is 25%, but does your overall probability/likelihood for success on the next trial increase each time you fail?
If I ran 10 trials with a 25% chance to win, but lost all 10, does the overall probability for a successful trial increase? I understand that per trial it makes no difference. But theoretically do you become "due for a win" at some point?
The way I am making sense of it is you have a 25% chance to win, the 25% chance has to (well, doesn't HAVE TO, but should) hit eventually, and the longer the period that it doesn't hit, the more likely it should hit.
Thanks
Best Answer
No, the likelihood does not increase, provided the trials are independent. The belief that it does is known as the gambler's fallacy.
To quote Wikipedia, "The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the erroneous belief that if a particular event occurs more frequently than normal during the past it is less likely to happen in the future (or vice versa), when it has otherwise been established that the probability of such events does not depend on what has happened in the past."