douglasm wrote:...That's missing the point. No one in this thread is saying "after X losses, the next must be a win". What we're saying is "after X losses, we're pretty sure the game is rigged".
You are pretty sure that the game is rigged BECAUSE you'd have expected at least one win by now, even though, no matter how many flips you do, you're NEVER guaranteed to get a win. The Gambler's fallacy is that, thinking that if you go long enough a win MUST HAVE happened, just because it was very likely to begin with. But every time you lose the chance of losing remains the same, no matter how many flips you do, the next flip will be as likely to lose, there's no n big enough that will ensure at least one win. You could keep getting loses forever because the next time you're flipping the coin it'll be as likely for you to get a loss as it was on your first flip.
They say if you put enough monkeys hitting random keys on a keyboard long enough they'll start writing the bible, the works of Shakespeare, books that will be written in 20 and 100 years in the future, a very detailed description of your life including events yet to come, and a description of how to simulate an universe that includes themselves. What they don't tell you is that, it's also possible that all those monkeys, by pure chance, just keep hitting the space bar forever and you get nothing written. This is also a possibility, because no key that was already hit will make less likely that the space bar will be hit or that any other key will eventually be hit.
That's how pure chance and randomness works, you can't predict the future, and the least likely outcome can still happen because it was still possible.
Cauchy wrote:Yeah, those both sound more plausible. I think you underestimate the unlikeliness of this event.
The actual unlikelihood of the event doesn't matter. I think the discussion was very hurt by having something so extraordinary happening, and I'm sure all the thread would have looked different if we spoke about 8 loses in a row instead of 8000. Let's stop discussing 8000 loses in a row and start discussing a much lower number, one that could make you doubt your prior knowledge, but doesn't make you go "this couldn't be happening."
And now, I'll provide some variation:
In this one, you get amnesia after every flip. That is, you get a result and are told if you won or you lost, and then decide to continue or not. All you know is how much money left do you have, but you don't know if you had more, or less, because of the amnesia.
So, you started with 1000000, and are down to 200000, but you don't know it. For all you know, you could have started with 500 and made a fortune by now.
What I will claim is, if you'd continue playing in this variation, then you should continue playing in the original one.
The thing with the gambler's fallacy is adjusting your beliefs and strategy based on recent events, even though those events have no effect whatsoever on future ones. If you know the coin is 70-30, then you can make a flip and forget it. This time you're not shocked after 8000 loses in a row and suddenly start believing in Santa.