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Monimonika18 t1_ja91klv wrote

Reply to comment by johrnjohrn in ELI5: why does/doesn’t probability increase when done multiple times? by Reason-Local

Because "not 6" is 5 times more likely to happen than 6 on a six sided die in a single throw. You're focusing on the one combination result that is 6 for all 1000 dice rolled and comparing it to the many combinations that are not that one single very specific result you want.

If the billionaire gave you a die to roll 1000 times to get a single specific order of numbers like "123545453621145..." you'd still have the same horrible odds of getting that one result.

Now if it were 1000 die to roll and the result must be all 6s except one single roll anywhere among the 1000 rolls, your odds of getting that goes up because there are more than 1 results that match that criteria.

Make it must get only one 6 anywhere out of 1000 throws/die while the rest are not 6 and your odds are much better because there are even more results that match that criteria.

Going back, if you had already thrown all 6s for 999 throws and you only have to throw the last die, your chances are 1/6 because the result you want is 1 out of 6 results now. The more 6s you got, the probability of getting the rest of the throws as 6s went up because there are less possible results available for the rest of the row of throws. Up until you achieve all 6s, at which point the probability is now 1 out of 1.

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johrnjohrn t1_ja92xlc wrote

Indeed, you have repeated the part I already understand, but it feels like saying that, "The probability that I could transform into a duck are the same in this moment that they were 10 seconds ago according to quantum physics". At some point it seems that a certain number of throws in a row would force us to consider things differently. If I did indeed turn into a duck, folks would not shrug that off as a quantum possibility, even if highly improbable. Hypothetically, if you had one quintillion throws in a row, you would have a team of scientists on the scene and it would make international news. Nobody would ever shrug that off and say "ah well, the probability of the next roll doesn't change." At that point, all involved scientists and statisticians and any interested parties would effectively be falling victim to the gamblers fallacy, but it still seems to make sense that they would, right?

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atheism-blocker101 t1_ja99500 wrote

I feel bad for you because I 100% think the exact same way as you do about this and am second-hand frustrated that nobody has dealt with your actual point

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johrnjohrn t1_ja9a36l wrote

Thanks for validating. I empathize with the math. When it comes to casinos or whatever, there are likely strings that will come out of any number of dice throws, but you bet your ass that at some point the pit bosses will start watching closely, never dismissing the lead up to this point. At some point the manager is called in from off duty. At some point the game is shut down. The gambler can't just get away with saying, "But each roll has an independent probability!" No, the casino crew has now "fallen victim to the gamblers fallacy". But inherently, we understand they haven't. They have made a reasonable decision that they can't afford that person throwing the dice one more time. But what was the point of shutting it down if the dice were fair and any number of gamblers could start doing the same thing on any other number of tables? Do all casinos just shut down forever, therefore falling victim to some version of the fallacy?

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