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Unfortunately while this applies to (fair) coin tosses, it does not apply to the normal situations statistics is applied to. For example. Suppose you have bad

Unfortunately while this applies to (fair) coin tosses, it does not apply to the normal situations statistics is applied to. For example. Suppose you have bad thing X. Homelessness, soil pollution, ... whatever. You measure it. It's bad. You have policy Y. You want to know if policy Y improved X. You measure it again. The measurement is better. Did X improve? Correct answer is: you don't know! The problem: suppose policy Y is "fake measurement X". Then it's obvious why X didn't improve. If you think about it, you'll quickly realise: X and Y need to be independent. But Y was a response to measuring X! They cannot ever be independent! The very existence of policy Y is dependent on X! So the standard way statistics is used, to measure something, then make changes to improve it ... is a fallacy. Exactly because it causes the gambler's fallacy to not apply anymore! The gambler's fallacy only applies to situations where successive measurements are independent. And if you actually use your statistical measurement, well that's an excellent way to make successive measurements dependent, and makes measurements invalid.

jollybean 5y ago
In situations where we don't know the probabilities, the 'Gambler's Fallacy' cannot apply.
- dragonwriter 5y ago
  Gambler's fallacy applies if we know events are independent even if we don't know probabilities. Of course, when we don't know the baseline probabilities, its possible that updating one’s prior in the opposite direction of the experienced results ends up accidentally getting the right estimate are some point before heading off in the wrong direction, but that's a “right answer by wrong logic” coincidence, not Gambler's Fallacy failing to be wrong.
  - candiodari 5y ago
    ... which is the point I'm making. If you measure something, then create a policy to change the thing you measure, then measure it again. At that point measurement and policy are designed to be dependent on each other. If the measurement had given a different outcome the policy would have never seen the light of day. You can't get much more dependent than that. Stating these are independent is like saying your parents had nothing to do with your birth. And if you will allow me a different statistical fallacy: this is 99.9% of what we do with statistics. You can measure once, then change things. Then you can never measure the same thing again. Stating "we saw 5% unemployment, then did policy X, now we see 4% unemployment. Success!" ... that's mathematically wrong and a statistical fallacy. The issue is: this is how government is run.

jollybean 5y ago

In situations where we don't know the probabilities, the 'Gambler's Fallacy' cannot apply.

dragonwriter 5y ago
Gambler's fallacy applies if we know events are independent even if we don't know probabilities. Of course, when we don't know the baseline probabilities, its possible that updating one’s prior in the opposite direction of the experienced results ends up accidentally getting the right estimate are some point before heading off in the wrong direction, but that's a “right answer by wrong logic” coincidence, not Gambler's Fallacy failing to be wrong.
- candiodari 5y ago
  ... which is the point I'm making. If you measure something, then create a policy to change the thing you measure, then measure it again. At that point measurement and policy are designed to be dependent on each other. If the measurement had given a different outcome the policy would have never seen the light of day. You can't get much more dependent than that. Stating these are independent is like saying your parents had nothing to do with your birth. And if you will allow me a different statistical fallacy: this is 99.9% of what we do with statistics. You can measure once, then change things. Then you can never measure the same thing again. Stating "we saw 5% unemployment, then did policy X, now we see 4% unemployment. Success!" ... that's mathematically wrong and a statistical fallacy. The issue is: this is how government is run.