> If I flip a coin 20 times and happen to end up with a 15:5 split that doesn’t mean the chance of heads is 3:1.
Isn't it the best you can say, though? 20 is a small number but when it's all you have, there's nothing you can do about it. Of course we know the "real" probability is a 1/2 because we know how coin tosses work, but if we didn't know it and coin tosses were black boxes, we'd have to go with this 3:1 chance.
The chance of heads being 3:1 is the maximum likelihood estimate, which indeed is the best we can do if we don't know anything else. But usually we do have an idea of reasonable values.
Isn't it the best you can say, though? 20 is a small number but when it's all you have, there's nothing you can do about it. Of course we know the "real" probability is a 1/2 because we know how coin tosses work, but if we didn't know it and coin tosses were black boxes, we'd have to go with this 3:1 chance.