If I only have 1 bit of memory space, and the probabilities I am remembering are uniformly distributed from 0 to 1, then the best I can do is remember if the chance is > 1⁄2.
And then a year later, all I know is that the chance is >1/2, but otherwise uniform. So average value is 3⁄4.
The limited memory does imply lower performance than unlimited memory.
And yes, when was in a pub quiz, I was going “I think it’s this option, but I’m not sure” quite a lot.
But if I only remember the most significant bit, I am going to treat it more like 25%/75% as opposed to 0⁄1
So if one day you decided that P of X ≈ 1, you would remember “it’s true but I’m not sure” after one year?
If I only have 1 bit of memory space, and the probabilities I am remembering are uniformly distributed from 0 to 1, then the best I can do is remember if the chance is > 1⁄2.
And then a year later, all I know is that the chance is >1/2, but otherwise uniform. So average value is 3⁄4.
The limited memory does imply lower performance than unlimited memory.
And yes, when was in a pub quiz, I was going “I think it’s this option, but I’m not sure” quite a lot.