Comment by twoodfin
3 days ago
If I’m trying to guess a 9-letter English word, and test whether the first letter is “x”, there are only the same two answers: Yes/No.
But “Yes” obviously gives me much more than one bit of the information I need to know the answer.
But that "yes" is so unlikely that your expected/average information is still 1 bit or less.
The claim was that one bit was the maximum amount of information you could gain, which is clearly false.
Just to make this unambiguous: If you ask me to guess a number between one and one billion, and by fantastic luck I guess right, your “yes/no” answer obviously gives me more than one bit of information as to the right answer.
> The claim was that one bit was the maximum amount of information you could gain, which is clearly false.
That's not what I see.
https://news.ycombinator.com/item?id=46282343 the expected information (which is the sum of the outcome probability times the outcome information for each of the two possible outcomes) is always less than or equal to one.
The specific comment you replied to had one sentence that didn't say "expected" or "average", but the surrounding sentences and comments give context. The part you objected to was also trying to talk about averages, which makes it not false.
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