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A comment on Seven Puzzles You Think You Must Not Have Heard Correctly (2006) [pdf]. Parent comment

Re:Seven Puzzles You Think You Must Not Have Heard Correctly... by posterboy on Monday August 29, 2016 @08:46PM (#12386571)
Numbered Hats: Are the guesses secret?

Colored Hats:

The first one makes a sacrifice and says the color of the next hat. He has a 0.5 chance. The next person thus has a chance of 1. The third has to make a sacrifice again. Naively that is an average 0.75 chance over all. An exact calculation is too complicated for my taste.

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Re:Seven Puzzles You Think You Must Not Have Heard Correctly... by twhb on Monday August 29, 2016 @09:25PM (#12386754)
Numbered hats: yes, they don't hear what the others guess. Of course, they could still "know", if they'd agreed upon guesses beforehand.

Colored hats: true, but you can do better than 75%-ish.

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