Itai Zukerman posted an interesting solution to the Three Prisoners with Skullcaps puzzle (in response to Gerrymandering Probability — the post with the solution). Apparently comments don’t support tables, so I’m posting a response here with a table laying it out:
|White||White||White||Groucho guesses White, others pass||Win|
|White||White||Black||Chico guesses White, others pass||Win|
|White||Black||White||Harpo guesses White, others pass||Win|
|White||Black||Black||Groucho guesses Black,
Chico guesses White,
Harpo guesses White
|Black||White||White||Groucho guesses White,
Chico guesses Black,
Harpo guesses Black
|Black||White||Black||Harpo guesses Black, others pass||Win|
|Black||Black||White||Chico guesses Black, others pass||Win|
|Black||Black||Black||Groucho guesses Black, others pass||Win|
So the outcome is the same as the solution I proposed: there are six correct guesses “cracked” among six scenarios for six wins overall, and six incorrect guesses “packed” into two scenarios for two losses overall.
I wonder how many other ways the prisoners can plan to accomplish the same thing.