three prisoners, paradox of

There are three prisoners, Archie, Bertha, and you, in the unfortunate situation of knowing that two of you will be executed in the morning. In the night you ask the guard if he can give you the name of one of the others who will be executed. ‘OK’, he replies, ‘Archie will.’ Looked at one way this is good news: it is now either Archie and Bertha, or Archie and you, so your chances have diminished from 2/3 to ½. But looked at another way it is not significant news at all: you already knew that the guard could truly name one of the others, and it does not affect your chances whether he names Archie or Bertha. The problem bears some relation to the Monty Hall problem : it would certainly be worthwhile swapping places with Bertha after this event, suggesting that your chances have, unfortunately, remained at 2/3.

Philosophy dictionary. . 2011.

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