[treis]

The success criteria goes from the prisoners randomly picking correctly to the warden not randomly creating a loop larger than 50. If the warden creates no loop greater than 50 then the prisoners win. If he creates one of 51 or more then the prisoners lose because the 51st number wont be found.

[MrBuddyCasino]

That was the shortest description that worked for me. Framed this way, its obvious - thanks, also to all the others!