I think this explanation makes the most sense, since it explains the non-independence of the player's actions. Another way I thought of it was this: imagine (de

I think this explanation makes the most sense, since it explains the non-independence of the player's actions. Another way I thought of it was this: imagine (despite the prisoners' knowledge) each prisoner actually had the same number. The "choose at random" strategy would still have a vanishingly small probably of success, while (any) deterministic strategy would yield a 50% rate of group success.