I’d probably broaden this beyond 1⁄2 - I think the base case is the host gives you a chance to gamble with a question or test of skill, and the result is purely dependent on the player. The swap-box scenario is then an extreme case of that where the result depends less and less on the skill of the player, eventually reaching 50% chance of winning. I wouldn’t say evolutionary-optimised, but maybe familiarity with the game-show tropes being somewhere along this scale.
Monty Hall is then a twist on this extreme case, which pattern-matches to the more common 50% case with no allowance for the effect of the host’s knowledge.
I’d probably broaden this beyond 1⁄2 - I think the base case is the host gives you a chance to gamble with a question or test of skill, and the result is purely dependent on the player. The swap-box scenario is then an extreme case of that where the result depends less and less on the skill of the player, eventually reaching 50% chance of winning. I wouldn’t say evolutionary-optimised, but maybe familiarity with the game-show tropes being somewhere along this scale.
Monty Hall is then a twist on this extreme case, which pattern-matches to the more common 50% case with no allowance for the effect of the host’s knowledge.