Monty Hall

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Monty Hall was the host for Let's Make A Deal, a game show in the United States starting waayyy back in 1963. The show's final stage was The Big Deal, featuring three doors. Hall's iconic catchphrase was "let's look at what's behind Door Number [positive integer]!".

Hall co-produced L[u]MaD with one Stefan Hatos, and served as host for Three. Whole. Decades. So Hall's name became synonymous with the show itself: as witness, the game-theorist Steve Selvin, who in 1975 published a logical problem to the American Statistician as "The Monty Hall problem" rather than as "the LuMaD problem" or even "the TBD problem".

Anyway, /tg/ relevance is that LuMaD was, in fact, a game, even if a /tv/ hosted game; it has game-theory in it.

As role-playing games go, a party will - somewhere - come across a door in the corridor which may host a trap or may host a treasure, or a monster, or all three. A well-designed dungeon will apportion these in accordance with the plot, preferably also foreshadowing which door goes what way. Against that Q1: Queen of the Demonweb Pits is a notorious offender - it is Monty Hall design.

Gary Gygax, with the benefit of hindsight, came to disown "Monty Haul" design, wherein the special door might have too much treasure, which the DM couldn't easily take away from the players, thus unbalancing the game.

In 1990, a mathematician named Marilyn vos Savant received a question in Selvin's vein, to which she claimed that you should switch your choice after one of the doors got opened. She got a lot of rage for her answer by a bunch of people who called bullshit. Somehow, Selvin is correct; the math is hard to explain, so it's best to just look at this table and take her word for it--other than to point out that this is one of those problems that rely very heavily on how the rules of the game are laid out.