Monty Hall

This article or section is about a topic that is particularly prone to Skub (that is, really loud and/or stupid arguments). Edit at your own risk, and read with a grain of salt, as skubby subjects have a bad habit of causing stupid, even in neutrals trying to summarize the situation. In Particular: The math problem.

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 (to quote a famous line, "A Gygaxian dungeon is like the world's most fucked up game show. Behind door number one: INSTANT DEATH! Behind door number 2: A magic crown! Behind door number 3: ten pounds of sugar being guarded by six giant KILLER BEES!"). 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.

Monty Hall Problem

Based on (a common misunderstanding of) the LMaD finale, the Monty Hall Problem goes like this: Monty Hall presents you with three doors, one door hiding the treasure and two doors hiding goats. You pick one door, but that door doesn't open yet, Monty opens one of the goat doors instead. Now Monty asks you, do you want to swap your first pick with the other closed door? (This exact situation never showed up on LMaD, it comes from an 1889 puzzle book and got conflated with Monty Hall much later)

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; just remember that this is one of those problems that rely very heavily on how the rules of the game are laid out.

In more detail:

1. If you're presented with three doors in a blind pick and asked "which door has the treasure?" you have a 1 in 3 chance of being right. The second question "do you want to change your pick?" is, statistically, the same as asking "was your first pick wrong?" And yes, there's a 2 in 3 chance your first pick was wrong.
2. That being said, the problem, as usually written up, leaves open the possibility that the host only offers you the chance if you selected the correct door, sometimes known as the "Evil Monty" scenario; since most versions of the problem unintentionally leave open this possibility, we're left, much like the "third word in the english language ending in -gry" riddle, with only the option of cutting off the arm of the person who asked the question as a correct answer.