Tuesday, May 20, 2014

The Montie Hall Problem

   Let's talk a little about Who Wants to Be a Millionaire?.

   There's the classic game show problem of three doors. Behind one is a (presumably fabulous) prize. Behind the other two are the dreaded ZONKs. You select one door at random, and the host shows you a ZONK behind a door you didn't pick. You had a 1/3 chance of selecting the (presumably fabulous) prize one the first random selection, now there are two doors, and if you select one of them at random you'd have a 50/50 chance for the prize. Meaning, switch that door, you. It's mathematically sound.

   How does this tie into Who Wants to Be a Millionaire? The 50/50 lifeline on Who Wants to Be a Millionaire let's say you chose an answer, but didn't make it your final one.

Unlike here. Ouch.

   You decide not to risk it so early, and select the 50/50 to see if you were on the right track. You were! That's the equivalent of two ZONKs eliminated, right? So, the question is, do the same principles apply here? Would switching tracks, even though you thought you were on the correct path before, yield a more favorable result? It makes sense. There was a 25% chance of the selection of the correct answer, and now there's a 50% chance. That's 50% better odds, or a 37.5% chance over a 25% chance (that's how that works, right? Somebody who knows this stuff correct me if I'm wrong, please.)

   Remember, though, that's only if the answer you thought it was was one of the ones to remain up on the board (once again, there's a 50% chance of that happening.) If it doesn't, then it truly is a 50-50 chance. If there's a 50% chance of there being a 50% chance and a 50% chance of there being a 37.5% chance, then instead of being called 50:50, maybe the lifeline should be called, shoot, 565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656565656. (The cat just stepped on the keyboard there (apparently pressing two keys at the same time types both of them alternating?), but, why not, let's call it that, as it's still numbers, and reminiscent of Who Wants to be a Millionaire?'s $?$?$?.) 43.75:56.25.

   No, but really, pressing two keys at the same time makes them alternate. Try it. And, holding down the shift key while pressing 4 and / at the same time... $?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?$?

   It takes some practice, but it is possible.

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