The Monty Hall problem is a famed mathematical puzzle whose name derives from the host of the game show Let’s Make A Deal. Fair warning: there is a little bit of math ahead.
The Monty Hall problem is this: A person has three doors and is told that a prize resides behind one of them. They are allowed to pick a door, and claim whatever is on the other side. Then, from the remaining two doors, one which contains nothing behind it is opened, leaving the contestant with their original door or the remaining unopened alternate. They are then given the opportunity to switch. Should they?
The answer is yes. No matter how the probabilities may seem to change when the empty door is opened, the initial choice gave them a 1/3 chance in choosing correctly and a 2/3 chance the prize is behind one of the other two doors. That probability still hasn’t changed. The appearance of it being a 50/50 chance is false, because the “empty” door wasn’t chosen at random… it was selected by the host, who knows behind which door the prize lurks.
Sticking with your original choice gives you a 1/3 chance of winning. Changing gives you a 2/3 chance. It’s counter-intuitive, but the math works, and it bears out in real life testing.
But let’s be honest: we all can’t be Monty Hall… although Wayne Brady makes a very genial replacement. So this week, I’ve decided to try to step up and give some other game shows and game show hosts an even playing field. Even if they don’t get the cool math conundrum, they can at least get their own defining questions.
The Bob Barker (The Price Is Right) Problem – How often can you encourage people to spay and neuter their pets before you walk out of your dressing room to find your bodyguard on the ground and Fluffy and Fido wielding shanks?
The Alex Trebek (Jeopardy!) Problem – How simple can you make the Celebrity Week questions without insulting the audience?
The Gene Rayburn (Match Game) Problem – If Betty White takes four glasses of wine to get drunk, Nipsey Russell has trouble staying upright after seven beers, Charles Nelson Reilly brings white wine spritzers with him before the open bar starts and Richard Dawson drinks straight from a bottle of Jack Daniels, how many episodes can you tape before someone passes out?
The Pat Sajak (Wheel of Fortune) Problem – Should he let people forget the Pat Sajak Show and let himself seem like a one-hit wonder, or remind them of it and risk them recalling that he let Limbaugh guest-host?
The Richard Dawson (Family Feud) Problem – Are there more women who brag to their descendants that they were kissed on television by Dawson, or grandchildren who tell people that their grandmothers were “sexually assaulted” by a kiss from him?
The Donald Trump (The Apprentice) Problem – If someone’s signed a non-disclosure agreement about you in order to have their statements edited and publicly aired, does the release of some of those statements negate the NDA? (Interestingly, this is the only one of these problems likely to be settled in a court of law.)
Okay, there are a LOT more problems with Donald Trump than that one. But, to be fair, I’m feeling a bit sick and the notion of considering Trump’s issues just makes me more ill. So I’m taking a pass on any others.
If anyone wishes to kick in problems for other hosts, or alternates for the ones I’ve presented, that’s what the comments are for.