The Problem of Evil: Almost Solved
I have to ask Ricochet's patience in waiting for my father's adjudication of the weekend contest. Unsurprisingly--to his daughter, anyway--he got caught up in figuring out which door to open for the prize. He sent me his argument, asking that I look it over carefully to see if there were any obvious errors in his reasoning before I posted it. He would, he promised, get to the problem of evil next.
Thing is, my phone rang last night at two in the morning. Whoever it was hung up, but I couldn't fall back asleep, not even with the help of the most boring book in my library. Then I fell into the insomnia trap, you know the one: If you don't fall asleep, you'll be unable to think straight tomorrow. The second you start worrying about that, it's a done deal.
Anyway, switch, stay, democracy, anarchy, good, evil, the future of the Middle East, counting beyond five--all I can say is thank God I'm not scheduled to do live radio. Or perform a craniotomy. I'll get some rest, figure out which door to open, then we can solve the problem of the problem of evil.
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Aug '10
Re: The Problem of Evil: Almost Solved
Could be worse. We could be trying to figure out if Let's Make A Deal style door games are evil, or merely showmanship.
Is tempting a contestant with the promise of a bigger prize morally wrong? Has the contestant sinned if he gives in to greed? Do atheists on game shows pray for divine wisdom to guess correctly?
Jan '11
Re: The Problem of Evil: Almost Solved
Sorry, wrong number.
Mar '11
Re: The Problem of Evil: Almost Solved
Claire, you need to keep a proper collection of boring books around for such situations.
A Government as Good as Its People by Jimmy Carter works for me, and it's still in print, although only God and the University of Arkansas Press know why.
Jul '10
Re: The Problem of Evil: Almost Solved
And Here I sat all weekend in a pink dress, face paint, and holding a parasol waiting to get picked as a contestant when all I had to do was join in the conversation... come to find out.... the dress wasn't all that uncomfortable....
Oct '10
Re: The Problem of Evil: Almost Solved
It's OK, Claire - we know you're secretly working on a 100-page response to Romney's foreign policy white paper, together with brief biographical sketches of his advisory team, concentrating on the history of the MEK and Phalange...
Apr '11
Re: The Problem of Evil: Almost Solved
If your father had stuck to his last, he'd have found an adequate explanation of the Monty Hall Problem in DocJay's post #3. I sure he would not have been misled by the added stipulations in #11.
Edited on Oct 10, 2011 at 9:03amMay '10
Re: The Problem of Evil: Almost Solved
DocJay was exactly right in his post #3, but only under the conditions stated by Don Hanson in post #11. (That is, assuming Claire's Skylark had an equal chance of being behind any of the doors, and that whatever door you pick, she will always open door that reveals a badge.)
I have demonstrated that game to my relatives using playing cards ("find the face card") using up to 15 cards. It is easily shown that you ought to switch. The more doors/cards, the greater the payoff by switching.
Edited on Oct 10, 2011 at 8:29pmJun '10
Re: The Problem of Evil: Almost Solved
The clearest explanation of the problem is that 2 times out of three the prize will be behind a door you don't pick, and 1 time out of 3 it will be behind the door you pick.
If after you pick a door you are shown a goat prize (the host can never show you the prize else he only confirms your loss, so intent is unimportant) behind one of the doors you didn't pick, you are 100% certain to capture a 2/3 probability by switching your choice. To prove this so we go back to the first sentence in the post, which reads "…2 times out of 3 the prize will be behind the door you don't pick."
Do nothing and the probability of winning is 1 in 3, because probability can never exceed 1 (2/3 + 1/3 = 3/3 or 1),
Edited on Oct 10, 2011 at 10:04amJun '10
Re: The Problem of Evil: Almost Solved
I would only add that the probability of your winning will never be fifty-fifty. The probability that the prize may be behind one of the unopened doors is fifty-fifty, but the chances of you winning the game remain either 1 in 3 if you don't change or 2 in 3 if you do.
Apr '11
Re: The Problem of Evil: Almost Solved
Uh-unh. It doesn't matter what Claire knows, because 1) it doesn't change where the car is and 2) it doesn't change what I know. All I know is that the two-member subset has twice the chance of containing the car as my one-member subset, and if I can get some of those better odds, I should.
The Let's Make a Deal scenario is equivalent to saying "You can trade what's behind your one door for what's behind both the other two doors, and, btw, there's a badge here". But that isn't new information; I already knew one of the two doors hid a badge. Claire's knowledge just ensures that a non-car door is opened: showbiz distraction. I should always trade one chance to win for two chances.
Edited on Oct 10, 2011 at 6:28pmMay '10
Re: The Problem of Evil: Almost Solved
Grendel
Uh-unh. It doesn't matter what Claire knows, because 1) it doesn't change where the car is and 2) it doesn't change what I know.
The only reason it matters what Claire knows is so she makes sure to eliminate (by opening) a badge door. That is DocJay's #1 and #2 condensed into a single stipulation. The whole thing breaks down if Claire might remove the car from play.