Question about the movie 21

BB Bobcat · Aug 21, 2008

Rusty Shackleford said:

Here's how I understand it, correct me if I'm wrong.

Your initial door choice only has a 33% chance of being correct. That means it has a 66% chance of being wrong, meaning there's a 66% percent chance one of Monty's doors has the car. On that we can all agree and understand, yes?
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That's a great explanation.

I actually just saw the movie on DVD last week and I had been wondering the same thing. I'm usually pretty good with numbers, especially when in relation to gambling, but that had me confused until reading this thread.

Buck · Aug 21, 2008

I didn't think it was possible to not get this. I need to start a SportsJournalists.com poker game as soon as possible.

By the way, amraeder, that was the perfect explanation.

amraeder · Aug 21, 2008

Easiest way to see it, IMO, is to just play the game out. Gets kinda tricky otherwise.

Diabeetus · Aug 21, 2008

Excellent thread! I'm thoroughly enjoying this wiki article.

Matt1735 · Aug 21, 2008

For gambling explanations and other probability problems, the best site on the web is wizardofodds.com; it's a site run by an actuary named Mike Shackelford and his explanation is actually the one used by amraeder.

http://wizardofodds.com/askthewizard/tvgames.html

Buck · Aug 21, 2008

Mostly a poker site, but has good info about other forms of gaming:
http://www.twoplustwo.com/

Simon_Cowbell · Aug 22, 2008

CentralIllinoisan said:

Just like poker. You fold that gutshot straight draw if the pot odds don't figure a call, but you always wince when it hits. But you will be a more consistent winner if you fold.

In this goat problem, yes, you will be wrong a third of the time. But speaking mathematically, you have to switch.

Take three cards: Ace of spades, 2 of hearts and 2 of diamonds.

If you have the Ace of spades at the end of the problem, you win $100.

Now, I shuffle the three cards (without looking at them) and deal you one. You had a 66.67 chance to get a red 2, yes?

Now, I take the remaining two cards, look at them, and show you a red 2 (you haven't looked at your card). You switch because the first time you picked the odds were against you picking the black Ace ... now they are in your favor because you know the other card.
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anyone have a decoder ring?

Simon_Cowbell · Aug 22, 2008

amraeder said:

Let's just run through the game.
No matter what door you pick, you're going to start with one of three things: Goat 1, Goat 2 or The Car.
So a run through each scenerio, and remember, Monty will always show you a goat. Said another way, he'll never show you a car.

So first, assume you always switch.

1) You start with Goat 1. Monty shows you Goat 2. The Car remains hidden. You switch. SUCCESS.
2) You start with Goat 2. Monty shows you Goat 1. The Car remains hidden. You switch. SUCCESS.
3) You start with The Car. Monty shows you Goat 1 or 2 (doesn't matter). The other goat remains hidden. You switch. FAILURE.

You're successful 2/3 of the time.

Now, if you don't change.

1) You start with Goat 1. Monty shows you Goat 2. The Car remains hidden. You don't change. FAILURE.
2) You start with Goat 2. Monty shows you Goat 1. The Car remains hidden. You don't change. FAILURE.
3) You start with The Car. Monty shows you Goat 1 or 2. The other goat remains hidden. You don't change. SUCCESS.

Since you obviously have no clue what you start with, the smart play is to change. Becuase your odds of winning are 2/3 instead of 1/3 if you keep your first choice.
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Best explanation yet.

amraeder · Aug 22, 2008

Matt1735 said:

For gambling explanations and other probability problems, the best site on the web is wizardofodds.com; it's a site run by an actuary named Mike Shackelford and his explanation is actually the one used by amraeder.

http://wizardofodds.com/askthewizard/tvgames.html
Click to expand...

Cool, bookmarking that site to peruse at a later date. Thanks!

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Question about the movie 21

BB Bobcat Active Member

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