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Adrian Fern
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Kevin - the best way to look at the Monty Hall problem (which is where the host KNOWS where the car is) is this:

1. When you point at a door, you are twice as likely to have selected a goat than the car (because there are two goats and only one car).

2. When the host opens a door to reveal a goat (which is always possible for him to do, no matter which door you are pointing at) you are STILL twice as likely to be pointing at a goat door than the car door.

3. Therefore, it is in your interests to switch and point at the other remaining door. (Assuming you prefer cars to goats).

Use that same reasoning for the problem using 99 goat doors and 1 car door, and it is even easier to see!
Kevinh5
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Yeah, I'm one of those guys who has to work it on paper myself to believe it. I finally got it, though. Lots of encouragement from others here to keep trying until I did get it.
S2000magician
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Kevin: great news!

Now, can I interest you in trading your car for what's behind door #1?

;)
Slim King
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Let's pretend my wife and I were playing from home... She chose door 2 and I chose door 3 ... Monty then eliminated door 1... are you saying that if I now change my choice to door 2 my chances of winning would increase ..... and that if she would change to door 3 her chances to win would increase? Can't be!!!!

And that's my Dilemma with the Monte Hall Dilemma..... Smile

So if "I" was actually "on the show" and picked door 3 I would do better by choosing 2 .......but if "I" was home and my wife was "in the studio" and she picked 2 she would do better to pick 3 ?????

So picking 2 or 3 doesn't change a thing ... How could you do BETTER by choosing either 2 or 3... You've already done better by having Monte eliminate one ... but that's it!!!!.. LOL
THE MAN THE SKEPTICS REFUSE TO TEST FOR ONE MILLION DOLLARS.. The Worlds Foremost Authority on Houdini's Life after Death.....
Adrian Fern
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Slim - ony one person is playing at a time in the Monty Hall problem. i.e. only ONE door is pointed at, then the host opens one of the TWO remaining doors (i.e. one of the two doors that the single player didn't choose!). So whichever door (1, 2 or 3) the single player is pointing at is one of the two remaining closed doors at the end. And the player should then swap.
S2000magician
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Quote:
On 2012-10-15 16:27, Slim King wrote:
Let's pretend my wife and I were playing from home... She chose door 2 and I chose door 3 ... Monty then eliminated door 1... are you saying that if I now change my choice to door 2 my chances of winning would increase ..... and that if she would change to door 3 her chances to win would increase? Can't be!!!!

And that's my Dilemma with the Monte Hall Dilemma..... Smile

So if "I" was actually "on the show" and picked door 3 I would do better by choosing 2 .......but if "I" was home and my wife was "in the studio" and she picked 2 she would do better to pick 3 ?????

So picking 2 or 3 doesn't change a thing ... How could you do BETTER by choosing either 2 or 3... You've already done better by having Monte eliminate one ... but that's it!!!!.. LOL

The problem with your scenario, Slim, is this:

She chose door 2 and I chose door 3 ... Monty then eliminated door 1 . . . .

Unfortunately, sometimes when she chooses door 3 and you choose door 3, Monty cannot show you door 1: there's a car behind it. So he's stymied. And on the occasions when Monty can show you door 1, he has no choice: it's door 1 or go home.

In the one-person game, Monty's never stymied: he can always show you a door with a goat, and sometimes he has a choice of doors to show you.
Adrian Fern
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Yes, it's vital that the host can SEE which door you are pointing at. If you are in the studio playing it, you are the real player because the host can see you and your choice. Meanwhile, your wife can be pointing to a different door on the TV screen, but the host has no knowledge of that, so she is not actually playing the same game!
S2000magician
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Quote:
On 2012-10-15 17:20, Adrian Fern wrote:
. . . so she is not actually playing the same game . . .

. . . and the host might open the door she selected to show a goat to you.
LobowolfXXX
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[quote]On 2012-10-15 14:29, Kevinh5 wrote:
If Monty never revealed the car but always revealed a goat, I agree: he had to know.



Who wants to take my challenge and figure out how much fun it would(n't) be if Monty only knew where ONE GOAT was?
[/quot]

If Monte would always show you the known goat when you didn't pick it (rather than risk showing you the car), then you should switch for the same reasons as in the original problem.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
Kevinh5
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Monty CANT always show you a known goat if D1=G and that's all he knows.
LobowolfXXX
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Right. The issue is whether he'd always show it to you when he can. For instance, let's say the goat he knows is D2. If he would reveal D2 whenever D1 or D3 is selected (rather than risk exposing the car), then you should switch.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
S2000magician
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Quote:
On 2012-10-15 18:03, LobowolfXXX wrote:
Right. The issue is whether he'd always show it to you when he can. For instance, let's say the goat he knows is D2. If he would reveal D2 whenever D1 or D3 is selected (rather than risk exposing the car), then you should switch.

And if you originally choose D2, he . . . what? . . . leaves the stage on a pretext and never returns?
LobowolfXXX
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One of the conceptual errors is this: let's say (original version of the game) you pick D1 and GW shows D2. The error is to think that the only think you've learned is that D2 is a goat. That's incoorect. You've also learned that Monte, who can't show you the cat, chose not to reveal D3. SOME of the time, that will because he had no choice (because D2 is the only remaining goat). That's critical to the proven. When you keep the original choice, you're actually betting a parlay - that D1 is the car, AND that with a 50-50 choice, he chose to show you D2. When you switch, you're betting that D3 is the car, period. There's no further reduction, because 100% of the time D3 is the car, he has to show you D2.

Or to put it yet another way, it's better to assume he had no choice than to assume he exercised a choice in a specific way (which is why in bridge circles, this idea is called "The Principle of Restricted Choice."
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
LobowolfXXX
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Quote:
On 2012-10-15 18:07, S2000magician wrote:
Quote:
On 2012-10-15 18:03, LobowolfXXX wrote:
Right. The issue is whether he'd always show it to you when he can. For instance, let's say the goat he knows is D2. If he would reveal D2 whenever D1 or D3 is selected (rather than risk exposing the car), then you should switch.

And if you originally choose D2, he . . . what? . . . leaves the stage on a pretext and never returns?


Well, it's not my modified game... I'd have him pick one and hope it was the other goat, personally.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
S2000magician
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Quote:
On 2012-10-15 18:13, LobowolfXXX wrote:
. . . in bridge circles, this idea is called "The Principle of Restricted Choice."

Someone should have mentioned this fact a whole lot earlier.
LobowolfXXX
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Oh, I don't know...without the "which is why," it's just kind of cute trivia.

The interesting thing about all this is that it's pretty easy to verify empirically, yet still receives steadfast opposition.
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
S2000magician
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Quote:
On 2012-10-15 19:03, LobowolfXXX wrote:
Oh, I don't know...without the "which is why," it's just kind of cute trivia.

The interesting thing about all this is that it's pretty easy to verify empirically, yet still receives steadfast opposition.

Not unlike the two-children-one's-a-boy-what's-the-probability-that-the-other's-a-boy problem.
landmark
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Quote:
On 2012-10-15 02:43, LobowolfXXX wrote:
Now, about the water level in a swimming pool if you drop a brick off of a raft and it sinks to the bottom of the pool...

Okay, I know this one. There's as much raft in the brick as there is brick in the raft if the pool is filled with wine.
Jonathan Townsend
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You got those grape juice concentrate bricks?
...to all the coins I've dropped here
owen.daniel
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Quote:
On 2012-10-15 16:27, Slim King wrote:
Let's pretend my wife and I were playing from home... She chose door 2 and I chose door 3 ... Monty then eliminated door 1... are you saying that if I now change my choice to door 2 my chances of winning would increase ...


As we have now seen, unfortunately in this situation the classical Monty Hall problem is of no help. However, several posts back I posed the following variant in which there are two players. Suppose that each of the players chooses a distinct door, and that Monty then eliminates one of the players, telling them that their door had a goat behind it (he doesn't lie about this). Now should the remaining player stick with their original door, or switch?

The solution should be quite simple for people who've been following all the posts.

Owen
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