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Because you now have a 2 to 1 chance of picking the right door. If you chose the wrong door in the first guess (a 2 to 1 chance) by changing you will get the right door.
Huh? My point?
Look Faldage, I don't want to call attention to your inarticulate sentence structuring but this is my point: Just what the heck does your sentence mean? Changing will not get you the right door; changing will only give you a 66.6% probability of getting the right door.
Geez! What you meant is not what you said. Apologize.
Wait! Now I get it. You are omnipotently proclaiming the knowdledge of which is the right door. Sure, Faldage, now I understand your words as they are so...so...you. Good. Now you are ready for Monty Hall Part Two. Oh boy, this should be fun. 
Last edited by themilum; 11/06/06 02:35 AM.
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Inasmuch as the Monty Hall Paradox works and can be tested it seems likely that we humans might have incorporated this manner of decision making in the course of our evolution. In order to explore this possibility let us re-examine the Monty Hall Paradox, but this time let's use one hundred doors.
This time you select a door from a group of doors numbering from 1 to 100 in order to win a car. Monty Hall will then open a door with only a sack of dog food there and ask you if you would like to change your selection. You say "yes" and so Monty then opens another door and again asks you if you would like to change your selection, you say "yes" and etc..
So the question is...how does the percentage rate of likely success increase as you and Monty Hall work your way towards one hundred.
You have exactly one seventh of a sennight to register your answer.
Last edited by themilum; 11/06/06 03:28 AM.
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Carpal Tunnel
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Quote:
Quote:
Because you now have a 2 to 1 chance of picking the right door. If you chose the wrong door in the first guess (a 2 to 1 chance) by changing you will get the right door.
Huh? My point?
Look Faldage, I don't want to call attention to your inarticulate sentence structuring but this is my point: Just what the heck does your sentence mean? Changing will not get you the right door; changing will only give you a 66.6% probability of getting the right door.
Wull, I spose it might could be inarticulate if you don't understand the basics of logic and if/then statements. What's that? You don't see no "then" in there? OK, if you cain't read between the words here it is:
Quote:
If you chose the wrong door in the first guess (a 2 to 1 chance) then by changing you will get the right door.
I redded up the "if", too, so you could see it. Parboly you missed it the first three, four times through the sentence.
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The most convincing and intuitively palatable approach to this problem IMO is to make diagrams of your choices and the possible outcomes. While one may argue the philosophical point that nothing has changed between the first choice and the first reveal, making a diagram of each strategy makes it clear that a strategy of switching after the reveal will result in a successful outcome (in this case, apparently, some interaction with the comley Ms. White) two-thirds of the time vs sticking with the original choice.
Short of the diagrams, here is my best explanation™ of why switching works: When you first picked, you had a 1/3 chance of picking the winner and a 2/3 chance of picking a loser. Once shown one of the losing options, the strategy of switching will only result in a bad outcome in the event that you had picked the right one in the first place. And since you originally had only a 1/3 chance of winning, you now have only a 1/3 chance of losing if you make the switch, vs a 2/3 chance of winning.
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Marilyn Savant's solution—that choosing a new door increases your odds from 1:3 to 1:2—doesn't seem very controversial to me. In a single instance it probably doesn't make a great difference, but I think if you played this game a number of times, the decision to change doors would yield better results.
This problem divides people into lateral thinkers (who choose to change doors) and vertical thinkers (who stick with their first choice). Lateral thinkers view the problem in time and in terms of two discrete sets of initial conditions and reason: "Under the first set of initial conditions my first choice yields a 1:3 probability, under the new set of initial conditions a change yields a 1:2". Vertical thinkers view the problem in space and say, "There was a 1:3 chance that my first choice was correct. Now there is a 1:2 choice that my first choice was correct—after all, either choice will be 1 of two doors!"
Personally, I would change my first choice.
Consider instead a bifurcation in time, which gives you two sets of doors. Set A consists of three doors (two bags of dogfood and one girl). Set B consists of two doors (one bag of dogfood and one girl). Which set of doors yields the greatest chance of getting the girl? Clearly, Set B. Making a decision under condition B yields a greater chance of getting the girl. If you allow this fact to have retroactive effect on the first choice (which was out of three doors) it is simply a case of choosing bewteen a 1 in 3 chance and a 1 in 2 chance.
Last edited by Hydra; 11/08/06 03:08 AM.
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Wonderfully clear, Alex, you too, Hydra, and Faldage...I heard that!
Now to the point. If in fact a counter intutive or a seemingly trans-logical method of decision making exists such as that which we have demonstrated here, then the processes of our evolution must have incorporated those methods within the circuits of our brains. (You known like a woman's intuition; or a woman's prerogative to change her mind,)
As an example of how the Monty Hall Paradox could be utilized to assist in our survival I offer this hypothetical as a case in point...
Al Gore was right. Global Warming has come and gone, leaving only four people alive and who are camped out in the top floor of the Empire State Building eagerly awaiting the comming Ice Age.
They are a throughly modern crew -- one woman and three New York Metrosexuals -- their mission is to re-populate Earth.
The woman, a good Christian lady from Alabama, must choose between the three men -- Freddy, Perk, and Tony -- but all are equally dull and she can't decide, so (what the hell) she flips a coin and selects Tony.
Bad luck. Before she can tell Tony of his fate by chance she intercepts a love letter writtten by Perk to either Freddy or Tony. (New York has a 2006 law that decrees a person's biological sex is officially immaterial, anyone can be whichever sex they want to be as long as they openly declare it so) Hmmm?
Now your question: Does the nice woman from Alabama now change her choice from Tony to Freddy or stay with Tony?
Take your time. Only the fate of all future mankind awaits your answer.
Last edited by themilum; 11/08/06 10:19 AM.
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...(New York has a 2006 law that decrees a person's biological sex is officially immaterial, anyone can be whichever sex they want to be as long as they openly declare it so) Hmmm?
Then, logically, I can be whatever Height I wish to be. The physical attribute is immaterial. Better yet, I can be whatever WEIGHT I desire. WOOOHOOO!! I am no longer overweight!!
"I am certain there is too much certainty in the world" -Michael Crichton
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Quote:
Quote:
...(New York has a 2006 law that decrees a person's biological sex is officially immaterial, anyone can be whichever sex they want to be as long as they openly declare it so) Hmmm?
Then, logically, I can be whatever Height I wish to be. The physical attribute is immaterial. Better yet, I can be whatever WEIGHT I desire. WOOOHOOO!! I am no longer overweight!!
Sorry, ParkinT, that is not the way the world works in wambly New York.
The bill up for vote in the New York legislature is an attempt to circumvent any judicial ruling against marriage between the same sexes.
You will be required to document the sex that you wish to be in writing and then wait two years, then the state will go back and change the sex listed on your birth certificate if it differs from the sex that you want to be.
Soon, in a world gone mad, being overweight in New York will land you in jail.
Strange World.
Last edited by themilum; 11/08/06 11:36 PM.
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Whatsamattau, big boys, have you all no balls for contesting the fact that the paradoxical nature of the question that I have posted has had a postive impact upon the thinking processes of all humanity? What? Don't you understand the implications? You do? Well, has the cat's got your tongue? 
Last edited by themilum; 11/09/06 03:33 AM.
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