The part that I have a hard time with is, what if we add another contestant or viewer partway through?
Suppose the scenario all plays out just as described in the example, and after that I turn on the TV and start watching. For me, I see 2 doors and a goat. From the two of them talking, I get the general idea that there’s a car behind one of the two doors, and a goat behind the other. It seems like in that situation, I’d have a 50/50 chance of picking the right door, if I didn’t know which one the contestant picked originally. Right?
Can someone explain to me how discovering which door the contestant picked would provide information that makes one door more likely than the other? What is it about the contestant picking door 1 that makes me go, “Ah, it’s probably door 2!”
Has anyone read ‘The Man Who Only Loved Numbers’? Some good stories in there about how some of the finest mathematical minds of our century couldn’t grasp this. For my part, I understand the proof I saw, but its still very counter-intuitive. If Paul Erdos didn’t understand it, I don’t feel so bad.
Be simple enough to test with 2 people and a deck of cards, wouldn’t it? The stats aren’t just numbers in space, if the example is right, switchng really should get you the car (or ace) 66% of the time.
someoneatwhatever is always making absurd and nonsensical claims that he doesn’t even try to justify. Of course his beliefs are irrelevant, its not just numbers in space, which anyone intelligent enough to operate a deck of cards should be able to find out for themselves. His beliefs won’t alter any probability when making the choices or the statistical outcome. Don’t expect any coherency besides complaints about my repeated use of the word ‘absurd’ sad and pathetic.
people don’t believe it only because they don’t ‘get’ it. It works out that way in the real world, regardless of personal opinion. thier lack of belief doesn’t change the probability difference between picking thier card or the non revealed. if they don’t believe, they don’t get it, because thats just how it works out. again master the playing card and get back to us.
How can a prediction be “unjustified”? It’s either going to turn out accurate or inaccurate between subjective opinions based upon the criteria it self-describes.
Men only gather around the predictions that keep proving themselves true, which is the error of taking science as a faith…
That’s exactly the definition of ambiguity – whatever a person is compelled to do is whatever a person is compelled to do.
The situation says nothing until beforehand or afterward in context, until it is discussed and made sense of, otherwise we’re just being. Actions speak louder than words, yes, but what are we doing here on this forum – acting or writing? Where do word acts begin and end? Is this even the problem at hand?
The hypothetical is a memory of something that may or may not be real, according to fiction or nonfiction. Predicating events based on hypothetical contexts are what men instinctively do in order to anticipate the exchange of gunfire. The hypothetical can be true when what is “true” is definitely going to happen (like that I’m going to drive my car within the next two hours).
I want some clarification…
Skepticism & Nihilism continually beg the question. Pragmatism ends it, so it also forces men to decide what is “valid” and what is “invalid”.
It’s only as flawed as flawed men allow it to be. The fallacy of logicians (and most other logically predicated sciences) is that they don’t know how, where, or when to update their language after mistaking it as an absolute authority. I won’t speak for others, but my authority rests in the same place I put my faith…
Ihate my threads degrading to this drivel. This is a testable prediction, people who don’t believe simply can’t wrap thier heads around it, as the same statistical results or close enough happens consistently in the real world WHEN TESTED. leave the BULLSHIT run of the mill arguments against science/statistical predictions until you can show that in the real* world they don’t routinely come true.
again i suggest a deck of cards for those people too incompetent to do the mental math if you don’t ‘get’ it grab some cards if the people in question thinks its faith 200 rounds with a deck will prove them wrong, the correct card *will be in the dealer’s hand consistantly enough to say the prediction is correct.
seriously not all my threads need to be dragged down by philosophy based on the standards of a seven year old. real world ideas have testable predictions, the worth of claims depends on the accuracy of those predictions, not any mental midget’s ideas about thier worth…
Here’s what I consider to be the most easily grasped explanation for this problem:
Assume that there are ten doors to choose from to begin with, with goats behind nine of them and a car behind only one.
You pick one of the ten doors. Your chance of selecting the door with the car behind it is 10% and the chance that the car is behind one of the other nine doors is 90%.
Then the game show host, who knows which door the car is behind and will not open that door, opens eight of the remaining nine doors to reveal goats behind them. In no way does the fact that eight of the other nine doors have now been opened to reveal goats behind them affect the 10% chance that you selected the correct door to being with. It doesn’t affect it, because YOU ALREADY KNEW THAT AT LEAST EIGHT OF THOSE NINE DOORS HAD GOATS BEHIND THEM!
You are then given the option of keeping the door you picked or of switching to the only other unopened door.
Since it is obviously 90% likely that the car is behind the sole remaining unopened door that you didn’t pick and only 10% likely that it is behind the door that you did pick, only an idiot would keep the door that he originally picked, right?
Well, the same principle applies whether there are three doors to choose from to begin with or ten or a million. The only difference is, is that the odds that you selected the door with the car behind it to begin with obviously get much worse the more doors that there are to choose from. This also means of course that the odds that the car is behind one of the doors that you didn’t select get much better.
I believe the point that Cyrene is making is how cognitive probabilities are processed in more basic and “stupid” people. On a game show, for the host to pick all the incorrect doors and leave the final “chance” at 50-50, then people misinterpret that the odds of picking the correct door ends up as a 50% chance. In reality, those who are more intelligent see through the “game” of the “show” … that they detect that the host is misleading the contestant and the viewers (conceptually) by a “sleight of mind”. In the end, it appears as the pick comes down to a 50% chance, when in reality, the chance was very low to begin with (depending on the amount of doors w/goats behind them).
The “problem” here is how the probability changes in a real-time context. The human mind works cognitively in this manner (compared against an intelligent or ignorant person) by anticipating possible changes and adhering expectations toward them. Most people cannot account for this, because they are literally stupid. However, a more intelligent person will pick up on the clues and eventually understand that the door situation stayed consistent in context from the beginning to the end and the “game show” is a mere illusion to those who are fooled by it.
What would really throw such an “intellect” off is if the game show host randomly picks the correct door from time-to-time rather than leaving it to the last. Then, the odds become randomized again in expectation only … and the “game” loses its appeal (of anticipation of coming down to the final two doors rather than seeing the result straight-out).
You don’t even need two people. You can do it yourself.
Just shuffle two deuces and an ace (the deuces represent the “goats” and the ace, the “car”), and deal them face down in front of you. Pick one of the three cards, being sure to keep it face down. Turn over one of the two cards that you didn’t pick. Then:
A) if the card revealed is an ace (i.e., “the car”), start over because in the “Monty Hall problem,” remember, the host never reveals the car when he opens one of two doors that weren’t picked by the contestant. He always opens a door with a goat behind it.
B) if the card revealed is a deuce (i.e., “a goat”), then either keep your original card OR switch to the other face down card.
By switching, you’ll switch to the ace close to 67% of the time. By keeping your original card, you’ll keep the ace about 33% of the time . . . guaranteed.
If you don’t believe it now, do the experiment and you’ll believe it then.