Ignore Bait: Highest IQ, Many Questions, Odds makers invited...
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You asking me? I do not know. Yeah yeah, the odds say...
Math has killed more people than um, lotsa stuffand it's getting better at it.
There’s only two answers.
Neither is 100%
Keep your door, 33% you live, change doors, 66% you live.
Math has never killed anyone.
Manhattan Project for stahtahz.
I think I'll go there but that's not what I'm talking about. Even on LMAD the lucky participant only had the one shot. I have no doubt Lucky Participant (henceforth LP) was not as informed as those on 66%. Still I wonder how many of those won the big deal or anything similar to this.
I’ve heard of suicide because of math…..students jumping out of windows in Japan.
J/k
Math is pure and honest, it’s always true
The stress of entrance exams made it to CNN I believe.I’ve heard of suicide because of math…..students jumping out of windows in Japan.
J/k
Math is pure and honest, it’s always true
Math doesn't care about anything. It shows people places no one should visit. For instance "well meaning" scientists doing un-securable research on the nature of reality but enough NPR...
Lol. You’re really having trouble with this.
33% of people who didn’t switch won big. 66% of people who did switch won big.
Anything different is pure statistical variance.
Statistical variance is why casinos stay in business. Many people win in the short term. But almost everyone loses in the long term.
Another way of looking at it……
When using the always switch strategy, to win, your first pick has to be a goat.
If there are two goats and one car…..what are the odds of picking a goat (which is the requirement to win when you switch)??
66% chance of picking a goat. Which in turn means 66% chance of winning with the switch strategy.
When using the always switch strategy, to win, your first pick has to be a goat.
If there are two goats and one car…..what are the odds of picking a goat (which is the requirement to win when you switch)??
66% chance of picking a goat. Which in turn means 66% chance of winning with the switch strategy.
I’ll add my 0.02.
vapoolplayer’s explanations are spot on. Dave in FL and PoolBum also had good explanations. I will offer yet another that is a little more subtle, but essentially the same.
As was explained, Monty knows which door has the car and he will never open that door. When you choose a door initially, you have a 1/3 chance of guessing correctly. You know that the car is in one of the other two doors with a 2/3 probability. But you also know that at least one of the other two doors has a goat. When Monty shows you a door with a goat he is telling you something that you already know—that at least one of the doors has a goat. Opening the door provides no new information, so the chance of winning with your original pick is the same: 1/3. Therefore, the chance of winning by switching 1 − 1/3 = 2/3. Just because there are only two choices left doesn’t mean that the odds are 50-50.
Like vapoolplayer said, it’s like getting to pick two cards instead of one.
MajorMiscue, your name is appropriate on this one. But you shouldn’t feel too bad. When Marilyn vos Savant posted the answer, a professor of statistics wrote to tell her she was wrong.
vapoolplayer’s explanations are spot on. Dave in FL and PoolBum also had good explanations. I will offer yet another that is a little more subtle, but essentially the same.
As was explained, Monty knows which door has the car and he will never open that door. When you choose a door initially, you have a 1/3 chance of guessing correctly. You know that the car is in one of the other two doors with a 2/3 probability. But you also know that at least one of the other two doors has a goat. When Monty shows you a door with a goat he is telling you something that you already know—that at least one of the doors has a goat. Opening the door provides no new information, so the chance of winning with your original pick is the same: 1/3. Therefore, the chance of winning by switching 1 − 1/3 = 2/3. Just because there are only two choices left doesn’t mean that the odds are 50-50.
Like vapoolplayer said, it’s like getting to pick two cards instead of one.
MajorMiscue, your name is appropriate on this one. But you shouldn’t feel too bad. When Marilyn vos Savant posted the answer, a professor of statistics wrote to tell her she was wrong.
You're right except for one thing. Monty is giving you new information when he opens a door, which is that there is a goat behind the door that he opens. That doesn't change the probability that you picked the car on your initial pick, but it does change the probability that the car is behind the door he didn't open.
Pretty close overall.
But, he is definitely revealing new info.
He is revealing exactly where the car is 66% of the time. Which is new info and it’s huge info.
Monty is revealing new information, but the information is not relevant. Knowing which of the two doors has the goat does not tell you anything useful. That is, the information doesn't affect the decision of whether or not to switch.
Yes, it does. Knowing that there is a goat behind the door he opened is what tells you that there is now a 2/3 chance that the car is behind the door he didn't open.
But that information does not affect your decision on whether to switch. You already know that one of the two doors has a goat. Knowing which one it is doesn't matter for your decision.
If you initially choose door #1, then you know that there is a 2/3 chance that the car is in door #2 or door #3. Whether Monty reveals #2 or #3 doesn't matter--he always reveals a door that has a goat. By switching, you are choosing the door that he didn't reveal--that is, it doesn't matter whether the door is called #2 or #3. You should switch in either case.
If you initially choose door #1, then you know that there is a 2/3 chance that the car is in door #2 or door #3. Whether Monty reveals #2 or #3 doesn't matter--he always reveals a door that has a goat. By switching, you are choosing the door that he didn't reveal--that is, it doesn't matter whether the door is called #2 or #3. You should switch in either case.
tomatoshooter
Well-known member
Maybe we should just talk about aiming systems.
Saying that it doesn't matter which door Monty reveals the goat behind is not the same thing as saying that it doesn't matter that Monty reveals a goat behind one of the doors. The former doesn't make a difference, the latter does.
Depends on the scenario. The exact scenario says you pick a door. Then the host opens a door showing a goat and gives you the option.
If you knew going in that he was going to open the door and show a goat, you should have already made the decision to switch.
If you didn’t, know that, then he opens a door and reveals a goat, even if it was random and he could have opened the car, you now have additional information you didn’t have. Then he offers the switch.
It would be the same as two players in a hold ‘em game. One had a big decision and the other turns over one of their cards. There was the decision before that that was proper for the scenario and there was a decision after that is proper with the added information.
The only reason I say he has to open the goat or bring up that he knows what’s behind the doors is to highlight the odds to the non believers.
You pick a door and it’s a 33% chance.
If Monty doesn’t know what’s behind the cards, it’s also 33% that he picks a goat or the car. But if he knows where the car is, and is not allowed to pick it, then it’s 66%.
But, the actual scenario is that you pick a door. Then you’re shown an open door with a goat. Then you are given a choice of keeping or swapping. Is it to your advantage to swap?
That sounds like semantics, however in game theory and such, it’s extremely important to have the exact order of options and information if one is to take the example and extrapolate it to be useful decision making.
PAY CLOSE ATTENTION, YOU CAN GET THIS.
1 - There are 3 doors.
2- Monty has 2 doors, you have one.
3 - Monty knows what door has the big prize behind it, you don't.
4 - Monty has either 1 goat plus the grand prize, or 2 goats.
5 - Being that Monty cannot possibly have less than one goat means that him showing you one goat is smoke and mirrors.
6 - If you trade, you are getting both of Monty's doors. It is a mortal lock that at least one has a goat, so back to smoke and mirrors.
It really comes down to this ... do you want one chance to win or two chances to win.
I have long advised you that you need to read some books.
Why are you working so hard to prove me correct?