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re: Marilyn vos Savant and the history of the Montel Hall question
Posted on 2/23/15 at 4:33 pm to Monk
Posted on 2/23/15 at 4:33 pm to Monk
quote:I think I get what you are saying now. By conceptually, you mean our intuition to say 50/50? In this case, intuition would lead us astray.
The actual results are what they are. There is nothing to discuss, except conceptually with regard to one's view of the presentation of the choices made available to the contestant.
This post was edited on 2/23/15 at 4:34 pm
1
Posted on 2/23/15 at 4:37 pm to link
quote:You switch again. You have a 99.9999% chance of winning if you switch.
no, a million cards flipped upside down. one of them is a million dollar grand prize. you can pick any card, then 999,998 incorrect cards are flipped over. you're given the choice to stay with your original 1-in-a-million chance or switch. remember, you're all jason's got, and he's depending on you.
Here is the formulation for any scenario from Wikipedia:
quote:
D. L. Ferguson (1975 in a letter to Selvin cited in (Selvin 1975b)) suggests an N-door generalization of the original problem in which the host opens p losing doors and then offers the player the opportunity to switch; in this variant switching wins with probability (N-1)/[N(N-p-1)]. If the host opens even a single door, the player is better off switching, but, if the host opens only one door, the advantage approaches zero as N grows large (Granberg 1996:188). At the other extreme, if the host opens all but one losing door the advantage increases as N grows large (the probability of winning by switching approaches 1 as N grows very large)
This post was edited on 2/23/15 at 4:51 pm
Posted on 2/23/15 at 4:41 pm to buckeye_vol
quote:
There is never a 50/50 chance though.
This is where we begin to swim in circles and folks seem to forget what the article explains about the "initial" odds and the importance of their focus on the words "initial" and the significance of some viewing the test as a 2 step process versus a view of the whole game and the requirements placed on the Host.
The Host is forced to drop a goat. I can't imagine that a ton of people here would try to argue that you have a 2/3's chance of picking the car if you are only picking between 2 doors with one containing a goat.
The only way this puzzle works is because of the way it begins, with 3 doors and 2 goats. That's the beauty of it. In reality, you can't ignore the beginning regardless of what follows.
Posted on 2/23/15 at 4:47 pm to PygmalionEffect
quote:
It's 2/3.
You are confused but there is no shame in that. As stated repeatedly (and proven in the article), the "initial" odds is 2/3's. Those are the proven results.
Most everyone else but you (prolly even some college guys included) is discussing something else.
Posted on 2/23/15 at 4:48 pm to Monk
quote:Sure, but those that incorrectly assume the odds change will be wrong.
This is where we begin to swim in circles and folks seem to forget what the article explains about the "initial" odds and the importance of their focus on the words "initial" and the significance of some viewing the test as a 2 step process versus a view of the whole game and the requirements placed on the Host
In fact, what may be most fascinating by this paradox in this scenario is it is the exact opposite reasoning that people apply to "runs" at the casino. In other words, they choose black because there has been 5 reds in a row because the assumed dependency of independent events. In the Monty Hall Problem, the assume step two is independent of step 1. So they assume independence of dependent events.
Posted on 2/23/15 at 4:54 pm to link
quote:
I have to disagree with the "always switch" conclusion. The correct answer about the probability is that it is 50/50.
Not treading all this but the real answer is:
Door A (your initial selection) = 1/3 chance of winn
Doors B & C (initially not selected) = 2/3 chance of winning.
Show host eliminates Door C (knowing it does not have the car), therefore door B now has the full 2/3 chance of winning.
Door A has 33.3% chance.
Door B has 66.7% chance.
If the car was randomly assigned after the elimination of Door C, the chances would revert to 50/50, but it doesn't happen that way.
Posted on 2/23/15 at 4:55 pm to KosmoCramer
quote:
I'm not reading this whole thread which I'm sure is full of stupidity,
and posts no pics, she was hot in the day
Posted on 2/23/15 at 4:57 pm to Sid in Lakeshore
Solid simple explanation Sid.
Posted on 2/23/15 at 4:58 pm to Sid in Lakeshore
quote:
If the car was randomly assigned after the elimination of Door C, the chances would revert to 50/50, but it doesn't happen that way.
Or if Monty doesn't know and sometimes opens the door with the car, then it is 50/50 as well.
In Let's Make A Deal, you aren't better off switching at the end because all results are independent of each other.
Posted on 2/23/15 at 4:58 pm to KosmoCramer
quote:Those are the individuals you do not listen to while gambling.
Some will still refuse to believe it.
Posted on 2/23/15 at 5:00 pm to KosmoCramer
quote:Yeah that game is completely random, and the odds change every time a case is open. The skill in this game is weighing the odds vs. the offer.
In Let's Make A Deal, you aren't better off switching at the end because all results are independent of each other.
Posted on 2/23/15 at 5:00 pm to KosmoCramer
Thanks for your video, KosmoCramer.
It shows that if you randomly switch or don't switch, you will get the car 3/6 times, or a goat 3/6 times.
That looks like 50/50 to me.
It shows that if you randomly switch or don't switch, you will get the car 3/6 times, or a goat 3/6 times.
That looks like 50/50 to me.
Posted on 2/23/15 at 5:01 pm to link
quote:
Thanks for your video, KosmoCramer.
It shows that if you randomly switch or don't switch, you will get the car 3/6 times, or a goat 3/6 times.
That looks like 50/50 to me.
I hope you're trolling.
Posted on 2/23/15 at 5:04 pm to link
quote:
That looks like 50/50 to me.
Give this a try, although Kosmo may be right that you are trolling.
Monty Hall Simulator
Posted on 2/23/15 at 5:10 pm to link
quote:
link
Shirley, you cannot be serious!
Posted on 2/23/15 at 5:13 pm to buckeye_vol
quote:
Monty Hall Simulator
That simulator is crap. It's always in door number 1.
Posted on 2/23/15 at 5:14 pm to WG_Dawg
quote:
Agree. I always get a kick out of people who think the odds of H/T varies on one single coin flip based on what's happened in previous flips. I'm horrendous at math and statistics, but one thing I DO know is that it's still 50/50 per flip ha.
If I recall, I think she actually gave the best possible answer - it was about a roulette wheel. The question was something like "the wheel comes up red ten times in a row...certainly you have to bet black, right". Her answer said it was an independent event UNLESS the wheel was fixed, so if anything other than a random selection, you should bet red on the 11th.
Posted on 2/23/15 at 5:20 pm to KosmoCramer
quote:
In Let's Make A Deal, you aren't better off switching at the end because all results are independent of each other.
In let's make a deal, in this 3 door game, you are better off switching every damn time, unless you think they hurry up and move the car after Monte eliminates one door. Period, end of discussion, it is a point of probability theory that is easily proved.
If the car is randomly placed behind one of three doors, and never moved, your first pick yields 2 sets in the statistical universe, one with 33% chance and another with 67% chance of having a car. Monte's removal of one door does not at all change the probability of them choosing to place the car behind the door they did, which still yields a 33% chance of it being behind your original selection and a 67% chance of it not being behind there.
Since we know one door is removed from set #2, the remaining door now is the only option in set #2 which still has 67% chance of containing the car.
I'm done, this is funny.
Posted on 2/23/15 at 5:26 pm to Sid in Lakeshore
quote:agreed. keep an eye out for my annual monty hall question thread next january.
this is funny.
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