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re: Time to discuss the Monty Hall problem (strategy and game show)
Posted on 4/8/14 at 6:45 pm to link
Posted on 4/8/14 at 6:45 pm to link
It's not that simple. It's not just removing one door, the host did not pick a door at random. He knows which is which. You have to remember that.
Now, if you initally pick a goat, you should switch because that means he picked the other goat.
If you initially picked the car obviously you should stay.
Are you with me so far?
Your initial choice does matter because it decides which door the host will choose. He did not just eliminate one door at random. He did it based on your choice. And your choice had a 2/3 chance of being a goat (thus you should switch)
Now, if you initally pick a goat, you should switch because that means he picked the other goat.
If you initially picked the car obviously you should stay.
Are you with me so far?
Your initial choice does matter because it decides which door the host will choose. He did not just eliminate one door at random. He did it based on your choice. And your choice had a 2/3 chance of being a goat (thus you should switch)
This post was edited on 4/8/14 at 6:46 pm
2
Posted on 4/8/14 at 6:46 pm to link
Monty Hall simulation
Keep choice: 1000 times Wins: 326 cars (32%)
Losses: 674 goats (68%)
Change choice: 1000 times Wins: 662 cars (66%)
Losses: 338 goats (34%)
Keep choice: 1000 times Wins: 326 cars (32%)
Losses: 674 goats (68%)
Change choice: 1000 times Wins: 662 cars (66%)
Losses: 338 goats (34%)
This post was edited on 4/8/14 at 6:48 pm
Posted on 4/8/14 at 6:46 pm to link
i agree with you, fwiw...i just don't argue it. it is 2 different games where you're dealing with very imperfect information
Posted on 4/8/14 at 6:47 pm to genro
Should you switch or not =
should you take one or the other of the two remaining doors =
what is your chance of getting the car if you take one of the two remaining doors.
It is still 50/50.
should you take one or the other of the two remaining doors =
what is your chance of getting the car if you take one of the two remaining doors.
It is still 50/50.
Posted on 4/8/14 at 6:48 pm to SlowFlowPro
SFP + Link vs. a Bama fan..
Posted on 4/8/14 at 6:48 pm to SlowFlowPro
I argue that they are not two independent events because of the crooked host. His choice depends on your response in the first game.
Monty Hall is a dick, and that's they key to the whole thing.
Monty Hall is a dick, and that's they key to the whole thing.
This post was edited on 4/8/14 at 6:50 pm
Posted on 4/8/14 at 6:49 pm to genro
quote:
He knows which is which. You have to remember that.
but even then, he'll always be removing a "goat" door and you'll always be left with 2 doors. one with a goat, and one with a car. the initial choice is logically irrelevant, since you get to "do it again" anyway
so cut out the first step. one "goat" door is eliminated. that step is irrelevant. your initial choice is irrelevant.
now you get to choose between 2 doors. one with a goat. one with a car
Posted on 4/8/14 at 6:49 pm to Broseph Barksdale
quote:
I argue that they are not two independent events because of the crooked host. His choice depends on your response in the first game.
well i'm assuming he's going to pick a "goat" door 100% of the time.
Posted on 4/8/14 at 6:50 pm to link
Forget about the number of doors.
If you pick a goat, switch and win.
If you pick a car, switch and lose.
What are the odds that you picked a goat? 2/3
That's where it is. Thats all that matters. The number of doors is more or less extraneous.
If you pick a goat, switch and win.
If you pick a car, switch and lose.
What are the odds that you picked a goat? 2/3
That's where it is. Thats all that matters. The number of doors is more or less extraneous.
This post was edited on 4/8/14 at 6:51 pm
Posted on 4/8/14 at 6:51 pm to SlowFlowPro
Your initial choice is not irrelevant because if you pick the car you will lose, and if you pick one of the 2 goats you win.
Posted on 4/8/14 at 6:52 pm to SlowFlowPro
quote:
well i'm assuming he's going to pick a "goat" door 100% of the time.
That's what I was saying. Prior knowledge of the game tells you that there's only two doors to choose from. You picking the first one just gets past the bullshite and on to the real selection.
Posted on 4/8/14 at 6:53 pm to StickyFingaz
quote:
Your initial choice is not irrelevant because if you pick the car you will lose, and if you pick one of the 2 goats you win.
wait i may misunderstand the game
are you saying that if you pick the car, then you win and there is never a 2nd step?
Posted on 4/8/14 at 6:53 pm to StickyFingaz
Right.
I was once a doubter way back in the day and wrote a Matlab simulation that justifies this
I was once a doubter way back in the day and wrote a Matlab simulation that justifies this
Posted on 4/8/14 at 6:54 pm to genro
quote:
Forget about the number of doors.
If you pick a goat, switch and win.
If you pick a car, switch and lose.
What are the odds that you picked a goat? 2/3
This explained it better.
So it has nothing to do with turning the game into a 50/50 shot but more to do with saving yourself from the 66% chance you lose.
Posted on 4/8/14 at 6:54 pm to SlowFlowPro
Well if you always switch your pick after one of the goats is revealed then the odds are in your favor.
ETA No you don't win if you pick the car first... It just shows that if you played the game many times it is in your best interest to change doors every time.
ETA No you don't win if you pick the car first... It just shows that if you played the game many times it is in your best interest to change doors every time.
This post was edited on 4/8/14 at 6:56 pm
Posted on 4/8/14 at 6:55 pm to SlowFlowPro
The host is guaranteed to pick the goat. His choice will change based on what you pick.
What are the odds you picked a car and he just picked at random one of the two goats? 1/3
What are the odds that you picked and thus he was FORCED to pick the other goat? 2/3
Thus you should switch.
What are the odds you picked a car and he just picked at random one of the two goats? 1/3
What are the odds that you picked and thus he was FORCED to pick the other goat? 2/3
Thus you should switch.
This post was edited on 4/8/14 at 6:56 pm
Posted on 4/8/14 at 6:56 pm to StickyFingaz
quote:
Well if you always switch your pick after one of the goats is revealed then the odds are in your favor.
but if 1 of the 3 is always revealed to be a goat, and it will always be removed, then i'm still asking how you're not left with a 50/50 coin flip every time. we know that no matter what, we will be left with 2 doors and one has a goat and one has a car. we have to choose one of the 2 doors
Posted on 4/8/14 at 6:57 pm to genro
It is important to remember that it doesn't mean you WILL win (obviously) just that you have better odds of winning.
Posted on 4/8/14 at 6:58 pm to genro
All cards face down. I can look at them, you can't.
Try to pick the Ace of Spades, so pick one, but don't look at it.
I turn over all the remaining cards but one. So either your card or mine is the Ace of Spades.
Would you switch?
Try to pick the Ace of Spades, so pick one, but don't look at it.
I turn over all the remaining cards but one. So either your card or mine is the Ace of Spades.
Would you switch?
Posted on 4/8/14 at 6:58 pm to SlowFlowPro
It is a 50/50 coin flip if you totally negate the information you gained in the first part of the game.
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