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re: Time to discuss the Monty Hall problem (strategy and game show)
Posted on 4/8/14 at 7:00 pm to StickyFingaz
Posted on 4/8/14 at 7:00 pm to StickyFingaz
quote:
It is a 50/50 coin flip if you totally negate the information you gained in the first part of the game
This is the part people struggle with, it's the knowledge that you gain from the fact that the host knows. He is actually helping you (if you are smart enough to take it).
1
Posted on 4/8/14 at 7:00 pm to genro
quote:
What are the odds you picked a car and he just picked at random one of the two goats? 1/3
i don't even acknowledge my initial choice as having value. i'm going to be re-picking on gut with 2 doors, knowing one door will have a goat and one will have a car.
quote:
What are the odds that you picked and thus he was FORCED to pick the other goat? 2/3
i get what you're saying, and i understand the stats behind it, but if he's always removing a goat, in the end you're left with a 50-50 decision. i really wonder what the difference is between either keeping or switching and just flipping a coin at that point
Posted on 4/8/14 at 7:00 pm to StickyFingaz
I have a better idea.
Take any two doors, where you know that there is a car behind one and a goat behind the other. Pick one. Switch or don't switch, I don't care. Record your results over 100 tries. (Hint: if you flip a coin this will be the same, and easier).
The point is: If you accept carrying the initial 3-door probabilities forward, the mathematical proofs are correct. But that is a lie; the problem has been changed to eliminate one non-car door. That is what people intuitively understand, and why they say that it is a 50/50 shot at that point.
Take any two doors, where you know that there is a car behind one and a goat behind the other. Pick one. Switch or don't switch, I don't care. Record your results over 100 tries. (Hint: if you flip a coin this will be the same, and easier).
The point is: If you accept carrying the initial 3-door probabilities forward, the mathematical proofs are correct. But that is a lie; the problem has been changed to eliminate one non-car door. That is what people intuitively understand, and why they say that it is a 50/50 shot at that point.
Posted on 4/8/14 at 7:01 pm to SlowFlowPro
quote:
i really wonder what the difference is between either keeping or switching and just flipping a coin at that point
About 33.3333333333333333333333333%
Roughly.
Posted on 4/8/14 at 7:01 pm to SlowFlowPro
quote:
You're left with a 50-50 decision
You are, but I would rather have a 66-33 decision
Posted on 4/8/14 at 7:01 pm to KosmoCramer
quote:
This is the part people struggle with, it's the knowledge that you gain from the fact that the host knows.
but he eliminates a door that you didn't pick, won't be able to choose from, and has no meaning on the final solution
Posted on 4/8/14 at 7:02 pm to SlowFlowPro
Right... And that means you had a 66% chance to pick a goat and a 33% chance to pick a car! This is the most important part.
Posted on 4/8/14 at 7:03 pm to link
quote:
The point is: If you accept carrying the initial 3-door probabilities forward, the mathematical proofs are correct. But that is a lie; the problem has been changed to eliminate one non-car door.
what about this
-make the initial pick
-host removes 1/3 of the choices
-then they mix up and randomize the remaining 2 choices. what are the odds you pick the car or goat?
Posted on 4/8/14 at 7:04 pm to SlowFlowPro
quote:Which door did he eliminate? It depends on which one you pick. Did he eliminate the OTHER goat? There's a 2/3 chance that he did.
but he eliminates a door that you didn't pick, won't be able to choose from, and has no meaning on the final solution
Posted on 4/8/14 at 7:05 pm to SlowFlowPro
That is totally different... You gain the advantage knowing that your first pick is not changed (when you made the pick with lower odds of winning)
Posted on 4/8/14 at 7:05 pm to SlowFlowPro
quote:
-make the initial pick
-host removes 1/3 of the choices
-then they mix up and randomize the remaining 2 choices. what are the odds you pick the car or goat?
Do you know what he picked? Does he know?
And it really doesn't matter because you lost all the pertinent information you learned from the first round, so it's a true 50/50 at that point.
Posted on 4/8/14 at 7:06 pm to LSUtoOmaha
I am looking at as an actual game show. The host is always gonna open one of the doors with a goat behind it first. After that, it is a 50/50 shot. Changing your answer does nothing
You pick 1, he'll open 2 or 3, whichever one has a goat behind it. You pick 2, he'll open 1 or 3. Doesn't matter if you're first pick is right or wrong, he's gonna open a door with a goat behind it first
You pick 1, he'll open 2 or 3, whichever one has a goat behind it. You pick 2, he'll open 1 or 3. Doesn't matter if you're first pick is right or wrong, he's gonna open a door with a goat behind it first
Posted on 4/8/14 at 7:07 pm to Hammertime
quote:Which is exactly what makes it not 50/50
Doesn't matter if you're first pick is right or wrong, he's gonna open a door with a goat behind it first
Posted on 4/8/14 at 7:07 pm to LSUtoOmaha
I will never believe you have an advantage by switching. NEVER!
Posted on 4/8/14 at 7:08 pm to genro
quote:I totally understand this. And I have a liberal arts degree.
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.
Posted on 4/8/14 at 7:08 pm to genro
These people must be trolling at this point
Posted on 4/8/14 at 7:09 pm to StickyFingaz
Must be. The host's knowledge is what makes the difference.
Posted on 4/8/14 at 7:11 pm to lsu480
quote:
I will never believe you have an advantage by switching. NEVER!
Think of it this way.
Let's say there are 100 doors. You pick one.
Monty narrows it down to just 2 other doors out of the 100.
Do you stick with the door that you picked out of 100? Or do you go with the one that was narrowed down?
Posted on 4/8/14 at 7:12 pm to StickyFingaz
Have to be.
I mean, the Simulation link with empirical evidence has already been provided.
I mean, the Simulation link with empirical evidence has already been provided.
Posted on 4/8/14 at 7:13 pm to Broseph Barksdale
Logically, it makes absolutely zero sense...but it works. The host's knowledge is the key.
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