Monte Hall Hoax

[Hanarchy Montanarchy]

mea culpa: I've changed my mind on the Monty Hall problem.

ON THIS SITE, MARCH 5TH, 2021
AN OPINION WAS CHANGED ON THE INTERNET

Your comment about the superiority of getting the goat is a good comment on the trick of the paradox.

[Martin Hash]

Someday I’ll be famous and you’ll be like: “I knew that guy back when I was smarter than him.”

[DBTrek]

Someday I’ll be famous and you’ll be like: “I knew that guy back when I was smarter than him.”

Dudes ... really ... consider the same problem with 100 doors. You pick one door. Monte opens 98 that are goats. Is it really a 50/50 shot that you picked the right door the first time? Or is it more likely that you picked a goat, and Monte is showing you the other 98 goats then asking if you want to switch?

[Hanarchy Montanarchy]

I'll do you one better.

Imagine there are infinite doors and there are always 2 goats for every car. I think we can agree that it doesn't matter how many doors Monty opens, the ratio of goats to cars remains unchanged, so it doesn't matter if I stick with my first choice or switch.

What is happening in the Monte Hall problem is that ratio of goats to cars is changing. The trick is that it is assumed I don't want the goat, so I imagine revealing a goat is giving me information about where the car is. It isn't. It is giving me information about where one of the goats is. If I am still allowed to pick the open door, I am still playing the n/3 game, but with 100% odds of getting a goat.

The false assumption of the Monty Hall problem is that I could still pick the revealed goat if I wanted.

[DBTrek]

I'll do you one better.

Imagine there are infinite doors and there are always 2 goats for every car. I think we can agree that it doesn't matter how many doors Monty opens, the ratio of goats to cars remains unchanged, so it doesn't matter if I stick with my first choice or switch.

What is happening in the Monte Hall problem is that ratio of goats to cars is changing. The trick is that it is assumed I don't want the goat, so I imagine revealing a goat is giving me information about where the car is. It isn't. It is giving me information about where one of the goats is. If I am still allowed to pick the open door, I am still playing the n/3 game, but with 100% odds of getting a goat.

The false assumption of the Monty Hall problem is that I could still pick the revealed goat if I wanted.

You had a 2/3rds chance of picking the goat the first time - and Monte ALWAYS has a chance to show you the other goat. Whether you pick a car or a goat is irrelevant, he'll always have a goat to show. So, you make your pick at 2/3rds odds of getting a goat. Monte does what he was always going to do regardless - shows you a goat. His actions have no effect on the odds of your initial choice. It's neither more nor less likely that you picked a car or a goat, still 2/3rds chance your initial pick was wrong.

BUT - if you make a new decision after the reveal - then you're playing new odds of 50/50.

If you want the goat, keep your first choice. You can't pick the revealed goat, but the odds are in favor of you initially picking a goat. If you want the car, switch.

[Hanarchy Montanarchy]

The Monty Hall problem says my odds are 2/3 if I switch. Not 1/2. This is what reveals the assumption that the revealed goat is still in play, and that we are adjusting the odds of an n/3 game.

This isn't true. We are playing a whole new game of n/2, with Monty screwing me out of my 2/3rds chance of getting a goat in the first game.

[Martin Hash]

So far you all still think you’re smarter than me...

It’s just a statistical illusion: the odds are 50/50 once one of the goats is revealed.

[DBTrek]

The Monty Hall problem says my odds are 2/3 if I switch. Not 1/2. This is what reveals the assumption that the revealed goat is still in play, and that we are adjusting the odds of an n/3 game.

This isn't true. We are playing a whole new game of n/2, with Monty screwing me out of my 2/3rds chance of getting a goat in the first game.

No, there are no 2/3rds odds when you make a second decision involving two doors.
Unless, of course, you stick to your original guess which was made at 2/3rds odds.

It's been tested.
/shrug

[Hanarchy Montanarchy]

There are no 1/3 odds when you make your second choice either. The incentive to switch in the Monte Hall paradox assumes collapsing 2/3 odds onto one door.

[DBTrek]

There are no 1/3 odds when you make your second choice either. The incentive to switch in the Monte Hall paradox assumes collapsing 2/3 odds onto one door.

No, you're making the mistake of thinking that the revelation of goats has somehow affected the odds of your initial decision, and it has not. It can only affect the odds of your next decision. If you make no next decision (aka you make no new door picks) then you're holding a door that carries its initial odds. The trickery of revealing goats that the host always knew he could reveal regardless has confused your reasoning. Monte could reveal 1 goat, or (in my example) 98 goats no matter what you pick. The only thing changing the odds of your initial pick is making a new choice.