What Book Are You Reading at the Moment?

[Martin Hash]

Definitely NOT standardized test material.

[DBTrek]

It’s not about the prize location as much as leveraging the knowledge of the second participant (who knows the prize location) to your advantage. You made a random choice. There is a 2/3rds chance the game host did not. That’s where the odds shift.

[Fife]

It’s not about the prize location as much as leveraging the knowledge of the second participant (who knows the prize location) to your advantage. You made a random choice. There is a 2/3rds chance the game host did not. That’s where the odds shift.

Precisely.

At the time you are asked if you want to switch, the game host is offering you your original choice (1/3 chance at the prize) against the field (2/3 chance at the prize).

Nothing has changed your original chance at winning (1/3) vs. the field (2/3); HOWEVER the host has helped you out greatly by reducing the field from two options down to just one. Easy pickings.

Imagine the same set-up, but with 1,000 doors. Then the host reveals 998 losing doors after your choice, and lets you decide if you want to keep your original 1/1000 chance door or switch to the only remaining door in the 999/1000 field. What would you do?

[Speaker to Animals]

It’s not about the prize location as much as leveraging the knowledge of the second participant (who knows the prize location) to your advantage. You made a random choice. There is a 2/3rds chance the game host did not. That’s where the odds shift.

Precisely.

At the time you are asked if you want to switch, the game host is offering you your original choice (1/3 chance at the prize) against the field (2/3 chance at the prize).

Nothing has changed your original chance at winning (1/3) vs. the field (2/3); HOWEVER the host has helped you out greatly by reducing the field from two options down to just one. Easy pickings.

Imagine the same set-up, but with 1,000 doors. If the host reveals 998 losing doors after your choice, and lets you decide if you want to keep your original 1/1000 chance door or switch to the only remaining door in the 999/1000 field, what would you do?

Your odds do not change, though. You still have a fifty percent chance whether you change your selection or not.

[Fife]

Negatory.

Did you run the simulation? IRL don't lie to you.

It really is a neat book, and the math is correct.

[DBTrek]

The statistical change comes not from the actual prize location, but from the knowledge that the game host *cannot* reveal the prize. There is a 2/3rds chance the other cup was not revealed because doing so exposes the prize. There is only a 1/3rds chance you made the correct guess initially.

Now, remove the game host from the equation and simply choose between two cups and the odds are 50/50, as expected.

[Speaker to Animals]

Negatory.

Did you run the simulation? IRL don't lie to you.

It really is a neat book, and the math is correct.

Look at it another way..


Let's say you and I both play at the same time. I chose cup A. You chose cup A. Cup C is overturned and there is no prize. We are given the option to choose again, whereby I refrain and you choose cup B.

I think at that point is where our disagreement begins.

You claim that my choice to not change cups means I still only have a 33% chance of having chosen the correct cup, and your decision to change to cup B somehow magically increased your odds to 50%.

But if DB were playing, and he had originally chosen cup B, and he the decided to go with cup A, then your argument dictates my odds should also magically go up based on DB's decision to choose again.

But the location of the prize is not affected by our choices, and adding DB to the game should not somehow magically increase my odds.

You are assigning probabilities to choices and not physical locations. It's a semantic mistake.

[Fife]

Negatory. (and switching increases your odds to 66.7%, not 50%)

Each cup has a 1/3 chance of being a winner and a 2/3 chance of being a loser. That doesn't change.

The host giving away one of the 2 losing cups doesn't change the chance your first choice (no matter which one of the three it was) has a 1/3 chance of having the prize; and the remaining field having a 2/3 chance in the aggregate of containing the winner.

Run the simulation for yourself.

[Speaker to Animals]

Negatory. (and switching increases your odds to 66.7%, not 50%)

Each cup has a 1/3 chance of being a winner and a 2/3 chance of being a loser. That doesn't change.

The host giving away one of the 2 losing cups doesn't change the chance your first choice (no matter which one of the three it was) has a 1/3 chance of having the prize; and the remaining field having a 2/3 chance in the aggregate of containing the winner.

Run the simulation for yourself.

You are not reading what I wrote.

Read it again.

My choice to refrain and DB's choice to switch end on the same cup. The probability cannot be different for the same cup based on the choices of the participants.

Once you add more than one chooser, the error is pretty obvious. If you bother to read.

[DBTrek]

In your example none of us know where the prize is. The odds only shift when someone who knows the prize location is forced to reveal a non-prize.