OK, smarty-pants, what's the best move?

[givememyleg]

I know I've heard this before, and I remember, "you should always switch." But no matter what, I cannot understand why.

you have to think of it in two separate parts.

1) 1 out of 3 boxes is $300. 2 out of 3 boxes is $0.

2) 1 out of 2 boxes is $300. 1 out of 2 boxes is $0.

if you have your choice between the two, obviously you would pick #2.

The first "coin toss" was three side, whereas the next one is two sided.

Also, if it helps, try replace 3 boxes with 300 boxes. Then go through the problem again:

- Choose 1 box out of 300
- Of the remaining 299 boxes, 298 boxes are revealed as $0
- Do you stick with your box (at 1/300) or pick the new box (at 1/2)?

[jackvance]

you have to think of it in two separate parts.

1) 1 out of 3 boxes is $300. 2 out of 3 boxes is $0.

2) 1 out of 2 boxes is $300. 1 out of 2 boxes is $0.

if you have your choice between the two, obviously you would pick #2.

The first "coin toss" was three side, whereas the next one is two sided.

Also, if it helps, try replace 3 boxes with 300 boxes. Then go through the problem again:

- Choose 1 box out of 300
- Of the remaining 299 boxes, 298 boxes are revealed as $0
- Do you stick with your box (at 1/300) or pick the new box (at 1/2)?

Math is still wrong here. It's still a 3-side cointoss, but now two of them net you $300. You basically get to choose between your first choice, or 'both of the others'.

And in the example of 300 boxes, you go from 1/300 to 299/300 chance.

[MadMojoMonkey]

You had a 3/1 shot the first time. now its 2/1.

It is not 50/50 on the 2nd choice; it's 33/67. This is a common mis-assessment of the effect of the revealed information.

In this case, the revealed box is ALWAYS empty. There is 0% chance the revealed box contains the money.

And in the example of 300 boxes, you go from 1/300 to 299/300 chance.

This is correct. You do NOT go to 50/50 on the 2nd choice.

[kiwiMark]

you have to think of it in two separate parts.

1) 1 out of 3 boxes is $300. 2 out of 3 boxes is $0.

2) 1 out of 2 boxes is $300. 1 out of 2 boxes is $0.

if you have your choice between the two, obviously you would pick #2.

The first "coin toss" was three side, whereas the next one is two sided.

In your second part, there's still no reason to pick Box B over Box A. Yes it's a better situation to be in than Situation One, but you're in this new better situation 100% of the time and your choice comes now, your choice doesn't come first and put you in the new better situation.