Another logic riddle, a lot tougher, builds on principles from the others

[Anomalism]

At the start the odds are 1/3. After one cup is revealed empty the odds of either remaining cup containing the $300 increase to 1/2.

The odds on cup 1 don't change statistically after cup 3 is lifted because you didn't have any information about cup 3 when you originally chose cup 1. It's still the same game and cup 1 remains a 1/3 chance after cup 3 is revealed. There are still three cups. It's just that one of them has been revealed now. If you switch to cup 2 after cup 3 has been revealed you've now elevated yourself to 2/3 because you know what's in cup 3 now and you're picking cup 2. You didn't have that same perspective when you chose cup 1.

 

[Grumblenuts]

The odds on cup 1 don't change statistically after cup 3 is lifted because you didn't have any information about cup 3 when you originally chose cup 1. It's still the same game and cup 1 remains a 1/3 chance after cup 3 is revealed. There are still three cups. It's just that one of them has been revealed. If you switch to cup 2 after cup 3 has been revealed you've now elevated yourself to 2/3 because you know what's in cup 3 and you're going with cup 2. You didn't have that same perspective when you chose cup 1.

Understood. But now that you know cup 3 is empty your odds for cup 1 have indeed increased to 1/2. Sequential logic. This all assumes a fair game where the monte dealer really has no idea where the money ends up after the initial shuffle and there are no trap doors in the table.

 

[Anomalism]

Understood. But now that you know cup 3 is empty your odds for cup 1 have indeed increased to 1/2. Sequential logic. This all assumes a fair game where the monte dealer really has no idea where the money ends up after the initial shuffle and there are no trap doors in the table.

It's about the odds at the moment you made your choice. By switching to cup 2 after 3 is revealed you're making your choice from a much more informed position. Statistically you're better off choosing cup 2, even though you might still lose.

 

[Grumblenuts]

Initial Possibilities:
100
010
001

Possibilities after 1 cup flipped:
10
01

 

[Anomalism]

Initial Possibilities:
100
010
001

Possibilities after 1 cup flipped:
10
01

The riddle is counter-intuitive, but I suppose that's how good riddles are. I'll take another crack at explaining it tomorrow.

 

[Fort Fun Indiana]

At the start the odds are 1/3. After one cup is revealed empty the odds of either remaining cup containing the $300 increase to 1/2.

So, you say it does not matter if you switch.

 

[Fort Fun Indiana]

Initial Possibilities:
100
010
001

Possibilities after 1 cup flipped:
10
01

No.

Getting warmer, though.

You are counting combinations instead of permutations, in your second step.

 

[Grumblenuts]

I

So, you say it does not matter if you switch.

In this case, meaning the carnival worker is completely fair and ignorant, yes, no it does not matter.

You are counting combinations instead of permutations, in your second step.

I do what makes sense to me. You do you. Perhaps I'll change my mind.

 

[Fort Fun Indiana]

I

In this case, meaning the carnival worker is completely fair and ignorant, yes, no it does not matter.

I do what makes sense to me. You do you. Perhaps I'll change my mind.

Well that's a nice thought,but one answer is correct, and the rest are not.

 

[Grumblenuts]

Monty Hall always knew what was behind each door so the big prize was never revealed on the first round. There the 2/3 odds analysis applied. This case is presumably different.

one answer is correct, and the rest are not.

Obviously. Now you've got mine. Enjoy.

 

[meaner gene]

Maybe it's best understood by:
Reductio ad absurdum is also known as "reducing to an absurdity." It involves characterizing an opposing argument in such a way that it seems to be ridiculous, or the consequences of the position seem ridiculous.

Start with 100 cups. You chose one, placed on the left table, and the other 99 on the right table.. It's clear that the odds on the left is 1 in 100, and on the right 99 in 100

You are told that from those 99 cups on the right, the carney will turn over empty cups (98 of them) until there is only one cup remaining.

Do you keep the left table (1 out of 100), or switch to the right table (99 of out 100)

This holds whether the split is 1/100 and 99/100, or 1/3 and 2/3.



Do you stick with the

 

[Fort Fun Indiana]

Monty Hall always knew what was behind each door so the big prize was never revealed on the first round. There the 2/3 odds analysis applied. This case is presumably different.

Obviously. Now you've got mine. Enjoy.

It's not different. So you get it.

 

[Fort Fun Indiana]

Maybe it's best understood by:
Reductio ad absurdum is also known as "reducing to an absurdity." It involves characterizing an opposing argument in such a way that it seems to be ridiculous, or the consequences of the position seem ridiculous.

Start with 100 cups. You chose one, placed on the left table, and the other 99 on the right table.. It's clear that the odds on the left is 1 in 100, and on the right 99 in 100

You are told that from those 99 cups on the right, the carney will turn over empty cups (98 of them) until there is only one cup remaining.

Do you keep the left table (1 out of 100), or switch to the right table (99 of out 100)

This holds whether the split is 1/100 and 99/100, or 1/3 and 2/3.



Do you stick with the

Yup

 

[Grumblenuts]

He knows what is under each cup.

I missed that caveat is all.

For $100, you get to choose a cup to be flipped and keep whatever is underneath.. You pay your $100 and point to Cup #1.

That would get mighty expensive with 100 cups!

 

[Dadoalex]

Noted.

Now, think about what you are stating:

You believe your odds have improved, because the carney showed you an empty cup after you made your bet. You believe Cup #1 had 1/3 odds, but it now has 1/2 odds. Because the carney showed you an empty cup.

Does that feel right to you?

Didn't say that.
When cup 3 was exposed the game changed. The odds of the original game were 1/3. The new game's odds are 1/2.

But, whether the 1st or 2nd game changing the decision does not change the probabilities.

 

[Fort Fun Indiana]

Didn't say that.
When cup 3 was exposed the game changed. The odds of the original game were 1/3. The new game's odds are 1/2.

So yes, it's exactly what you are saying.

You think your odds improved because the carney showed you an empty cup. Does that feel right to you?

So if you pick a cup each time, no switching allowed, and he shows you an empty cup before flipping your cup...

Do you think this increases your odds? Do you think you have better than 1/3 odds for your bet, after the flips an empty cup?

 

[Rogue AI]

Better to discourage gambling at carnivals and applying logic on more practical things. Plus how much are you really enjoying the frivolity of the carnival if you are wracking your brain on the odds? This is why many hate math.

 

[Dadoalex]

So yes, it's exactly what you are saying.

You think your odds improved because the carney showed you an empty cup. Does that feel right to you?

So if you pick a cup each time, no switching allowed, and he shows you an empty cup before flipping your cup...

Do you think this increases your odds? Do you think you have better than 1/3 odds for your bet, after the flips an empty cup?

Obviously you don't understand the difference between dependent and independent probabilities.

the odds, unless the money is returned and a new game started with 2 cups, do not change for the 3 cup game.
It was 1/3, it remains 1/3.


Again, you ask the question NOT about cup 3 but whether the odds change if, after showing cup 3, the player chooses to move to cup 2.

The original be remains the same and the probability of the original bet does not change.

 

[Grumblenuts]

The OP should have made two things clear:

1. Carnival games are for suckers. Like at a casino, the fix is in or the game wouldn't appear.
2. Switching cups costs you an additional $100.

 

[Fort Fun Indiana]

the odds, unless the money is returned and a new game started with 2 cups, do not change for the 3 cup game.
It was 1/3, it remains 1/3.

Yes I know, that was my point