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

[Fort Fun Indiana]

You step up to a carnival booth. The carney running the game has 3 numbered cups upside-down on the table in front of you. He tells you there is $300 under one of them, and nothing under the other two. He knows what is under each cup.

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.

The carney flips over Cup #3 to reveal nothing is under the cup. He then asks you if you would like to keep your choice or change it to Cup #2.

What do you do? Does it even matter whether or not you switch your choice from Cup #1 to Cup #2?

 

[Dogmaphobe]

Your odds have been improved from one out of three to one out of two so you get the carnie to agree to allow you to play as many games as you wish where the same terms apply -- assuming, of course, that the carnie is telling the truth.

 

[Fort Fun Indiana]

Your odds have been improved from one out of three to one out of two

No. They haven't.

So, keep your choice, or switch? Does it even matter?

 

[Anomalism]

I'd keep my original choice. If the dude is offering me a chance to switch with only two cups active I'm going to assume he gave me that choice for a reason that benefits him. He wants me to second guess. If the one I picked was wrong he should have just flipped it and kept my money rather than giving me a chance to switch and win.

It wouldn't make sense for him to offer the switch if cup 1 is empty.

 

[Fort Fun Indiana]

I'd keep my original choice. If the dude is offering me a chance to switch with only two cups active I'm going to assume he gave me that choice for a reason that benefits him. He wants me to second guess. If the one I picked was wrong he should have just flipped it and kept my money rather than giving me a chance to switch and win.

Noted.

But maybe the carney is an idiot. Maybe it's his first day.

Or maybe he knows exactly what he is doing, and you are on to him.

The answer is in the mathematics...

 

[Fort Fun Indiana]

It wouldn't make sense for him to offer the switch if cup 1 is empty.

He offers everyone the opportunity to switch.

 

[Anomalism]

He offers everyone the opportunity to switch.

The answer to the riddle is that you should switch, but in a real life situation I'd probably stay. There's definitely a psychology element to consider if it's the real deal. Lol

The odds of cup 2 being a winner are better than the odds when you originally picked cup one.

 

[Fort Fun Indiana]

Not really relevant to the riddle:

The smart carney makes the prize only $280. Or $250. That would be the house edge. Otherwise, the game makes no money for the carney.

 

[Fort Fun Indiana]

The answer to the riddle is that you should switch, but in a real life situation I'd probably stay. There's definitely a psychology element to consider if it's the real deal. Lol

The odds of cup 2 being a winner are better than the odds when you originally picked cup one.

Noted.

 

[Fort Fun Indiana]

The odds of cup 2 being a winner are better than the odds when you originally picked cup one.

Are they?

Better than... what?

Better than your starting odds (1/3)?

 

[Anomalism]

Are they?

Better than... what?

Better than your starting odds (1/3)?

Once 3 is gone and you have a chance to pick cup 2 your odds will be better than the 1/3 odds when you originally picked cup one.

I think...

 

[Fort Fun Indiana]

Once 3 is gone and you have a chance to pick cup 2 your odds will be better than the 1/3 odds when you originally picked cup one.

I think...

Okay. But it wouldn't be an advantage to switch, if Cup #1's odds are the same or better than Cup #2's odds, at this point.

So, switch or stay? Or does it not matter?

 

[Dogmaphobe]

No. They haven't.

So, keep your choice, or switch? Does it even matter?

You are not describing the situation properly, then.

If there are three cups and he shows you what is underneath one of them, that only leaves two cups. One of them is therefore empty and one contains 300 dollars.

 

[Fort Fun Indiana]

If there are three cups and he shows you what is underneath one of them, that only leaves two cups. One of them is therefore empty and one contains 300 dollars.

These things are all true. Exactly what I am describing.

 

[Anomalism]

Okay. But it wouldn't be an advantage to switch, if Cup #1's odds are the same or better than Cup #2's odds, at this point.

So, switch or stay?

I believe the strictly mathematical answer to the riddle would be to pick cup 2. My gut tells me to stick with cup 1 though.

 

[Fort Fun Indiana]

I believe the strictly mathematical answer to the riddle would be to pick cup 2. My gut tells me to stick with cup 1 though.

Ha, noted

 

[Dadoalex]

You step up to a carnival booth. The carney running the game has 3 numbered cups upside-down on the table in front of you. He tells you there is $300 under one of them, and nothing under the other two. He knows what is under each cup.

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.

The carney flips over Cup #3 to reveal nothing is under the cup. He then asks you if you would like to keep your choice or change it to Cup #2.

What do you do? Does it even matter whether or not you switch your choice from Cup #1 to Cup #2?

Does not matter.
There is nothing in the OP hinting at either 1 or 2 and, assuming it is not a scam, after all, it is at a carnival, the probability of being correct or incorrect are equal.

 

[Dogmaphobe]

These things are all true. Exactly what I am describing.

Which means your odds are then 50/50. Like, DUH!

There is obviously no advantage or disadvantage to switching choices since revealing the empty cup only affects the odds and not the likelihood as to what either contains.

You aren't very good at this, are you?

 

[Fort Fun Indiana]

Does not matter.
There is nothing in the OP hinting at either 1 or 2 and, assuming it is not a scam, after all, it is at a carnival, the probability of being correct or incorrect are equal.

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?

 

[Anomalism]

Which means your odds are then 50/50. Like, DUH!

There is obviously no advantage or disadvantage to switching choices since revealing the empty cup only affects the odds and not the likelihood as to what either contains.

You aren't very good at this, are you?

It's a statistics riddle that is going over your head. You're supposed to pick cup 2. It's about compounded odds. You're taking a better gamble by switching to cup two.