how would you answer this brainteaser?

[VAisforlovers]

There are only 6 cards in the universe with the given values

$5, $10, $20, $40, $80, $160

There are two participants and one of them is you. Whatever you receive, the other participant can only receive the one on the left or the right. For example, if you receive the $40 card, the other participant has $20 or $80. You can request to trade your card to whatever the participant is holding and he can reject/accept it.

If you received the $40 card, do you keep $40 or request a trade?

 

[ALIVE]

There are only 6 cards in the universe with the given values

$5, $10, $20, $40, $80, $160

There are two participants and one of them is you. Whatever you receive, the other participant can only receive the one on the left or the right. For example, if you receive the $40 card, the other participant has $20 or $80. You can request to trade your card to whatever the participant is holding and he can reject/accept it.

I you received the $40 card, do you keep $40 or request a trade?

there is no point to ask
cause in any given card the other will go for the bigger one
and since he can reject why to bother
so why ask so he has taken the 20$ and trade it for the 40$ you hold??

whatever you take keep it
the other holds all the trading after your choice
if you want to loose go and ask

 

[Schmide]

This is a value of the game problem.

I would take the trade as you gain $40 or lose $20, therefore the value of the game is $20. Meaning if you apply the same chance over and over you gain $20 on average.

 

[ALIVE]

This is a value of the game problem.

I would take the trade as you gain $40 or lose $20, therefore the value of the game is $20. Meaning if you apply the same chance over and over you gain $20 on average.

well it does not matter you can not force the switch so
why bother to ask???

 

[baoytl]

There are only 6 cards in the universe with the given values

$5, $10, $20, $40, $80, $160

There are two participants and one of them is you. Whatever you receive, the other participant can only receive the one on the left or the right. For example, if you receive the $40 card, the other participant has $20 or $80. You can request to trade your card to whatever the participant is holding and he can reject/accept it.

If you received the $40 card, do you keep $40 or request a trade?

The other person either got a $20 or $80. Let's say it's $80. If you got $160 you wouldn't ask for a trade, therefore you got $40. Assuming the other person is aware of this, he should reject your offer. Therefore there is no upside to offer to trade. Either you get rejected or might get downgraded to a $20.

 

[videogames101]

i would look at the average values

40

vs.

(20 + 80) / 2 = 50

i'd ask for a trade, assuming that the whole accept/reject thing is blind?

 

[VAisforlovers]

I originally answered in a similar method as Schmide
But the guy said that he can reject or accept so I kind of froze up and screwed it up. It's pretty easy when having time to think about it but it's nerve wrecking when you're put on the spot in front of people and it came unexpectedly.

 

[Jaepheth]

E[x] = .5*20 + .5*80 = 50
50 > 40

therefore:
Request trade

Note: Assumes uniform distribution

If you're the one accepting/rejecting the trade then:
Given you have card with value x:
Case 1: other player has x/2 card
from their perspective: .5*x/4 + .5*x = 5/8 *x
5/8 > 1/2 -> Request Trade
Case 2: other player has 2x card
.5*x + .5*4x = 5/2 *x
5/2 > 2 -> Request Trade

Therefore, Player 1 Should ALWAYS request a trade unless they're holding the maximum value card, and likewise player 2 should always accept the trade unless they're holding the maximum value card.

EDIT: fralexandr brought up a good point. If player 2 assumes player 1 is rational, then they will reject a trade offer if they are holding the $80 card.

So player 1 will request a trade for any card except 160, and player 2 should accept any trade unless they have the 80 or 160 card.

 

[HeXen]

Well if I have a $20 card, at worst i'm still up 10 more than I had before, which was nothing. So its win win

 

[fralexandr]

edit: baotyl beat me

if it's given that both persons are intelligent enough and understand the rules (assuming the other contestant doesn't know your card and vice versa, AND that both contestants can see their own card):

if you have the $40 card, it would be pointless to ask for a trade, since if the other person has $80 he assumes either you have $160 or $40. If you're asking for a trade, he likely assumes you DON'T have $160. Thus he will reject the offer.

If the other person has $20, then he might choose to either accept or reject it, and would likely choose to accept.

 

[ALIVE]

if it's given that both persons are intelligent enough and understand the rules (assuming the other contestant doesn't know your card and vice versa, AND that both contestants can see their own card):

if you have the $40 card, it would be pointless to ask for a trade, since if the other person has $80 he assumes either you have $160 or $40. If you're asking for a trade, he likely assumes you DON'T have $160. Thus he will reject the offer.

If the other person has $20, then he might choose to either accept or reject it, and would likely choose to accept.

well you choose a card and the other can choose a card left or right
so one option will get him a lower value than you and the other higher
so why not on earth the other take always the higher option and simply reject your trade offer. and why on earth you want to trade
that will always lead to a lower value

1)player 2 got the higher value rejects
2)player 2 got the lower value accepts

so for player one stays the same or loose half
so if you are player1 never trade

 

[Dirigible]

The other person either got a $20 or $80. Let's say it's $80. If you got $160 you wouldn't ask for a trade, therefore you got $40. Assuming the other person is aware of this, he should reject your offer. Therefore there is no upside to offer to trade. Either you get rejected or might get downgraded to a $20.

Yup.

 

[Lifted]

The other person either got a $20 or $80. Let's say it's $80. If you got $160 you wouldn't ask for a trade, therefore you got $40. Assuming the other person is aware of this, he should reject your offer. Therefore there is no upside to offer to trade. Either you get rejected or might get downgraded to a $20.

This

 

[SKORPI0]

You already lost if/when you get the $80 card. Other person gets the $160 card.

$160>$5+$10+$20+$40+$80. ^_^

 

[disappoint]

i would look at the average values

40

vs.

(20 + 80) / 2 = 50

i'd ask for a trade, assuming that the whole accept/reject thing is blind?

It's not that you did the math wrong. It's that you did the wrong math.

 

[disappoint]

You already lost if/when you get the $80 card. Other person gets the $160 card.

$160>$5+$10+$20+$40+$80. ^_^

If you got the $80, how do you know the other person didn't get the $40? You haven't lost you just shouldn't ask for a trade.

 

[DrPizza]

This seems pretty simple to me, perhaps I skimmed over it too quickly.

If you receive $40, you can request a trade. (The other guy can say "yes" or "no" to the trade. Of you have $40, there are two cases: the other guy either has $20 or $80.

A: The other guy has $80. If he has $80, he knows that you either have $40 or $160. Since only a moron would trade away $160 in a game like this, he's going to know you have $40. And, he will say, "no thanks."

B: The other guy has $20. If he has the $20, he'll know you have either $10 or $40. Regardless of whether he accepts your proposal or not, you'll lose if he says yes. It's not a guarantee that he'll say yes though. Under this circumstance, he risks $20 to either get $10 or $40. Some might think he'd accept the trade every time. But, if he's intelligent to reason this out, and judges that you're also intelligent enough not to take a chance when you have $40, then he can assume you have $10 and will say "no."

*Now I read the posts & accept that several others (baoytl & fralexandr among others.)

 

[Schmide]

I thought about this for a bit (watching the caps lose) and my original answer was wrong. I would not request the trade.

Did not read responses sorry if I repeat something.

Logically you can only get the $10, $20, $40, $80 cards as the game would be void if you got the $5 or the $160.

The other dude would never trade the $160 and always trade the $5.

In addition he would not trade the $80 as if he had the $80 he knows you can't have the $160 and therefore he knows you must have the $40.

If he has the $20 he can either gain $20 or lose $10. This is the only trade the other guy would make.

So in the end the other guy has way better information and would win always except for the $10 $20 $40 triplet

 

[T_Yamamoto]

shoot the man, take all the money

problem solved.

 

[disappoint]

shoot the man, take all the money

problem solved.

Only if they don't let you post from prison.

 

[thraashman]

Does this sound like a variation on the Monty Hall problem to anyone else?

Always switch doors...

 

[baoytl]

Does this sound like a variation on the Monty Hall problem to anyone else?

Always switch doors...

Thinking about this more, it's actually the reverse of the Monty Hall problem. Don't switch.

Assuming that both people are logical,

Case 1:
Person A receives $160.
Person B receives $80. No upside for Person A to offer trade obviously.

Case 2:
Person A receives $80.
Person B receives $160 (which would reject any trade offers) or
Person B receives $40. No upside for Person A to offer trade.

Case 3:
Person A receives $40.
Person B receives $80 (Person A either received $160 or $40. Only a person that received $40 would offer to trade. Therefore Person B would reject trade.) or
Person B receives $20. No upside for Person A to offer trade.

Case 4:
Person A receives $20.
Person B receives $40 (Person A either received $80 or $20. Person A wouldn't offer to trade in Case 2, therefore Person A has $20. Person B would reject trade offer.) or
Person B receives $10. No upside for Person A to offer trade.

Case 5:
Person A receives $10.
Person B receives $20 (Person A either received $40 or $10. If Person A received $40, he shouldn't offer a trade as in Case 3. Therefore Person B should reject any trade offers since only a person that received $10 would offer a trade.) or
Person B receives $5. No upside for Person A to offer trade.

Case 6:
Person A receives $5.
Person B receives $10 (Person A either received $20 or $5. As in Case 4, Person A shouldn't offer a trade if he got $20. Therefore Person B should reject any trade offers from Person A. Person A should offer to trade but should be rejected by Person B.

So assuming both participants are somewhat intelligent and logical, Person A shouldn't offer to trade except when receiving $5. Person B should reject any trade offer because the only time Person A would offer to trade would be if he received $5.

 

[disappoint]

This thread is now declared downhill from this point forward.

 

[Mr. Pedantic]

Why would you ever want to switch?

 

[Phoenix86]

B: The other guy has $20. If he has the $20, he'll know you have either $10 or $40. Regardless of whether he accepts your proposal or not, you'll lose if he says yes. It's not a guarantee that he'll say yes though. Under this circumstance, he risks $20 to either get $10 or $40. Some might think he'd accept the trade every time. But, if he's intelligent to reason this out, and judges that you're also intelligent enough not to take a chance when you have $40, then he can assume you have $10 and will say "no."

Never bet against a sicilian when death is on the line!