2 boxes, you open one and find it has $100

[MrPickins]

I tell Monty that he can keep both of those boxes; I want what's behind the giant box of Rice-a-Roni.

 

[DigDog]

dont take the box. the actual laws of the universe dictate that 100% of people who chose to open the second box will find the $50.
https://en.wikipedia.org/wiki/Murphy's_law

 

[Mr.IncrediblyBored]

You stand to gain more than you lose.

No, you have a 50/50 chance of getting the lesser amount. There is no benefit to giving up the first envelope for the second.

 

[Rakehellion]

No, you have a 50/50 chance of getting the lesser amount. There is no benefit to giving up the first envelope for the second.

The amount lost is less than the amount gained. Let's say the first envelope contains $100 and the second envelope either contains $99 or $200. Do you switch or keep the same envelope? Take it a step further: Let's say the second envelope always contains $200. Do you switch?

Either way, it's a bullshit scenario involving magical money-generating envelopes that could never happen in real life. It isn't problem solving, it's just a riddle.

 

[MongGrel]

Id open the 2nd box

It's a trick, you'd only find a dead cat...

:sneaky:

 

[MagnusTheBrewer]

It's a trick, you'd only find a dead cat...

:sneaky:

He wasn't dead til you opened the box.

 

[WHAMPOM]

So there are two boxes. You open one, and it has $100 in it.

1- Between the two boxes, one has double the money as the other.
2- You don't if your box is the double box or not.

Given this information, you can choose to keep the $100 box, or switch to the other box.

What is the best strategy?

Greed out wins every time in the hope the second box has double the money. Human nature over math.

 

[JTsyo]

Given the analysis many have done above, everyone would switch. So, no matter which box you opened first, you would choose the second one. (Or rather, you would use that reasoning to determine that switching would lead to better payoffs in the long run.)

So, before you even look inside the box, you switch boxes. Think for a moment and realize that it doesn't matter.

edit: damn you chiropteran! In my defense, I was in the middle of eating the most awesome steak sandwich, with a cheddar cheese spread pasted on to the roll instead of mayo, onions and peppers, and incredibly tender strips of steak. I had to wait til I was done eating to start typing. That's why you beat me to a solution, though I didn't know this problem had a name.

The amount matters though. I rather take a shot at getting $200 than keeping $100. But if it was $10K, I would keep the $10K since that's good money.

 

[Raduque]

You are all wrong.

https://en.wikipedia.org/wiki/Two_envelopes_problem

Math and mathemeticians LITERALLY make everything more difficult than it needs to be.

Jaepheth had the correct answer.

 

[DrPizza]

No one was wrong. Switching doesn't harm, so you should switch. Not necessarily for this problem, but for all the other variants where switching is the good idea. And since then you will know the truth. Not switching means it'll eat at you for the rest of your life in wonder.

Now, if you could prove that switching was bad in the long run for this case, that would be another story.

Let's say that I'm the host of my own game show. There are 3 doors, and behind one of those doors, there's a big prize. Behind the other two doors, there's a non-prize. You pick a door. I then reveal what's behind one of the other two doors - a non-prize. And then, I offer you the opportunity to change your pick. Would you change your pick?

Spoiler

It would be a bad idea to change your pick.

Let's see who's truly good with logic, and who isn't.

 

[ImpulsE69]

Some people have too much time on their hands. You aren't given enough information to make a good decision and therefore it is simply gambling. It all comes down to how much risk you are willing to take for an unknown outcome. There is no better choice than the other given the known info.

 

[cubby1223]

You are all wrong.

https://en.wikipedia.org/wiki/Two_envelopes_problem

In the time it took me to read that wikipedia page, the contestant stole both envelopes from me... He has achieved the maximum sum possible.

 

[cubby1223]

Let's say that I'm the host of my own game show. There are 3 doors, and behind one of those doors, there's a big prize. Behind the other two doors, there's a non-prize. You pick a door. I then reveal what's behind one of the other two doors - a non-prize. And then, I offer you the opportunity to change your pick. Would you change your pick?

Spoiler

It would be a bad idea to change your pick.

Let's see who's truly good with logic, and who isn't.

Your spoiler is wrong.

And back to the original problem, it is always better to switch. At least at first. On the first run you have a 50% chance of receiving $50, 50% chance of $100. So switch. And if you argue it doesn't matter, then switching does no harm.

What switching does do is allows you to develop knowledge over time of how often you are presented the higher sum envelope, and what typical range do the envelope values fall within. Switching often early on allows one to make educated choices later on to beat the odds and maximize value.


Of course then we have to factor in what happens to the money in the envelope you don't take. If for example it's being donated to a minority girls orphanage, you may be better off using your knowledge to minimize your immediate totals in order to not receive public internet backlash from orphanage-loving SJW's ruining your ability to hold a job and ruin your future income. Lot's of factors to consider in what's the best choice.

 

[Mr.IncrediblyBored]

The amount lost is less than the amount gained. Let's say the first envelope contains $100 and the second envelope either contains $99 or $200. Do you switch or keep the same envelope? Take it a step further: Let's say the second envelope always contains $200. Do you switch?

Either way, it's a bullshit scenario involving magical money-generating envelopes that could never happen in real life. It isn't problem solving, it's just a riddle.

The only thing you said that makes sense is that it's a bullshit scenario that will never happen in real life. But that's not the point is it?

There is a 50% chance you've already picked the higher amount with the first envelope. With your fuzzy logic, that means you'll give it up for the lesser (by switching for the second envelope) amount 50% of the time. Go ahead and switch if it makes you feel better. Doesn't help your chances though.

 

[cubby1223]

No, you have a 50/50 chance of getting the lesser amount. There is no benefit to giving up the first envelope for the second.

On a piece of paper make two columns, and any amount of rows (at least more than 3 rows). On the left-hand side write $100 in each row. On the right-hand side alternate between $50 and $200 for each row. With two columns of equal length, sum up all the values of the left-hand column and all the values of the right-hand column.

Which summation is greater?

 

[DrDoug]

I'll take the first box and leave...lol! I'm not interested in what is in the second box because I'm already ahead, some fool gave me money for free!

A bird in the hand and all that...

 

[Rakehellion]

The only thing you said that makes sense is that it's a bullshit scenario that will never happen in real life. But that's not the point is it?

There is a 50% chance you've already picked the higher amount with the first envelope. With your fuzzy logic, that means you'll give it up for the lesser (by switching for the second envelope) amount 50% of the time. Go ahead and switch if it makes you feel better. Doesn't help your chances though.

Chances to do what? Pick the "correct" envelope or make the most money?

Your argument completely ignores the amount in each envelope and assigns them arbitrary values of "positive" and "negative." This is bad math. By your logic, you shouldn't switch even if your envelope contains $1 because you still have only a 50% chance of winning.

 

[Rakehellion]

Some people have too much time on their hands. You aren't given enough information to make a good decision and therefore it is simply gambling.

Every decision a person can make is gambling.

And I argue that you have all the information you need: The game is rigged. So you know you have no choice but to switch.

 

[Rakehellion]

Let's say that I'm the host of my own game show. There are 3 doors, and behind one of those doors, there's a big prize. Behind the other two doors, there's a non-prize. You pick a door. I then reveal what's behind one of the other two doors - a non-prize. And then, I offer you the opportunity to change your pick. Would you change your pick?

Spoiler

It would be a bad idea to change your pick.

Let's see who's truly good with logic, and who isn't.

Wrong. https://en.wikipedia.org/wiki/Monty_Hall_problem

 

[ImpulsE69]

Every decision a person can make is gambling.

And I argue that you have all the information you need: The game is rigged. So you know you have no choice but to switch.

You have a choice. You don't have to switch, which is the path most risk averse people would take.

 

[DrPizza]

Wrong. https://en.wikipedia.org/wiki/Monty_Hall_problem

You're the first person to be wrong. Any other flies want to get caught in my trap? Most people only have a superficial understanding of the Monty Hall problem.

 

[Subyman]

Since I don't get to do it over and over to get a large sample and make my $125, I'd choose to stay put.

 

[cubby1223]

You're the first person to be wrong. Any other flies want to get caught in my trap? Most people only have a superficial understanding of the Monty Hall problem.

No, it's a well-established situation with easily verifiable results through a computer simulation running a large number of randomized scenarios.

 

[DrPizza]

No, it's a well-established situation with easily verifiable results through a computer simulation running a large number of randomized scenarios.

I'm sorry, you're also wrong. Who wants to be the third person who is wrong? Read my post again, and assume that I'm pretty good at math. The Monty Hall problem is one of my biggest pet peeves (in mathematics), because so many people get it wrong. I'll consider this successful if even a few more people gain a better understanding of the Monty Hall problem. The computer simulations you're speaking of get the problem I proposed wrong - I'll explain why tomorrow at lunch time.

Or, maybe I'm wrong? Nah, I don't think so.

 

[cubby1223]

I'm sorry, you're also wrong. Who wants to be the third person who is wrong? Read my post again, and assume that I'm pretty good at math. The Monty Hall problem is one of my biggest pet peeves (in mathematics), because so many people get it wrong. I'll consider this successful if even a few more people gain a better understanding of the Monty Hall problem. The computer simulations you're speaking of get the problem I proposed wrong - I'll explain why tomorrow at lunch time.

Or, maybe I'm wrong? Nah, I don't think so.

You don't even need a simulation, just pen & paper. Choose 1 of 3 doors to be the prize, choose 1 of 3 doors to be the contestant's choice. That creates 9 unique scenarios of equal chance of occurrence. Continue the game show for each of the 9 scenarios. Switching your pick wins 6 out of the 9 scenarios.