The money in 2 evelopes "paradox"

[Guest GhostRanger]

What I mean is althuogh it is a 50/50 chance whether you gain or lose money, if you do gain money you will gain more money than you would lose if you lost money. So it is more profitable to switch.

 

 

 

Do y'see what I mean?

 

 

 

I see exactly what you mean and it still doesn't make sense. In fact, I saw exactly what you meant from the beginning when I made my post about how it doesn't make sense. But, to explain again, here's why:

 

 

 

It doesn't matter if the amount you make is more than the amount you lose. Either way, you lose money or you make money. Losing $50 surely isn't better than the chance that you MIGHT have gained $100, because at the end of the wrong choice, you've still lost $50.

 

 

 

It's a 50/50 choice, period. There's no paradox, and there's no weird formula needed to understand that it's a 50/50 chance.

[Quer_Skulll]

what's the point? free money either way :lol:

 

 

 

totally!

[Kashi]

Aaaaahaaaa. But!

 

 

 

Let's say each time it's random what amount of money is in the envelopes.

 

 

 

50% of the time it's $50 and $100,and the other 50% of the time it's $100 and $200. Basically ...

 

 

 

Since when you cut something in half, the amount decreased gets smaller each time, and when you double something the amount increased gets larger each time, there is more to be gained in this situation than there is to be lost.

 

 

 

So if I do this 10 times, with the results:

 

 

 

$200

 

$200

 

$50

 

$200

 

$50

 

$50

 

$50

 

$200

 

$50

 

$200

 

 

 

(Which is statistically what your average results would be.) Then I've won $1250.

 

 

 

If I stayed the same each time, I would win $1000 for sure. If I switch, I would win anywhere between $500 - $2000. Therefore, like I said, there is more potential gain in switching envelopes than there is potential loss.

 

 

 

So, in conclusion ...

 

 

 

IF YOU FOLLOW THE LAW STATISTICS, SWITCHING WOULD BE (on average) MORE PROFITABLE THAN OTHERWISE.

 

 

 

Why don't you get a bunch of envelopes and some pieces of paper and try it out for yourself. It depends about 50% on luck, but once again, on average switching will get you more money.

 

 

 

:| :) :D :mrgreen:

[Guest GhostRanger]

Aaaaahaaaa. But!

 

 

 

Let's say each time it's random what amount of money is in the envelopes.

 

 

 

50% of the time it's $50 and $100,and the other 50% of the time it's $100 and $200. Basically ...

 

 

 

Since when you cut something in half, the amount decreased gets smaller each time, and when you double something the amount increased gets larger each time, there is more to be gained in this situation than there is to be lost.

 

 

 

So if I do this 10 times, with the results:

 

 

 

$200

 

$200

 

$50

 

$200

 

$50

 

$50

 

$50

 

$200

 

$50

 

$200

 

 

 

(Which is statistically what your average results would be.) Then I've won $1250.

 

 

 

If I stayed the same each time, I would win $1000 for sure. If I switch, I would win anywhere between $500 - $2000. Therefore, like I said, there is more potential gain in switching envelopes than there is potential loss.

 

 

 

So, in conclusion ...

 

 

 

IF YOU FOLLOW THE LAW STATISTICS, SWITCHING WOULD BE (on average) MORE PROFITABLE THAN OTHERWISE.

 

 

 

Why don't you get a bunch of envelopes and some pieces of paper and try it out for yourself. It depends about 50% on luck, but once again, on average switching will get you more money.

 

 

 

:| :) :D :mrgreen:

 

 

 

1) What is this law of statistics that shows it's more profitable to switch? Actually, a better way to say that is, what is this law of statistics that says a 50/50 chance actually isn't a 50/50 chance?

 

 

 

2) What if I did the experiment 10 times and all ten times I switched to a lower one? You yourself say that it's a 50/50 chance that the other check will be $200 or $50. Why would switching be better when it's just as often as a chance that you'll lose money?

 

 

 

I think where youv'e confused yourself is that you did the experiment 10 times. And since the amount gained is double the amount lost, if you do it that many times in a row it is profitable to switch. But if you're just doing it once, as suggested in the original prompt, then it's a 50/50 chance of gaining or losing. Period.