Into two boxes I have placed a sum of money. The amount in one box is exactly twice what is in the other. I allow you to look into one box and there is $100 in there. This means that there must be either $50 or $200 in the other box. You are permitted to either keep the $100 from the box you looked in or switch.

If you switch, you will either lose $50 or gain $100. In other words, you can bet $50 to win $100 and it is an even bet. Betting $50 to win $100 is extraordinary. Lose $50, gain $100, lose $50, gain $100. Makes sense to switch.

On the other hand, switching can't make sense no matter which envelope you choose. Otherwise, you would just choose the other envelope and not switch. But the logic above says it would be better to switch.

Does it make sense to switch?

no, it doesn't....

A bird in the hand is better than two in the bush....

it depends on WHOSE bush
;-)))

Serge,

Assuming at least a casual interest in gambling - if you were in Vegas you'd love to bet $50 to win $100. You'd do it all day. Roulette pays a little less than $50 on a $50 bet. These are 2-1 odds! It doesn't make sense to switch?

ok, lets say there were two boxes. Serge was in one box and in the other box was CJ. You opened one box and saw Serge but you noticed he was also holding $1000.00 and a fifth of Jack Daniels.

no, it doesn't...

there are few possible outcomes:
1) you lose $50
2) you gain $200
3) you gain $100

if you don't switch,
there is no fuckin' way you can lose,
thus GUARANTEED a gain.

I buy CD's which pay me lousy 5% a year for this reason only,
I CAN'T LOSE...
;-))

can I switch the jack daniels for another spirit of equal value?
jack daniels gives me bathtub nightmares :P

No Colin - it doesn't make sense to switch.... I'm ahead 100 bucks just for looking in the box! Free MONEY! :bdance: Why risk having to give half of it back? I'd take the 100 and RUN! :redance:

Edd - if you don't switch, you keep the $100. That is true.

If you do switch though, you will either have $50 or $200. That averages to $125.

what's the average got to do with it? you can't win the average, you can win $50 or $200 or keep the $100!! there is no 'average' option!!

CJ, Then I can present it another way. Would you take this bet? Flip a coin. Heads you pay me $50. Tails I pay you $100.



Last edited by Colin at Dec 2 2002, 11:27 AM

I don't "win" - I have no "luck" (only with CJ! ;) ). I would not take the bet. Colin just gave me 100$ Woo Hoo! :nyanya:

yes, i regularly play a game called 'two up' at the casino

I bet $20 on a guess of heads or tales each time, with 2 coins
odds are about 30% each way with 40% odds to getting a split ? something like that

I would only play that game with what I could afford to lose, the rule I always gamble by ;-)

CJ,

Is the game like this?

I choose heads and then flip two coins. Two heads pays?

HH
TT
HT
TH

Push 50% of time, win 25% of the time, lose 25% of the time.

How do they make money?

i can't remember if its 3 or 5, i think its 3 ... if you get 3 ht ht ht in a row, the house wins

so there is good enough odds at this happening for the casino to pick up a good round every now and again

http://www.twoup.ws/table-layout.htm

http://www.twoup.ws/diagrams.htm

I'm with the non-switchers.

I'd rather have 100 real dollars than a chance at 200.

Especially if it's free.. $100 for no work makes me feel better and smarter. However, losing money I didn't have in the first place makes me feel like an :moon:

-Dennis

A bunch of risk aversive pornographers! I'm VERY surprised.

So now I am really curious.

What if the box you check has $100. There is either $50 or $300 in the other. Completely random. Do you switch?

Get Antrhony to wrestle with you while I steal both the boxes. :)

Then sell them to surfers as "mystery xmass boxes" on ebay (With a $300 reserve on each)

There is actually a classic study that asks the following question:

Which do you prefer?
A. A sure $1000
B. A 50% chance at $2500

And then ...

Which do you prefer?
A. A sure loss of $1000
B. A 50% chance of losing $2500

Answer for yourself. I'll tell you what most people choose later.

B.)




A.)

These are my real answers to these situations

However I am a moron :)

I wouldn't say you were a moron, Nick - I just think thats your Gypo Pikey showing is all! :awinky:

Colin - I'd take A for both questions - but then I don't gamble - I can't stand it myself - never saw the point in risking money on a "chance" to win! I wouldn't win, I'd just lose. and get all :grrr: at myself for losing! :unsure:

>> A bunch of risk aversive pornographers!

Nope not me, Colin if it was me i would gamble at 50% odds and go for it.
i wouldnt be mad with myself if i lost, you loose you move on.
you win, you're happy you move on.

otherwise one goes for days thinking what if.


but that is just me, i like living on the edge and taking risks.
i wouldnt be where I am and who I am, if i didnt take risks.

i also look at it like this

if i ended up with 50$ i can go and buy dinner at a decent place for 2.
if i ended up with $200 i would go to Tantra in South Beach, spend about $160 on dinner and leave a 40$ tip.

in both case i will walk out feeling good.

:)

Change the amounts and my answer is different assuming the same percentages apply. At that level I'd take a chance at the $200. Add zeros though and the answer will differ!!

they play this contest on the radio regularly

but the prizes are 'money or the booby prize' ...

the radio announcer tries to buy the person with the first box so they don't want to open the second, which contains either 1000's of dollars or a pack of chewing gum.

I always wonder what i would choose and the answer would never be the same twice.

but, i'm with slav ... i'd be happy to get the free pack of chewing gum, because i started with NOTHING!

Also.. at those amounts I would take the sure $1000 and the sure loss of $1000.

Whoa! How Freudian is THAT?
Personally, I LIKE putting MY bird in the right bush... :awinky:

According to game theorists, the "expectation value" (EV) is what is important.

expectation value (EV) = Probability * amount.

50% * $2000 = $1000 so there is the same amount on both sides of the equation and it is equally logical to choose either option. Making such decisions based on "expectation value" over one's lifetime will leave one with the most money.

In real life, the majority of the people choose the sure thing. One experiment gave people a choice between an 80% chance of winning $4000 or a sure $3000. 80% chose a sure $3000 - inferior according to EV based decision. I would think one's answer depends on how much money one has or how much $3000 means to you.

People offered a choice between losing $3000 or an 80% chance of losing $4000 chose the risk 92% of the time.

According to the researchers, people are risk averse when the choice involves gains and risk seekers when it comes to losses. According to Tversky "It is not so much that people hate uncertainty - but rather, they hate losing" and "people are much more sensitive to negative than to positive stimuli".