[Fluffy]

I just read this question (sorry for bad translation)

Say you are put into a room where there are 10.000 boxes.

On every box there are 1000$, except for one, if you open it it kills you.

So, how many would you open?.

[Trumpace]

Do we get to keep the money? What happens after we open the boxes and live, are we let go?

Assuming we are let go with the money found and that the money is American $, I would just open a 1000 boxes to have a reasonable chance of becoming a millionaire and not dying in the process.

btw, what is the point of this question? See how much ppl are willing to risk their lives for money?

[keylime]

Um, since I like terra firma a lot, and since I can't take it with me if I die...I choose zero boxes.

[pclayton]

$1,000 per box just isn't enough. Let's say its $10,000.

I hope its not a painful death.

I open one and take out a term life insurance policy for one day with the first $10,000. I'm guessing this buys me a lot of coverage ($50 MM ++) and hopefully I haven't violated any of the terms of the policy (yeah, right) .

I then open about 100 boxes. I take the $1 MM and invest it in equities.

[mrdct]

keylime, on Oct 29 2007, 08:20 PM, said:

Um, since I like terra firma a lot, and since I can't take it with me if I die...I choose zero boxes.

Do you apply that same philosophy to other risks that you take in life in order to make some money?

For example, if you drive to work there is a non-zero chances of getting killed in a car accident - but you are taking that risk for a pay-off that for the average Joe would be well less than $1,000.

[zman102]

You said "on" every box there was $1000, so I would open none (just gather up the money).

If this is a matter of language or a typo and u meant "in", I would take my trusty scale and weigh the boxes (is there a time limit?). DO NOT OPEN THE BOX THAT WEIGHS THE LEAST!

[jdeegan]

You are describing an upside down lottery situation. In the more usual 'right side up' version you have an eensie, teensie chance of winning a very large, 'life changing' prize [say $1 million] combined with a near certainty of losing an affordable amount of money [say $1]. Lotteries are goldmines for those who sponsor them because the playing public will routinely invest $1 to win a prize with an expected value of 60 to 70 cents.

In 17th century Jamaica, English settlers faced an 80% mortality rate from tropical diseases within five years, but a near certainty of becoming wealthy sugar planters if they did survive. Enough Englishmen took the bargain to turn Jamaica into a successful sugar producing colony. Big gamble [your life with a high probablity of loss] versus big reward [if surviving, you become a wealthy planter].

The situation you describe is a big gamble [your life with very low probability of loss] versus small gain [near certainty of a modest profit]. We never see this in real life because it is ass backwards from what does attract people to make a gamble. Most people who study these phenomena attribute all of this to the fact that individual human beings have difficulty in assessing the true probability of outcomes that have less than 1 chance in 20 of actually occuring - see: Friedman & Savage.

[gwnn]

I'd open 5, but would be tempted to try a 6th.

[P_Marlowe]

gwnn, on Oct 30 2007, 12:35 AM, said:

I'd open 5, but would be tempted to try a 6th.

If you start opemning one, it will be hard
to stop opening others.

You survivrd, you have a luck strain, nothing
bad can happen.

With kind regards
Marlowe

[P_Marlowe]

Jlall, on Oct 30 2007, 03:18 AM, said:

P_Marlowe, on Oct 30 2007, 03:09 AM, said:

gwnn, on Oct 30 2007, 12:35 AM, said:

I'd open 5, but would be tempted to try a 6th.

If you start opemning one, it will be hard
to stop opening others.

Except that there is diminishing returns on the value of the $1,000, and every box you open successfully means a higher chance of death the next time. If you are poor you should definitely open some boxes (not saying anyone who opens them is necessarily poor), but once you got to say, $50,000 the 1,000s are meaning less to you now and the risk is increasing, so you may decide just to stop.

Thats a logical explanation, and I understand this,
but I was refering to human behaviour.

Peoble sometimes forget to reason logical, I just
can speak only for myself, and I know that there is
a point, I may loose the control to reason logical. (*)

Ok, if only 2 boxes remain, I most likely wont open
one, but I am pretty sure, I wont be able to stop after
5, I would open 6, 7, ... and may loose all.

(*) And thats the main reason, why I dont gamble for money,
it would ruin me. I guess professional players have learned this.

With kind regards
Marlowe

[helene_t]

Right, Justin. Why do you say that you sucked at math in hi school? Was it because you fell a sleep during the lessons for lack of challenges?

Suppose your life is worth W dollars. Then you should open 10000 - W/1000 boxes. If your life is worth more than $10,000,000 then you should open zero. Here I have not taken diminishing return into account: the value of your life is assumed to be some constant, W.

[matmat]

helene_t, on Oct 30 2007, 03:39 AM, said:

Right, Justin. Why do you say that you sucked at math in hi school? Was it because you fell a sleep during the lessons for lack of challenges?

Suppose your life is worth W dollars. Then you should open 10000 - W/1000 boxes. If your life is worth more than $10,000,000 then you should open zero. Here I have not taken diminishing return into account: the value of your life is assumed to be some constant, W.

is it possible that the value of your life depends on the quality of your life, and thus is somehow related to how much money you have?

[zasanya]

I will open the 1st box the day I become convinced that there is no other way for me to earn money.I don't think that day would ever come,touch wood.

[helene_t]

Right, that is another way of putting the "diminishing returns" argument.

The value of money, as measured in Life units, decreases with the amount of money you have.

The value of your life, as measured in dollars, increases with the amount of money you have.

I think it's the same thing. Maybe there is a subtle difference at some level. For example if there is a universal currency (say ACBL masterpoints) you could consider whether it's your life's value, or the money's value, as measured in masterpoints, that change.

[Echognome]

Not sure if I've done this right, so someone can check. But ran this through Excel and I believe that here are the probabilities:

Boxes -- Survival Prob -- Value

100 -- 99% -- $100,000
500 -- 95% -- $500,000
1000 -- 90% -- $1,000,000
2500 -- 75% - $2,500,000
etc.

So basically every 100 boxes you open gains you $100,000 but gives you an additional 1% chance of death. So for opening 1000 boxes, your chance of survival is:

(9999/10000)*(9998/9999)*(9997/9998)*....*(9000/9001) which cancels every term except for 9000/10000 = 90%.

(i.e. Excel not needed after all )

[Mbodell]

P_Marlowe, on Oct 30 2007, 03:09 AM, said:

gwnn, on Oct 30 2007, 12:35 AM, said:

I'd open 5, but would be tempted to try a 6th.

If you start opemning one, it will be hard
to stop opening others.

Not at all, this is a declining marginal value of money. I'd want there to be $100K in the boxes before I'd start opening boxes (which is not really a rational cut off point given other life choices).

But I also wouldn't want to open very many boxes. But we can analyze the question in more depth.

Someone mentioned driving to work as a "risky" behavior people do. The equivalent number of miles you'd have to drive to have the risk equal to opening one box is 6250 miles. The average American driver drives a little less than twice that per year (all be it, not all of that to/from work).

So if the amount of money in each box is about half a year's salary and if taking it meant you could quit your work and eliminate driving associated with that (and not replace it with activities that also cause you to drive) then the driving savings alone might make it worth while.

Heck, if most people used some of the money to hire a personal trainer and nutritionist and then invest some of the time savings (from not working for that money) into improving their health these savings may well add to their quality-adjusted life years making the decision not to open many boxes very irrational. I.e., invest the money in interventions to increase your QALY and you are better off, on average, opening boxes.

For instance a 20 year old male who smokes is probably, just from smoking, engaging in more risk than the equivalent non-smoker who opens 1400 boxes. A 20 year old male who is obese is looking at the equivalent risk of the healthy one who opens 800 boxes.

However, a QALY savings is usually worth between $25,000 and $500,000 depending on who is calculating it (say $100K). Say I have about 45 QALY left, what should they be worth (this is imperfect too as there is a declining value of QALY so a QALY is worth much more to me if I only had 0.65 left than if I had 65 left)? So it should be worth, say, $4.5 million. If I opened 5000 boxes I'd have $5 million and only a 50% chance of death. If we assume the money is only worth something if we don't die (I.e., we really only have a 50% chance at $5 million and a perfectly correlated 50% chance of still having a 45 QALY life) then this leaves us better off than not opening the boxes, assuming my model number holds true. If my model is accurate than the rational maxEV answer (assuming $0 prior net worth) is to open 2750 boxes and this give $5,256,250 compared to $4,750,000 for 5000 boxes and $4,500,000 for 0 boxes.

Obviously the less healthy and more older you are the more likely you are to be willing to open boxes. If you area 15 year old Ontario girl with 65 QALY left you'd only open 1750 boxes in this model. If you had just 5 QALY left you'd open 4750 boxes.

Obviously you could do more sophisticated models that dealt with declining values of money and QALYs, risk aversion, etc. and also take into account your personal net worth since the richer you are the less you'll want to do this (my model above assumed a net worth of $0; if you have a net worth of $1 million you'd only open 2250 boxes, $2 million you'd only open 1750 boxes, etc.).

[sceptic]

I would chance a few, then a few more, probably up to a point when I open the wrong box or I lose my nerve, I think I would probably get greedy, especially if you keep all the money whether you live or die, also depends on what my personal situation was, if I was retired and had no money and I was ill, I would just keep going and leave the money to my kids hopefully after 5 000 boxes I would quit