You are put into a room....

[cherdano]

if the boxes were only 1000 dollars I would not open any. To get anything significant I would need to put up far too much risk, and if my risk is very small then so is my gain so it's still not worth it.

1/10,000 chance of getting killed?

 

 

Let's see. You have about a 1.5 in 1 million chance of getting killed for every mile you drive. So, unless my math is wrong, you have at least a 1/10,000 chance of getting killed every time you take a car trip of 70 miles or more.

 

So let's put it a different way. How far would you be willing to drive to get a thousand bucks?

 

I'd probably open half the boxes if I could be sure that my next of kin would get the money. Five million smackers on the average, huh? I hope that they'd appreciate it.

These numbers can't be right. A 1/100 chance of getting killed in a year of driving 7,000 miles?

[jtfanclub]

These numbers can't be right. A 1/100 chance of getting killed in a year of driving 7,000 miles?

It's not quite additive: your odds are dying on mile 1 are 1.5/1 million, your odds of dying on mile 2 are slightly less (since you may have died on mile 1).

 

But I may certainly have screwed up the math. Here's the site with the 1.48 per million miles traveled:

 

http://www.usatoday.com/money/autos/2004-0...ic-deaths_x.htm

[bid_em_up]

"Tougher drunken-driving laws, stricter seat-belt enforcement and safer cars combined to reduce the number of people killed in car crashes to 1.48 for every 100 million miles traveled in 2003"

 

This is not the same as saying any one individuals odds of being killed in car crash are 1 in 1.48 million. (And that's not even considering that it says 100 million miles, not one million).

 

According to the National Safety Council the odds are 1 in 6,498 that you will die in a motor vehicle accident (in the course of one year) and 1 in 84 over the course of your lifetime.

 

But, "One year odds are approximated by dividing the 2003 population (290,850,005) by the number of deaths."

 

http://www.nsc.org/lrs/statinfo/odds.htm

 

Of course, this same info lists your odds of dying by legal execuation as:

 

1 in 4,847,500 in the course of the next year, and 1 in 62,468 over the course of a life time, while the real odds of it actually occuring are probably actually nil. Unless, of course, you are planning to commit some kind of capital crime in the near future (and then only if done in a state that has the death penalty). :)

 

Your individual odds would vary based on your driving habits, number miles travelled, etc.

[matmat]

According to the National Safety Council the odds are 1 in 6,498 that you will die in a motor vehicle accident (in the couse of one year) and 1 in 84 over the course of your lifetime.

does that mean that ~1.3% of deaths are vehicular?

[jtfanclub]

According to the National Safety Council the odds are 1 in 6,498 that you will die in a motor vehicle accident (in the couse of one year)  and 1 in 84 over the course of your lifetime.

does that mean that ~1.3% of deaths are vehicular?

Actually, it's 1.7%. Dunno why it's higher- pedestrians, maybe?

 

Bid is right, it's per 100 million, not per 1 million. So it would take a 7,000 mile drive to be equal to 1/100 of 1%. With the usual caveats, not every driver is equally stupid, etc.

[bid_em_up]

According to the National Safety Council the odds are 1 in 6,498 that you will die in a motor vehicle accident (in the couse of one year)  and 1 in 84 over the course of your lifetime.

does that mean that ~1.3% of deaths are vehicular?

No. Yes. I don't know. :)

 

The NSC's report considers a lot of things to be "motor vehicle accidents"

 

Animal rider or occupant of animal-drawn vehicle

Bus Occupant

Car Occupant

Air and Space Transport accidents

Construction Equipment

Pedestrians

 

etc.

 

There does not appear to be a category specifically for "drivers of automobiles".

[keylime]

My view is that, since I can't take it with me, I'm not going to be that interested in taking a risk that at age 31, my life ends because of heightened greed. Even if I sorely needed the money, life is just too precious and is meant to be lived. It is too vague and non-equivalent of an argument to assert that because I'm bypassing money, that I am not being philosophically adherent when I hop on the Metro to go into work or drive the 4 hours to Pittsburgh.

 

Greed is a recipe for bad things to happen.

[Echognome]

How about a couple of variants that are less severe than dying?

 

Game 1:

You have 10 boxes in a room, nine of them with $10,000 in them. However, one of them is the "Bankrupt" box and gives you nothing. How many boxes would you open?

 

Game 2:

Same set-up. Only 10 boxes, but nine of them are "prizes" and one of them is "Bankrupt". For opening up the first "prize" box, you get $1000. For each subsequent successful "prize" box you open you double your money. However, if you ever open the "Bankrupt" box, you get nothing. How many boxes would you open?

 

Which game would you rather play?

[Mbodell]

I'd much rather play game 2. I'd open 8 boxes and have an EV of $51,000. Much better than open 5 boxes with an EV of $25,000 from game 1. The down side here is much better than death and the stakes aren't so super great, especially when you phrase it in the win fall model.

[helene_t]

Game 1: When I have opened four boxes, the value of opening a fifth is 5/6 * 10000 - 1/6 * 40000, this is just positive. The sixth box I would not open. This gives me a 50% chance of EUR 50000, or 25000 on average.

 

Game 2: As long as the probability of doubling is higher than bankrupt, I would go on. Say 8 boxes. This gives me a 20% chance of winning EUR 128000, or 25600 on average.

[Guest Jlall]

How about a couple of variants that are less severe than dying?

 

Game 1:

You have 10 boxes in a room, nine of them with $10,000 in them. However, one of them is the "Bankrupt" box and gives you nothing. How many boxes would you open?

 

Game 2:

Same set-up. Only 10 boxes, but nine of them are "prizes" and one of them is "Bankrupt". For opening up the first "prize" box, you get $1000. For each subsequent successful "prize" box you open you double your money. However, if you ever open the "Bankrupt" box, you get nothing. How many boxes would you open?

 

Which game would you rather play?

So in game 2:

 

I open a box. I get 1,000. (10% chance bankruptcy). 1000 total

I open a box. I get another 1,000 (11% chance bankruptcy). 2000 total

I open a box. I get another 2,000 (12.5 % chance bankruptcy). 4000 total

I open a box. I get another 4,000 (14+ % chance bankruptcy). 8000 total

I open a box. I get another 8,000 (16.5 % chance bankruptcy). 16000 total

I open a box. I get another 16,000 (20 % chance bankruptcy). 32000 total

I open a box. I get another 32,000 (25 % chance bankruptcy). 64000 total

I open a box. I get another 64,000 (33 % chance bankruptcy). 128,000 total

I open a box. I get another 128,000 (50 % chance bankruptcy). 256,000 total

 

Clearly I would not open the last box as I am neutral EV and the extra 128,000 would mean less to me than the first 128,000. Until that point I am always +EV to take another box, so the only reason I would not do so is if the money would change my life so much that I would not gamble it. Certainly I would risk 32k to gain another 32k as a 3:1 favorite.

 

It gets close for me when I can try and double my 64k as a 2:1 favorite, I think I would go for it. Keep in mind I am a sick degen gambler though.

 

So pretty much I would pick 8 boxes. I think that gives me roughly a 20 % chance to walk away with 128,000, and an 80 % chance of going bankrupt.

 

As far as the first game:

 

I open a box. I get 10,000. (10% chance bankruptcy). 10,000

I open a box. I get another 10,000 (11% chance bankruptcy). 20,000 total

I open a box. I get another 10,000 (12.5 % chance bankruptcy). 30,000 total

I open a box. I get another 10,000 (14+ % chance bankruptcy). 40,000 total

I open a box. I get another 10,000 (16.5 % chance bankruptcy). 50,000 total

 

Up until now we are +EV with our gambles. Then:

 

I open a box. I get another 10,000 (20 % chance bankruptcy). 60,000 total

 

So here we risk 50k to gain 10k as a 4:1 dog, -EV.

 

So clearly at most we should open 5 boxes. Again life considerations are in effect, and risking 40k to gain 10k as a 5:1 favorite, though +EV, may be decided against. I think I would pass on the 5th box just because I would be sick if I lost my 40k and if I gained another 10 it wouldn't be that great (ie, the value of the last 10k has diminished enough to me relative to the first 40k that I would be willing to play it safe).

[Guest Jlall]

Game 1: When I have opened four boxes, the value of opening a fifth is 5/6 * 10000 - 1/6 * 40000, this is just positive. The sixth box I would not open. This gives me a 50% chance of EUR 50000, or 25000 on average.

 

Game 2: As long as the probability of doubling is higher than bankrupt, I would go on. Say 8 boxes. This gives me a 20% chance of winning EUR 128000, or 25600 on average.

ok guess helene beat me to it, I am surprised you are such a sick gambler though :huh: haha. Most people are very risk averse with stuff like this, maybe you're just rich :)

[Echognome]

So would you rather have a coin flip for $50,000 or a 20% chance at $128,000? The EV for the latter is slightly greater.

 

I modelled the games adding some risk aversion and it doesn't take a whole lot to make the first game better, despite the second game having a higher EV.

[barmar]

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.

That seems to suppose that this game is played as an alternative to earning money some other way. But this game is presumably played during your leisure time, not in place of your job or other money-making activities. It's earned in addition to anything else you might earn, so I don't think it makes sense to compare it against other ventures.

 

Furthermore, the nature of thought experiments like this is that they're a "closed universe". Your only choices are to open boxes or not open boxes -- there's no third choice of "play rubber bridge for $100/point." That would be a different game.

[P_Marlowe]

So would you rather have a coin flip for $50,000 or a 20% chance at $128,000? The EV for the latter is slightly greater.

 

I modelled the games adding some risk aversion and it doesn't take a whole lot to make the first game better, despite the second game having a higher EV.

The coin flip, and it is not even close.

 

While the EV in the other game is slightly

higher, I will more often win money with

the coin flip.

 

With kind regards

Marlowe

[han]

You willl more often win money if you open only one box.

 

I would go for the coin flip as well btw.

[vuroth]

Game 1:

You have 10 boxes in a room, nine of them with $10,000 in them. However, one of them is the "Bankrupt" box and gives you nothing. How many boxes would you open?

 

Game 2:

Same set-up. Only 10 boxes, but nine of them are "prizes" and one of them is "Bankrupt". For opening up the first "prize" box, you get $1000. For each subsequent successful "prize" box you open you double your money. However, if you ever open the "Bankrupt" box, you get nothing. How many boxes would you open?

I only open 1 box either way. The power of gambling is the lure to risk your winnings against the possibility of future winnings.

 

Sure, if it's a mathematics exam, I calculate EV and work out risk vs potential earnings. But if it's real life, I do my darndest to NOT hand back any free cash.

 

V

[han]

Are you serious? If you had an 80% chance to win $1,000 and a 10% chance to lose $1,000 you would not take that bet?

[vuroth]

If I had a 100% chance to walk away with free money and a 20% chance to lose it all, you bet I'd take the free money.

 

I would MUCH rather walk way with the knowledge that I could probably have won more money than walk away having lost what I had.

 

I certainly don't expect my choice to be a popular one, but then, I've never grokked the common fascination with gambling.

 

V

[han]

Are there any odds where you would take the gamble? If you could pay $10 to have a 90% chance to win $100, would you take that?

[Al_U_Card]

The life and death scenario (original) is flawed because we will all die someday.

 

How about, you are starving to death and you have x number of boxes, one of which has a bomb in it and the others have food. You have no alternatives for getting a meal so.....(sounds like the premise for a horror flick...lol) you will certainly open a box....because you have nothing to lose and something to gain.

[vuroth]

Are there any odds where you would take the gamble? If you could pay $10 to have a 90% chance to win $100, would you take that?

There are undoubtably odds for which I would gamble.

 

And I'm sure if the odds of going bankrupt were sufficiently small that I would get greedy. I'm only human, after all.

 

I think the way that I look at it, winning $1000 would make me fairly happy. Would winning double the money make me twice as happy? Of course not, nowhere near. From that perspective, I'd be gambling a whole lot of happiness at having $1000 fall into my lap on very little return (happiness-wise).

 

For the stated cases, the chances of improving my winnings from "I won some extra cash" to "I won a life-altering amount of cash" are not very good. Ergo, I choose not to press on.

 

V

[EricK]

People do funny things when they are dealing with "free" money. I happened to see the end of an episode of "Deal or No Deal" a few months back. Down to the last two boxes, which were (if I remember correctly) £15,000 and £35,000, the banker offered £25,000 which the player declined.

 

Now how many people who had £25,000 of "spare" money would gamble £10,000 on the toss of a coin? But this is what the player was effectively doing.

[Al_U_Card]

Speaking of "Deal or no deal" (you did) I need the mathsters to tell me what the decision rule is for when to take the banker's offer. I always find that people quit too early or stay way too late.

[Echognome]

Speaking of "Deal or no deal" (you did) I need the mathsters to tell me what the decision rule is for when to take the banker's offer. I always find that people quit too early or stay way too late.

I have only watched this show a couple of times. Of the times I watched, it seemed that the banker's offers were much worse than the EV until later in the game. That is, as the risk was lowered for the player, the banker made better offers. It was as if the setup was to try to make the player decline offers for as long as possible. I presume this makes some sense to make the show last longer.