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1. Originally Posted by Santtu
No, the maximum increase of utility I expect from any amount of money is about 50%. SO I would accept a maximum of 1/3 risk of death for any amount of money, including infinite amount, but starting from \$2M. I would have to solve the theological arguments in my life first before accepting the deal tho. This approach will maximize the expected utility during lifetime.
Ah, gotcha Interesting approach... I'll have to think about that.

2. Santtu may be an exception but people are generally only risk neutral until the risk of death becomes high enough (say, 1/10,000). Then they become risk averse, and all bets are off, so to speak. (Well, not literally, but it stops being linear.)

3. Originally Posted by Economica
Santtu may be an exception but people are generally only risk neutral until the risk of death becomes high enough (say, 1/10,000). Then they become risk averse, and all bets are off, so to speak. (Well, not literally, but it stops being linear.)
Would you of answered the question the same as Santtu?

4. Originally Posted by ptgatsby
Would you of answered the question the same as Santtu?
I don't think I'd accept a 1/3 risk of death for any amount of money. I'm not sure where I draw the line... Below 1/10, but probably above 1/100.

Hypotheticals are hard, of course.

5. Originally Posted by ptgatsby
I'm not sure I understand... what would you pose as an alternative?
How about leaving it up to the posters? Which would lead to some interesting answers, I should think. (And would also allow those of us who don't dream of going on shopping sprees to participate as well.)

6. Originally Posted by Recluse
How about leaving it up to the posters? Which would reveal some interesting answers, I should think.
We must think in completely different terms

What would you pose as the question?

7. I got surprised by how little the money would matter when I studied it.
If \$4M of additional money would make my life twice as good, I could indeed gamble at a rate of \$6M/100&#37; of death for a gain of \$2M (and 50% increase in total life quality) and a chance of death of 1/3. This would balance out to the same expected total life quality as without gambling.

The maximum expected life quality would be had with \$1M and 1/6 chance of death. But this would only give

expected life quality
= chance to live * life quality IF alive
= (5/6)*(5/4)
= 25/24
= 1.0416..
or only 4.16% more than what I'd had to begin with.

What an insignificant improvement - a disappointment, really! This outcome is the weighted average of the value of life when dead (0) and that when winning the gamble (1.25), with the probabilities 1/6 and 5/6 to each outcome.

8. Originally Posted by ptgatsby
We must think in completely different terms

What would you pose as the question?
I would substitute the term "incentive" and see what people choose. Here I've rearranged your opening sentence a bit, but you could work on it some more if it's not clear:

"What is the least incentive that you would require to take one in one billion chance of dying?"

I just get frustrated when I feel I can't participate in an interesting question. It's not easy being a recluse!

9. Here's a reference chart for all your gambling needs

You can calculate your own optimal stake, and expected profit.

Lets assume that you can gamble your life at a rate of X\$/ 1&#37; chance of death, and you need Y\$ to get an improvement of 1% in life quality.

Then you must have Y>X for any gamble to be profitable. Lets denote the y/x ratio by r. We can then calculate the expected payoff as a function of the ratio of life gambled, g, as

expected payoff = (1-g)*(1+r*g)

which is maximal at g=(r-1)/2r for values of r=>1.

This maximum approaches the value g= .5 when r approaches infinity. So the most you'd ever want to gamble is half your life, if you are given near infinite rewards per unit of life gambled.

Here's few plotted values for easy reference!

Here's the "gambling ratio" is the ratio how much you appreciate % increase of life quality versus % chance to live, when using some mean of exchange. For example, if you are willing to accept 1% chance of death for \$100,000 and \$100,000 will improve the total life quality experienced by 2%, you have a gambling ratio of 2.

Originally Posted by ptgatsby
Originally Posted by Recluse
Why did you choose money as the main motivator?
I'm not sure I understand... what would you pose as an alternative?
You may notice that the unit of exchange cancels out in this model, meaning that something else than money could be used instead.

This model does not take into account the marginally diminishing returns from any bets won.

Disclaimer: the publisher does not encourage people to gamble their lives and takes no responsibility for lives thus lost.

10. Originally Posted by ptgatsby
Ah, gotcha Interesting approach... I'll have to think about that.
Why, has the devil offered a pact for you?

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