EV and Variance vs. magnitude (your personal preferences)

[knicknut]

I couldn't find anything along these lines, and I was curious.

While plus EV is plus EV, there is a monetary magnitude for all of us at which the variance outweighs the +EV. I made a poll to see different people's valuation of money vs. variance, to see how much of an EV premium people would need to make a 50/50 bet of large magnitude.

Scenario: you are offered a chance to win $Y on a single coin flip that will cost you $X.
1. You can only do it once (no long run).
2. You can borrow money and incur debt to make the bet, but you will have to pay off the debt for as long as it takes.
3. You can only use your own money--you can't split your bet with friends/family.
4. The money is tax-free and the time to make the bet is not a factor (although it could be for the small values).

Answer seriously. I know it may seem easy to say "ah, paying $24k to win $50k 1/2 the time is +EV, easy," but think about the financial hardship and true lifestyle variance that may cause. Is it worth $1000 in EV?

I just did a poll of my non-playing friends and got some interesting votes. I expected a steadily decreasing % of willingness to bet as the values got up (which it is for me). A couple kids had an inverted parabola (because low dollar amounts don't mean much to them), and one was a 3rd power equation with a dip in it (little means nothing, medium is worth it, high is too big a risk, but very high is a once in a lifetime opportunity and worth more risk).

Curious to see what the gamblers feel. Feel free to include your income or your limits (or family situation or other factors) along with your thoughts. I tried to keep the poll answers parallel, but if you think there's a better way to do it (or want to construct one with more options so we can really see a better distribution), let me know.

EDIT: I just realized this might go better in "Psychology" than "Math," so feel free to move it those who can (I'd be too lazy to remake the poll).

[MathEconomist]

Hypothetical bias is going to get the better of this poll. Even if people try to answer truthfully they simply don't have the ability to know what they would actually do when confronted with these large bets.

If you are really interested in this, there is a large literature on risk aversion in economics and also in psychology. I like the Holt/Laury studies a lot becaused they used really non-trivial amounts of real money. The Tversky/Kahneman prospect theory stuff is also pretty important in a more historical sense.

[madnak]

Due to the diminishing marginal utility of money, losing $100,000 would have more of an effect on me than winning $1,000,000.

I would bet all of my immediate disposable income on such a deal, and take on as much debt as I could expect to reasonably pay off in, say, 5 years without a major effect on my quality of life. If it takes more than 5 years to pay off, or has a dramatic effect on my quality of life over 5 years, it's not a debt I'm willing to accept.

I think those will be my standards for a long time to come. Of course, if my annual income is $5,000,000 I'll be willing to bet $490,000 for $1,000,000. But I very much doubt I'll ever have the wealth necessary to make those deals +EV for me after the diminshing value of money is taken into account.

EV has to do with value, not just pure quantity of assets. There are even some tournament poker situations in which a bet with a negative numerical EV has a positive monetary EV.

(By the way, can you imagine the sigh of relief after winning a bet like this?)

[Jshuttlesworth]

tl;dr

[knicknut]

I'll look into that stuff, ME. I was looking at getting a representation from those with a "gambling" background and see how that differs from random subjects.

[ThinkQuick]

[ QUOTE ]
I'll look into that stuff, ME. I was looking at getting a representation from those with a "gambling" background and see how that differs from random subjects.

[/ QUOTE ]

looks like its pretty similar to your steadily decreasing willingness