it is +ev to call, but would YOU?

[blaze666]

this isn't related to poker at all.


ok, lets say you and bill gates have a bet. it will cost you your entire networth to play, lets say it is $500,000. and if you win, bill will give you $50,000,000(50 mil), so you are getting 100:1. you have a 3% chance of winning, so it is +ev for you to accept. do you? if not, what percentage of winning would you have to have for you to call? or what would you be willing to risk here?

i would not play this, i would only play if i had 70% or more chance to win.

[pzhon]

A reasonably consistent approach to this type of question is to maximize your expected utility, where utility is a nonlinear function of money, time, and other resources.

The Kelly Criterion for rational gambling with an advantage suggests that you should maximize the expected logarithm of your bankroll. Note that log[0]=-infinity, so you should never risk going bankrupt. Of course, you may have resources in your bankroll beyond your net worth, such as the present value of future income.

Once you decide what your utility function is, it is a simple calculation to figure out how much you would be willing to risk getting 99:1 on a 32:1 gamble. If you don't determine the rough shape of your utility function, you may make inconsistent choices about this and other gambles, accepting high risks for low returns while passing up better opportunities.

[bigjohnn]

pzhon has pretty much answered it. Its all about your expected utility function, and more specifically your co-efficient of absolute risk aversion, r.

A higher r means you are more averse to risk i.e. the more you would be willing to pay for a guaranteed income y, than to play a lottery with expectation y.

The best example of the principle is the famous St. Petersberg paradox proposed by Bernoulli:

Someone wants to sell you a ticket to play a game with them. The game consists of the person tossing a fair coin. If it lands heads on the first toss, he will pay you $2. If it doesnt land on heads until the second toss, then he will pay you $4. If the first head occurs on the nth toss, he pays you $2^n. The question is, how much would you pay to play this game?

The game has an expected value of infinity, but most people wouldnt not pay this much. They are risk averse, and so would pay a lot less to play this game.

[txag007]

Pzhon is right. It's +EV in the long run if this game were played thousands of times. In the short term, however, the risk is too high. The same reasoning applies as to why one should exercise proper bankroll management.

[NMcNasty]

You're expected value for this game is $1015000. Where the game is strictly between me and Bill Gates I would probably play it if I had a 20% chance to win. However if this was a real life situation and it was somehow gauranteed that the payoff would be enforced, I would do everything in my power to try and get a billionaire to spot me the money. One option might be offering the billionaire everthing I win in exchange for 700k after I play the game. In that case his EV would be (.03*49300000)+(.97*-700000)= $800000 while I would be 100% certain to be profiting $200000 plus I get my 500k back when I win.

[kyro]

Very interesting paradox bigjohnn...one I've never heard of. Thanks.

[bigjohnn]

Pleasure.

[Dov]

We had a similar discussion a while ago that went somthing like:

You have AA and you know your opponent has KK in matching suits

The flop comes AKx

If your opponent loses this hand, you win $20 MIL. If you lose this hand, you die.

Your opponent goes all in.

Do you call?

BTW, I'm not trying to hijack your thread, just giving another perspective.

[phifediggy]

i call if it'd be an instant death in the case i lost, so i wouldnt have to suffer through post-bad beat pre-death trauma

[afk]

I wouldn't call.


What the hell would I do with 50 million dollars anyways?