> Well, which is it? You seem confused. First you shout out that I
> CAN PROVE IT. (Pretty sure of yourself.) Then you say, a little
> quieter, "I can't PROVE the laws of probability..."
Please check the attributions..."I can prove it" was Clint, not me. I don't care about proof, and said so.
> You say you've mastered the laws of probability. That's nice.
> How do we know they're real laws, not just some idea which has
> worked out for you?
In what way does "real" matter, except for the money in my pocket? That's the point I'm trying to make: I don't have to have "faith" in physics or math to bet on them and make money. I just have to make the bet, and I think it is rational to make the bet, even if I have neither "faith" nor "proof". There is a middle ground.
> Actually, this is not how most professional gamblers appraise a
> positive expected value (e.v.) situation. You're supposed to measure
> your risk aversion (you should have some if you have finite money,
> since you don't want to be wiped out) and use it to discount the value
> of a particular e.v. further, to get a certainty equivalent (c.e.) in
> dollars of the e.v. in dollars. A standard technique is to compute
> your "kelly" factor, which may be correlated to how much more likely
> you want to make it that you double your stake before you would ever
> see it drop by 50%.
Yes, when I played poker for a living, I played a lower-variance game, and did indeed sacrifice a bit of EV to prevent catastrophic loss (though not by the Kelly criterion, because there are better ways). I have a regular 9-to-5 job now, so I play high-variance high-EV poker and am willing to fade higher risk bets because I have savings to back them up. Over my year as a pro, I had an EV of 1.4 bets/hr, with a variance of 10. Now I play with an EV of 2.1 bets/hr, with a variance of 19. Those -50 sessions can be a killer :)