"Lee Daniel Crocker" says:
> >> I know the laws of probability are real not because I BELIEVE
> >> in it but because I CAN PROVE IT.
> >
> > <devil's advocacy>
> > Ahem. I assert that you cannot prove it. Robert attacked probability on
> > its strongest side... What would you say to this experiment?
> >
> > I assert that it is completely impossible for you to flip a coin 1 million
> > times and have it turn up heads every time. When I say completely
> > impossible, I mean that it will never EVER happen, no matter how many
> > times you try.
> > </devil's advocacy>
>
> You're being very sloppy with your language and your thinking here.
> PROOF, as in absolute inviolable certainty, is irrelevant to reality.
> I can't PROVE the laws of probability, but that doesn't mean I have
> to have faith in them to make use of them. There _is_ a useful middle
> ground--committment. I have committed thousands of dollars over the
> years to my mastery of the laws of probability, and given the
...
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..." I think that hissing sound is your argument deflating. 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?
> opportunity I will do so again, _until something better comes along_.
> Your million-coin-flip bet is a cop out; you know it isn't physically
> possible to test your theory within your lifetime, so you're safe. If
> you had any balls, you'd offer a bet that's feasible. I offer this
> one to any takers: flip an unmodified US dime 10 times. If it lands
> head-up all 10 times, I'll give you $100, otherwise I'll keep the dime.
>
> This in no way means I have unlimited unshakable faith in the laws
> of probability. It just means I'm willing to bet $100 on them
> (because I know that on average, I make 0.24 cents every time I take
> this bet).
...
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%.
Regards,
James