Physicist, this is the first time you've ever posted something I didn't agree with.
Your theory seems to boil down to this: that the expectation value of a random variable should not be calculated in the normal way if these two conditions are present: that the dimensions of the random variable are dollars, and that the strength of the delta function describing the random variable's distribution is very very large. That the integration by which this calculation is performed should be overlayed by some sort of non-uniform weighting function, that will make the expectation value of a $1 bet greater than $1.
As I see it, this weighting function is exactly this: the measure of a human emotion (perhaps "aspiration" or "hope"). In order to be true, your theory would be the flip side of the idea put out at the end of the movie Peter Pan, where the audience is asked to believe together; that the power of a group all believing in something together can make that something more real.
For some reason this makes me think of a lecture I heard once on "the nonlinearity of free space." Which, as I understood it, may actually exist.
I seem to recall an implication in one of your posts that you were leaving DRL to do something else. I hope all is well with you.
(steely)
On the contrary, I specifically said that the qualitative components are not reflected in the expectation value. I mentioned the political power that accompanies $100 million; others mentioned the entertainment value of anticipating a big win. But I don't take those things into account when I play: I only look at the expectation value.
The expectation value in the case of Powerball is the average payout per $1 play. That's strictly calculated in terms of dollars. Pick-3 games typically have a payout of $500 for a $1 play, so the expectation value is fixed at 50¢. There's a fool's game for you. Powerball seems to be even worse: one chance in something like 80 million to win 10 million dollars is only 12.5¢ on average.
[Geek alert: the expectation value for Powerball is actually much more complicated. There are a bunch of different ways to win smaller amounts of money, and these actually dominate at the low end, to the point that it's much better than a $500 pick-3 game. Then, too, you have to correct for the probability of multiple jackpot winners, which brings it down at the high end.]
If the payout gets high enough, however, the average payout--again, strictly in terms of dollars--becomes greater than $1 for a $1 play for that particular drawing. This is possible because the total probability includes a chain of prior drawings where no jackpot was paid out at all. You don't have to worry about the prior drawings when you play, though, as you have no chance of losing them. Those losers have already lost. A fraction of those payouts, however, is still in the kitty.
So the next time the Powerball jackpot gets really high, put a few bucks on it, and think to yourself: "This is a good investment. A lot of fools paid a lot of money to create this opportunity for me."
The probability of the event is constant, determined by the Powerball format. The jackpot varies (increasing if the previous draw produced no big winner). If the jackpot rises above $70-million-something, by basic arithmetic the expectation rises above $1.
The bottom line is that it's cheap entertainment, and harmless if you treat it as one item in a total entertainment budget you can afford without compromising higher budget priorities.