I'm not math-savvy enough to get the whole thing, but I am a gambler and I understand expectation, and the basic premise is false:
If one stops mining for a pool that has not found a share, one still gets a payment [...] even though now you contribute nothing to the pool chance of success. This enables cheating.
It doesn't matter if you contributed to the pool and a hash wasn't found. It still took your previous work as well as the work of everybody else to find the hash. You DID contribute to finding that solution. And you are getting paid for the amount of work that you did. If you then go and continue working on your own, that doesn't matter.
If I am playing in a re-buy poker tournament on a team's bankroll (a team I'm a part of), and if my win would get chopped with the team, but then I bust out, and the team doesn't want to re-buy me back into it, I can still go into my pocket and buy myself in on my own money.
If somebody on the team wins the tournament, I still get part of it because I AM part of that team, and if I cash on my own money with my re-buy, I get all of it because the team didn't pay for that.
That's not unfair to anybody. I was working for the team, and if the team wins money, I should get paid for my role in the team effort. If I then go off and put the effort in by myself and win, then I should get all of it. There's no conflict there.
The basic premise of your paper is false. The EV is the same for the miner--it's merely a function of his total effort put in, pool or no pool.
What you are describing is simply a "gambling system" that doesn't change the house edge. You've stumbled upon the Martingale system for blackjack and now think you have an edge.
You don't. Nothing has changed. The premise is false.
I will demonstrate what I'm saying must be true: If everybody in the pool mines for a bit then goes solo, the pool has done some work but now will never find a solution. However, one of the solo miners will (assuming no outside people in this example). The chance of any individual miner finding a winner is exactly the same as it was when he was part of a pool, it's just that when he was in a pool, he would have had to give most of his winnings away, but in return he got part of the winnings if somebody else won. By mining solo, he has merely given himself a bigger potential payout but at a cost of it being less likely. But his average monetary gain over the course of his lifetime will be the same, whether or not it's paid in small increments or in random 50 btc spurts. Thus, if the two are equal, it cannot be true that switching to one or the other at some magical point in time will somehow yield a higher profit.
100% of $5 is mathematically equivalent to 10% of $50. The only difference is variance.
The premise is false!