I have a theory that turning mining into a lottery ticket with a life-changing payout disproportional to the odds of winning would result in an increase in the number of solo-miners. These miners don't mine for the steady $30/month they could get from constant pool mining, but for the off chance that they could win the million dollar jackpot. The existence of the jackpot would not change those who traditionally mine in pools because they would have to divide the jackpot among everyone in the pool and thus not be life-changing. However, once the pot for the lottery grew large enough they would defect from pools in a bid to win big.
This will also change the trust relationship with pools. Suppose an normally honest pool operator suddenly wins big, do you trust him to divide it among his pool members?
So here is how you would modify ProtoShares to enable a lottery base mining reward:
1) the value of a coinbase transaction is not known until the block hash is found.
2) calculate ratio (R) of block_difficulty / target_difficulty which should be a number greater than 1
3) if R > 100 && < 1000 then R = 100
4) if R <= 100 then
COINBASE = MIN_BLOCK_REWARD * R
POT += 100 * MIN_BLOCK_REWARD - COINBASE
5) else R > 1000
COINBASE = 0.5 * POT
POT -= COINBASE
This system should result in a POT that constantly grows with a predictable maximum average inflation rate.
Now assuming this coin had other utility and thus a non-0 value, then this incentive structure would motivate gamblers to solo-mine... for the benefit of the large payout. The higher the value of the pot the more miners would solo-mine. If no-one solo-mines then the reward system is little different than current coins using large pools. By this theory I conclude the result is more decentralized.
Now to make this a free-standing DAC you must create a demand for the coins so that can be achieved by adjusting the payout of the POT proportional to the number of PowerBall shares are held at the coinbase address. 0 shares results in 0 payout and the more shares you own the larger the cut of the payout you get but never exceeding 50%.
As a free-standing system this coin will only be of interest to gamblers and the value of the POT will be proportional to the demand for the coin. You buy the coin so you can gamble on getting more coins by mining and selling your winnings to future gamblers!
If you don't solo-mine then your profits are limited to the appreciation of the coin and a small margin above electric costs. If you solo-mine however, then you could win big in a life-changing way