Leaving the distributed lottery technical issues aside for a moment,

4. If a miner includes a bet referring to a prev-hash whose block is NOT contained in the current branch, he can collect the coins for himself by including the bet.

This would provide a huge incentive to roll back the chain. With PoW you can't reclaim work done on alternative chains, so I think coins bet on alternate chains should be deemed toast (but only keep track of branches for so long).

9. I can think of many possibilities regarding the coins bet of users that loose:

a. They are awarded to the winner.

b. Some percentage is lost and some awarded

c. They are awarded to the winner of a the block that will be mined 100 blocks later .

d. Partially or totally returned to the original owners. (This is something like Proof of Auction)

e. They are lost forever. (**I like this one most**)

If they were all granted to the winner, then it makes betting all the more attractive. The more coins put on the line, the better, right?

Interestingly then, with these properties and where

w_i = size of wager i

W = sum(w_i) = pot size

B = block reward (inflation reward + fees)

P = probability of reorg

then the expected return on wager i is

E(R_i) = (B + W) * w_i / W * (1 - P)

Assuming the average expected return tends roughly to the average wager as the number of bets becomes large (efficient market hypothesis?), then

P = 1 / (1 + W / B)

i.e. the probability of a reorg can be estimated from the ratio of the total wager to the block reward in a very straightforward way. Kind of a nice feature, if the assumption is actually valid.

With a "house edge" of f, i.e. the average expected return actually tends to (1 - f) * w_ave because people are irrational gambling freaks, then this formula becomes

P = (1 + f * W / B) / (1 + W / B)

I guess this parameter would have to be estimated in practice from the actual frequency of reorgs.

It's also obvious from the first formula that it's in every habitual player's interest to minimize P going forward by cooperating.