Nothing ias wrong with 0 deposit. It helps speed it up to get players playing soon as they can. You can't double spend anymore.
If it is a problem the solution will be easy. Just make no withdraw until deposit is going through. Also if so many transactions fail then flag the account.
That solution doesnt work because they arnt double spending if they win. If they win they just let it go through. They only double spend
when they lost it all so basically they dont lose the btc they sent. I would just make people wait and get the 1 conformation to be safe