Merely proving that the game result was predetermined is not sufficient in a pool-backed game like a lottery, unfortunately. The problem is that the game operator knows the result ahead of time and could participate in the lottery himself with the winning ticket.
A simple solution would be to choose a block some time in the future and use its hash as the game result. That way players can be certain that the operator isn't (unfairly) partaking in the game. It is not completely provably fair as a big miner could still cheat, but it is probably sufficient for a small game.
The problem with that is, small lotteries grow bigger and 1BTC is still enough money for bigger miners to cheat. There have been a lottery on this forum, based on the blocks in the Blockchain and the miners did cheat. I cannot find it now, but it was pretty big and the operator was a well known user in the community.
The Millionairmakers concept on Reddit seems to work, if you want to try and get a hold of those guys. Go to :
https://www.reddit.com/r/millionairemakers/