I had an idea about that. Publish the algorithm by which you come up with each game's multiplier. Presumably it will be seeded somehow. Pick a random seed that you will use for game 1 billion. sha256 hash it to get the seed you will use for the game before that, and so on. Each games seed is the sha256 hash of the game that comes after it. So you have a billion-long chain of sha256 hashes. Before each game you publish the hash of the current game's seed, which allows everyone to verify all the previous games but none of the future games. Now you can't be accused of rigging the outcomes.
I used to use them for their secret. They publish one every hour. I need one that does it every minute (or more often).
The problem is with compromised secrets. But you know what, this very idea could prove useful for the "audit server" idea (the one about provable fairness for investors) but again it limits the speed of the game to as fast as the "audit server" can spit out the seeds.
I think I'm going to do a hybrid of this and something else.