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.