Wouldn't it be the same as betting on the same seed and having only two outcomes? I don't think it's impossible, though.

Possibly you could use that Shamir's Secret Sharing parts would be automatically given to the players. After that, they can verify the two that it's part of one game. It is preventing alterations or something. Have the tiniest elements of the secret to a minimum of two or three.

Or maybe have it like a trusted computer that would not cheat and act as a judge or an arbiter towards the game — giving another part of the secret making a minimum of three.