For the split or steal game (with the golden balls), here is what I what do.
I would not open either ball, and I would tell the other contestant to pick one at random. Then, he MUST choose split for his own ball if he wants any chance of winning money. If my ball happened to say "steal" after opening, then I would split what I won with him.
I think this would guarantee both of us winning unless he was willing to take the chance of winning nothing.
He also has to be willing to trust that you will actually split what you win after stealing the whole pot. Otherwise, he will worry that you could dupe him and walk away with everything, and then choose to steal.
I saw that video. That's what made me think of my idea. But mine removes the possibility that I might be holding out on "split" and I think has a better chance of guaranteeing we both split the money.
I would not open either ball, and I would tell the other contestant to pick one at random. Then, he MUST choose split for his own ball if he wants any chance of winning money. If my ball happened to say "steal" after opening, then I would split what I won with him.
I think this would guarantee both of us winning unless he was willing to take the chance of winning nothing.