The paradox: he persuades Mr Left to split based on him saying he’s going to steal and that he’s A MAN OF HIS WORD. Then he goes against his word to Mr Left’s benefit.

O’Henry would have loved this.

What Mr Right had to do was convince Mr Left that if he chose “Steal” then he would absolutely, positively, not get any cash.
And therefore his choices were “Choose to believe that Mr Right would not split afterwards, and to spite him.” and choose “Steal”, or “Choose to believe that Mr Right would split, and go along with it.”

That makes it a much better bet to choose to split, because that’s now the _only_ way Mr Left can make any cash. So he chooses to do that, and Mr Right, knowing that, chooses to Split too.

Very, very, clever thinking by Mr Right there.