Hand your own “split” ball to your opponent and state “I want you to choose this ball instead of either of your own.
It seems unlikely that the host would allow you to choose the other person’s ball. You are just trying to denying the decision problem and cheating doesn’t work when someone else with power is choosing the rules and overseeing the process.
There can be additional strategies if the rules require using physical artifacts to signal a decision. Another method would be for a player to visually reveal the choices inside each of the balls to the other player and offer to set the “steal” ball out of reach before decision time if the other player did the same, but to steal if the other player didn’t cooperate (perhaps setting the “split” ball out of reach as evidence). If the balls can’t be moved or revealed to the other player before the final decision then you are correct. However, in watching a couple videos of players in the Golden Balls, it appears that the host allows players to pick up and manipulate their own balls before the final decision.
It seems unlikely that the host would allow you to choose the other person’s ball. You are just trying to denying the decision problem and cheating doesn’t work when someone else with power is choosing the rules and overseeing the process.
There can be additional strategies if the rules require using physical artifacts to signal a decision. Another method would be for a player to visually reveal the choices inside each of the balls to the other player and offer to set the “steal” ball out of reach before decision time if the other player did the same, but to steal if the other player didn’t cooperate (perhaps setting the “split” ball out of reach as evidence). If the balls can’t be moved or revealed to the other player before the final decision then you are correct. However, in watching a couple videos of players in the Golden Balls, it appears that the host allows players to pick up and manipulate their own balls before the final decision.