Assuming that the Golden Balls are indistinguishable and the game host doesn’t interfere there is actually a way to pre-commit to splitting. Hand your own “split” ball to your opponent and state “I want you to choose this ball instead of either of your own. If you do so, I promise to choose whichever of your own balls you hand me.” This is quite similar to Nick’s ploy of promising to steal except by giving away the “split” ball it becomes impossible to un-commit to stealing unless your opponent gives you his or her own “split” ball. Short of sleight of hand or a last-minute switch (which could be avoided by setting both “steal” balls out of reach after the exchange and before the final decision) your opponent has no rational choice but to cooperate and split.
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.
Assuming that the Golden Balls are indistinguishable and the game host doesn’t interfere there is actually a way to pre-commit to splitting. Hand your own “split” ball to your opponent and state “I want you to choose this ball instead of either of your own. If you do so, I promise to choose whichever of your own balls you hand me.” This is quite similar to Nick’s ploy of promising to steal except by giving away the “split” ball it becomes impossible to un-commit to stealing unless your opponent gives you his or her own “split” ball. Short of sleight of hand or a last-minute switch (which could be avoided by setting both “steal” balls out of reach after the exchange and before the final decision) your opponent has no rational choice but to cooperate and split.
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.