If I were playing Split or Steal, my strategy would be exactly this: tell the other player that I'm going to choose "steal" and if they choose "split", I'll give them half of the winnings. We would shake on it on national television which forms a nice contract: an offer, consideration for both parties, and acceptance. The beauty of this is that if they're not an idiot they'll choose "split" and we each walk away with half. However, if they are an idiot and they also chose "steal" then nobody gets anything and I can sue them for violation of the contract in the amount of the 50% I would have won.
Sadly, I suspect everyone would then copy that strategy and much like everyone choosing the letters R, S, T, L, N, and E in Wheel of Fortune, it would quickly become a formula and would ruin the suspense the show hopes to create.
There's a twist in this example though. He says he's going to steal (but split after the show) and convinces the other guy to split. At the last minute he changes to split so that the split is governed by the rules of the game.
I think that's why the guy proposing the deal ended up splitting. If the other guy did steal to spite him, the fact he split would show that he was acting in good faith and would increase the chance of a split after the show.
"A more powerful variation would be to offer the same deal but without looking at the balls at the beginning, stating that you will pick one at random. The other player is then forced to split or risk walking away with nothing."
The thing that always bugged me about Golden Balls (aside from the terrible name) was the way stealers would act like it was just a game when they had in fact taken thousands of pounds from another person through deception. Certainly it was legal and even encouraged by the format of the show but it was never the right thing to do.
I've seen people immediately regret doing it when they see that their opponent shared. They seem more upset about it than the loser and tend to cite an expectation that the other person would steal as their reason for stealing, even though this makes no logical sense. It was a fascinating but horrible ending to sixty minutes of otherwise tedious viewing.
Logically you'd split every time, it's safer and guaranteed. However the expectation that someone else is going to steal so you steal makes twisted sense in a 'if I can't have they can't have it' way, which is human nature in children through to adults.
Sadly, I suspect everyone would then copy that strategy and much like everyone choosing the letters R, S, T, L, N, and E in Wheel of Fortune, it would quickly become a formula and would ruin the suspense the show hopes to create.