When the children return the next day, the older children tell them the correct solution to the original Ultimatum Game.

It goes like this:

When somebody offers you a 7:5 split, instead of the 6:6 split that would be fair, you should accept their offer with slightly less than 6/7 probability.  Their expected value from offering you 7:5, in this case, is 7 * slightly less than 6/7, or slightly less than 6.  This ensures they can't do any better by offering you an unfair split; but neither do you try to destroy all their expected value in retaliation.  It could be an honest mistake, especially if the real situation is any more complicated than the original Ultimatum Game.

If they offer you 8:4, accept with probability slightly-more-less than 6/8, so they do even worse in their own expectation by offering you 8:4 than 7:5.

It's not about retaliating harder, the harder they hit you with an unfair price - that point gets hammered in pretty hard to the kids, a Watcher steps in to repeat it.  The circumstances under which you should ever go around carrying out counterfactual threats in real life are much more fraught and complicated than this, and nobody's going to learn about them realistically for several years yet.  This setup isn't about retaliation, it's about what both sides have to do, to turn the problem of dividing the gains, into a matter of fairness; to create the incentive setup whereby both sides don't expect to do any better by distorting their own estimate of what is 'fair'.

They play the 2-station video games again.  There's less anger and shouting this time.  Sometimes, somebody rolls a continuous-die and then rejects somebody's offer, but whoever gets rejected knows that they're not being punished.  Everybody is just following the Algorithm.  Your notion of fairness didn't match their notion of fairness, and they did what the Algorithm says to do in that case, but they know you didn't mean anything by it, because they know you know they're following the Algorithm, so they know you know you don't have any incentive to distort your own estimate of what's fair, so they know you weren't trying to get away with anything, and you know they know that, and you know they're not trying to punish you.  You can already foresee the part where you're going to be asked to play this game for longer, until fewer offers get rejected, as people learn to converge on a shared idea of what is fair.

Sometimes you offer the other kid an extra jellychip, when you're not sure yourself, to make sure they don't reject you.  Sometimes they accept your offer and then toss a jellychip back to you, because they think you offered more than was fair.  It's not how the game would be played between dath ilan and true aliens, but it's often how the game is played in real life.  In dath ilan, that is.

When the children return the next day, the older children tell them the correct solution to the original Ultimatum Game.

It goes like this:

When somebody offers you a 7:5 split, instead of the 6:6 split that would be fair, you should accept their offer with slightly less than 6/7 probability.  Their expected value from offering you 7:5, in this case, is 7 * slightly less than 6/7, or slightly less than 6.  This ensures they can't do any better by offering you an unfair split; but neither do you try to destroy all their expected value in retaliation.  It could be an honest mistake, especially if the real situation is any more complicated than the original Ultimatum Game.

If they offer you 8:4, accept with probability slightly-more-less than 6/8, so they do even worse in their own expectation by offering you 8:4 than 7:5.

It's not about retaliating harder, the harder they hit you with an unfair price - that point gets hammered in pretty hard to the kids, a Watcher steps in to repeat it.  This setup isn't about retaliation, it's about what both sides have to do, to turn the problem of dividing the gains, into a matter of fairness; to create the incentive setup whereby both sides don't expect to do any better by distorting their own estimate of what is 'fair'.

They play the 2-station video games again.  There's less anger and shouting this time.  Sometimes, somebody rolls a continuous-die and then rejects somebody's offer, but whoever gets rejected knows that they're not being punished.  Everybody is just following the Algorithm.  Your notion of fairness didn't match their notion of fairness, and they did what the Algorithm says to do in that case, but they know you didn't mean anything by it, because they know you know they're following the Algorithm, so they know you know you don't have any incentive to distort your own estimate of what's fair, so they know you weren't trying to get away with anything, and you know they know that, and you know they're not trying to punish you.  You can already foresee the part where you're going to be asked to play this game for longer, until fewer offers get rejected, as people learn to converge on a shared idea of what is fair.

Sometimes you offer the other kid an extra jellychip, when you're not sure yourself, to make sure they don't reject you.  Sometimes they accept your offer and then toss a jellychip back to you, because they think you offered more than was fair.  It's not how the game would be played between dath ilan and true aliens, but it's often how the game is played in real life.  In dath ilan, that is.