The children start having to think harder, at this point. There are kids playing hard on puzzle-games, and hearing estimates of the other player's labor-effort that don't sound quite right; proposing splits afterwards, and seeing those splits rejected, and both getting nothing. Some of the kids start to get angry at each other. Others are trying to come up with a brilliant general solution; and, if they're wise, they know they haven't found one. Some children are not so wise, but they can't get anyone else to go along with their brilliant general solution.
Keltham plays through with as much cold and steely determination as a seven-year-old can muster, offering exactly what he thinks is fair, rejecting anything he thinks is less than fair; feeling awful when the other kid yells at him that he was being honest, but not swerving from his course. He can trust himself; he cannot trust the other. When his card tells him to be dishonest, Keltham gives ridiculously huge estimates for his own labor, and hopes the other child is wise enough to know that Keltham is, must be, lying. Sometimes he's told to be dishonest and he has to pick the split himself, and then he gives a huge estimate and pretends he believed the other kid's huge estimate. Sometimes the other kid doesn't catch on and then Keltham has to offer an unfair split, basically, and sometimes it gets rejected, and sometimes it gets accepted which is worse. It's a good thing this is only a game, because living life like this would be awful.
Lessons end for the day. It is sometimes good to let children dwell for a time on problems that don't have known solutions yet, or realize how awful life can become when not everyone has deduced the governing Law.