 Theorists who think of game theory as part of a normative theory of general rationality, for example most philosophers, and refinement program enthusiasts among economists, have pursued a strategy that would identify this solution on general principles. Notice what Player III in Selten’s Horse might wonder about as he selects his strategy. “Given that I get a move, was my action node reached from node 11 or from node 12?” What, in other words, are the conditional probabilities that Player III is at node 13 or 14 given that he has a move? Now, if conditional probabilities are what Player III wonders about, then what Players I and II might make conjectures about when they select their strategies are Player III’s beliefs about these conditional probabilities. In that case, Player I must conjecture about Player II’s beliefs about Player III’s beliefs, and Player III’s beliefs about Player II’s beliefs and so on. The relevant beliefs here are not merely strategic, as before, since they are not just about what players will do given a set of payoffs and game structures, but about what understanding of conditional probability they should expect other players to operate with.