If Player III reasons in terms of conditional probabilities, then Players I and II must conjecture about Player III's beliefs about those conditional probabilities.

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