An important consequence of this is that the rationality of choices at nodes that are only followed by terminal nodes are independent of the relevant player’s knowledge. Call a node \(v\) pre-terminal if all of \(v\)’s immediate successors are terminal nodes. At such nodes, it does not matter what strategies the player thinks are possible: If \(v\) is a pre-terminal node and player \(i\) is moving at \(v\), then for all states in \(w\) in an epistemic model of the game and for all strategies \(s_i\in S_i\), \(Out_i(v, s_i, S_{-i}(w))=\{s_i(v)\}\). This means, for example, that for any state \(w\) in an epistemic model for the extensive game in Figure 17, the only strategies that are rational at node \(v_3\) in \(w\) are those that prescribe that \(A\) chooses \(O_3\) at node \(v_3\). Therefore, if \(w\in \mathsf{Rat}_A\), then \(\sigma_A(w)(v_3)=O_3\). Whatever \(A\) knows, or rather knew about what \(B\) would do, if the game reaches the node \(v_3\), then the only rational choice for \(A\) is \(O_3\).