This last formula is interesting because it “pre-encodes” what player 1 would believe upon learning that player 2 is choosing \(R\). Note that upon receiving this true information, player 1 drops her belief that player 2 believes she is choosing \(u\). The situation can be even more interesting if there are statements in the language that reveal only partial information about the player strategy choices. Suppose that \(E\) is the event \(\{w_4,w_6\}\). Now \(E\) is true at \(w_4\) and player 2 believes that player 1 chooses \(d\) given that \(E\) is true (i.e., \(w_4\in B_2^E(D)\)). So, player 1 can “bluff” by revealing the true (though partial) information \(E\).