we reason that we're in one of these states with 50-50 probability. Now if we observe player one choose play, we would say, okay, well, in a Nash equilibrium, we would expect player one to choose play 80 percent of the time if we were in the left state, 30 percent of the time when we're in the tail state. So, we update our belief about what state we're in using Bayes rule, and now we can reason that we're in that left state with 73 percent probability, and in that right state with 27 percent probability. Now, we would just say, well, if