the Nash equilibrium is for them, and we figured out, well, they should be choosing play 80 percent of the time when the coin lands heads and play 30 percent of the time when the coin lands tails. Let's say, just for example. Now, if we assume that the opponent's playing this strategy, can we then reason about the distribution of states that we might be in and then solve optimally using that distribution. It turns out that doesn't work. So, let me give you an example of what this would look like. When the coin lands either heads or tails,