1. So this is an example of one unique Nash equilibrium that happened to be a very strong one, a dominant strategy, Nash Equilibrium.

2. Your original strategy, where you were each a quarter mile from the middle of the beach, didn't last, because it wasn't a Nash Equilibrium.

3. And we saw exactly that in the, in the, the second round of the, the beauty contest game, then people start moving down toward the Nash equilibrium.