How to Play the Average of Everything You've Done in the Past

In poker, you talk about this Nash equilibrium convergence. You actually have to keep all these past games around to go actively look up what the average is. Now, neural nets can help you with that interpolation. We use two neural nets, one that is generalizing between similar situations. And then also we have a second neural net that is approximating given what my strategy has been over all of these previous iterations,. What is the average over all these different situations? Like trying to compress that average into a single neural net.