Does your book have a name for the little equation you can put together to determine the strategy ratio?
It doesn't have a name, it's more of a recipe. I am not sure I understand why it works. The idea is to measure the difference between the two outcomes if you choose a move, and use that difference as the relative proportion with which you will choose the other move. You ignore how good or bad the outcomes are, and favor moves with a narrow spread in outcomes. It only works in these simple 2x2 games, but 2xN games can be reduced to 2x2 games. The idea is to eliminate any advantage the adversary can gain with strategy, and I see how using the derived proportion forces the other side to accept the same outcome regardless of what move they make. (Interestingly, if the other side fails to optimize, but stupidly chooses the same move every time, or uses a suboptimal distribution, the result will not change. Optimal strategy by one side forces a fair outcome for both, where "fair" means the best that either side can hope for when both sides use optimal strategy.)