Have you ever wondered what the best throw to use is? Should you do your most damaging throw? Should you mix up your throws? Should you do the weakest throw because no one breaks it?
Fighting games are based on two players making decisions simultaneously. Different choices give different payoffs.
Throws are an especially interesting situation in VF5:FS, because the attacker and the defender have to simultaneously choose from three options. The defender is trying to predict what the attacker will do, while the attacker is trying to do the most damage possible while not being predicted by the defender. It almost seems like a game of cats going in circles -- as soon as you develop a pattern, your opponent can develop a counter pattern to exploit your pattern. Is there any way to win the mind games?
Nash equilibrium is a strategy that cannot be exploited. In other words, you could tell your opponent what your strategy is, and he could do nothing to change your payoff. The Nash equilibrium strategy for the attacker means that you are playing optimally to maximize your damage, no matter what your opponent does. For the defender, it means your are playing optimally to minimize your average damage.
Either player can deviate from this strategy, but doing so exposes that player to being out-predicted. So you may find that your opponent is weak, and that you can always do your most damaging throw. This increases your damage, but your opponent may learn from this and always escape your throw. Then you modify your strategy, and so the game of cats begins again... Nash equilibrium is an escape from the mind games.
In this video, I outline the concept of Nash equilibrium, and go through a case study of deriving the optimal probabilities of Wolf's standing neck clutch throw stance. This video is lengthy and mathematical in nature:
For those of you that want to skip the math, this video shows the optimal throw percentages for each of Wolf's setups:
Some of the conclusions presented may be unintuitive.