Hate Speech: Theory Fighter University: Remedial Math

[iKotomi]

While game theory revolves around Nash equilibria, it's in general silly to apply it in practice.

Nash equilibrium is the set of players and strategies where nobody can do better by changing their strategy. It is the convergence point where strategy ceases to matter, at which point the game is pointless to play. Win or loss is just a matter of probability.

The existence of a nash equilibrium does not imply optimal play. Nash equilibrium is dependent on both player's strategies, and is a point of simultaneous optimal play.

This is almost never the case and playing the Nash equilibrium strategy will be a terrible choice given the other player's suboptimal strategy. This is why exceptional players will win 80-90% of the time rather than the more statistically likely 50-60.

An easy illustration is rock, paper, scissors. Nash equilibrium is everyone playing equal probabilities of each. If you opponent is playing rock every time, you'd be stupid to use the equilibrium strategy (optimal is paper 100%). Any other non-nash equilibrium strategy on the opponent's side has a more optimal strategy than the equilibrium strategy, and you just need to adjust the weights to reflect that (not really, there will always be a best pure strategy counter so you don't even need to worry about weights).

 

[BrewtusBibulus]

because you can actually turn an opponent's good decision-making against him with a bit of effort.

I was just making this point in the patroklos forums. When you choose to streamline your options and make for a minimal risk, your gameplay tells people "This isn't going to work" and they stop trying. Thus eliminating the opportunities to punish them for doing something stupid.

If you can find an intelligent way to work in an option that is the worst option in the book vs specific tactics you can exploit. You can never really go wrong, provided you adapt to the circumstance. The important thing is to keep those kind of things in your back pocket. That way when the opponent stops presenting certain opportunities you can have your gameplay remind them "HEY, THAT THING YOU STOPPED DOING WOULD TOTALLY WORK HERE!" until they start to use that thing again.

The idea of image is seldom considered in theory fighting, but I really believe it's one of the most important concepts to formulating an effective strategy. Every time you do something it leaves an impression and that will come into play impacting the later stages of gameplay. You have to not only create a scheme to stop the opponent from doing things in as efficient a manner as possible. You have to give them incentive to play into your hands as well.