Hate Speech: Theory Fighter University: Remedial Math

As much as I hate bringing this up I see Nirf and Signia trying to nitpick at math and I have to bring up the concept of the metagame. The metagame is basically how the commonly used options shape the matchup at hand. So lets take the Cervy vs Asta example from the article itself to illustrate a metagame shift.

Now if your goto option for defense as a player is block, you could think the Asta/Cervy scenario involved is fairly close to break even and not be too wrong. If your goto option for defense as a player is sidestep, you can lol in asta's face and light him the fuck up for doing bullrush. Neither of these assessments is really right or wrong, the difference is how the metagame matches up with who you are playing. Where a metagame shift happens is when the Cervy player who blocks realizes he should be sidestepping to tip the balance of the risk/reward in his favor.

We can take it back to what Nirf said earlier about people not using things at true 50/50 frequency, which is common everywhere. The thing is tailoring your options doesn't give you a mathematical advantage, if gives you an edge over their metagame. Why is it not mathematical? Because you aren't dealing with hard definite variables. There is no way to quantify he isn't going to block low until you throw a lot of them at him and then he will overvalue low guard and you can abuse him with mids. This is just something you have to do as a player using on the spot intuition. I would even go so far as saying that attempting to bring this out of the realm of intuition would be something left to an actual mathematician, because the variables are mind boggling in number and the method for calculating responses is almost infinitely variable.

I really want to take it back this is precisely why the math for hates deriving the weight of a mixup is ideal. You get to view the risk vs reward divorced of preference and/or metagame options. It shows the meat and potatos of what you are trying to accomplish, namely is this where I should be pressing my advantage in this matchup or should I try to pressure in more advantageous ways? The real heart of the matter is a question similar to this "If I don't let my opponent outguess me, will I still be ahead from using my planned options?"

Which brings us to the reason most theory fighter blows. People aren't made of numbers. They will change their gameplay as a game progresses and the best laid plans of mice and men get figured out all the time only to backfire. Why do they backfire? Plans are made of numbers, and as such people can figure them out and take the most advantageous options vs your strategy in a metagame shift that happens during a match. So if you want to plan your way to victory against an intelligent opponent you need a plan for things as they stand, a plan for when a dude adapts and a plan to smash his adaptation... Maybe on several levels.

PS - I miss starcraft... That is the only game ever where the concept of a metagame is easy to point out.
 
I feel I have greatly simplified the whole topic as it relates to math.

The math itself is just a metric to help you judge the weight of given options as they relate to each other. While it should to some degree dictate your move choice, you should never let numeric values dictate your gameplay. Gameplay should be variant based on your judgement of the situation at hand, only at that point should you account for player tendencies and other such variables.
 
The metagame naturally approaches Nirf's figures though, not "50-50." There's no reason we should assume equal preference to each option. Unpreferenced would be using a mix of options close to Nirf's equilibrium.

BrewtusBibulus said:
Gameplay should be variant based on your judgement of the situation at hand, only at that point should you account for player tendencies and other such variables.
Click to expand...
That's kinda what I said in my post, you need to look at their mix and counter it with your own mix. Which moves and how often depends on how often they do options in their mix. This can and has to be done intuitively, but the math tells you how it really works, and it can be an excellent tool in determining roughly how often each option should be done.
 
Brewtus, I'm an "actual" physicist, close enough? Anyhow, what Signia said is spot on. Yes, the model I gave is extremely simple and misses a ton of stuff, in fact most of the important stuff is not captured by it. But it captures at least some interesting behavior, which makes it a good starting point, unlike the 50-50 stuff which is just flat out wrong. You describe Hates math as "if I don't let my opponent outguess me, will I be ahead from using my planned options?". This is 100% false; that is actually an exact description of MY math. Hates' math, in addition to not having "outguessing" just has poor decision making from both players built in.

I understand what you are saying about metagame, yeah this model doesn't capture that and lots of other stuff. It captures the game at the level of being played by two robots that are randomizing their actions as optimally as possible.

By the way, if you've read a standard book on poker literature, they discuss game theory very similarly to how I do it here. They would of course never assume that someone's likelihood to call is 50%. And poker too is a game where the math and probabilities are just part of what's going on (and part of a metagame). They use these game theory ideas as a guide. It's probably more applicable to poker than fighting games (in fighting games there are far more options in particular) however the basic concept is similar.
 
I have played poker for a living for about 8 years... So I have read a poker book or two. The problem with using models for that and applying them to fighting games is in poker you have a truly random element. In fighters the random is a human factor that is beyond statistical prediction. It's not that your math is wrong I would say your fault in calculation was trying to quantify player tendencies.

Personally I don't even take it as far as hates does, I keep it nice and simple. I wouldn't take it farther then this
Damage outcomes for the payoff matrix:

BG: Asta bullrushes, Cervantes guards, = 0.
BC: Asta bullrushes, Cervantes crouches, = 28 damage.
GG: grab, guard = 36* damage.
GC: grab, crouch = -70 damage (i.e. Asta takes 70 damage).
Click to expand...
Right there you understand the inherent risk and reward. Everything beyond that is a strategic concern you can't factor into your gameplay.

Should you assume that bullrush is more common and you "adapt" by choosing to counter it more, you are making strategic judgements based on math. The reason this is bad is because strategy is made of numbers, so if a player looked at your gameplay and realized that. They can just grab you all day and should come out ahead... Don't ask me to prove this with numbers, fuck that noise.

So once again as plainly as I can possibly state. You need to view the weight of the options at hand differently then you weigh your strategic concerns. People favoring the safer option is a strategic concern and not one you should derive with math.

The main fault with it is that it grows off it's own logic. So if you have like minded individuals the result will probably hold true towards reality. But what about when someone doesn't give a fuck about numbers and just does things they think will work? Someone can essentially try and play you in a way that should hand over the match, but is so counterintuitive to your logic your adaptations are on the wrong spectrum and thus you lose.

Not to say you can't identify a shitty strategy and counter it. But simply that doing that needs to not be a math derivative or you better be damned good at your mental math.

When you try to quantify someones motivation to push buttons you better be doing it on an individual basis. Everyone who has done a decent amount of travelling for fighters will be able to remember at least one instance of travelling to another area and playing a character you normally feel very comfortable playing against. But in a style you are not familiar with and therefore you lose horribly in what you thought was one of your better matchups.

The bottom line is there is no right and wrong answer outside of what would work in a given instance. What really matters? Knowing how things will end up and applying that to what you know about the person at hand.

PS - If you want to use said equations to determine how you want your baseline strategy to look, that could be a very good application... or you could just favor safe options while gathering data on a new opponent. But if you get attached to the idea of favoring certain options because they are better on paper, it will bite you in the ass eventually.
 
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