IdleMind
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And now you know why (mathematically) Asta is all gimmicks.
Hate Speech: Theory Fighter University: Remedial Math
- Thread starter Dr. Hates
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And now you know why (mathematically) Asta is all gimmicks.
Heaton
嶋野の狂犬
Agreed. Sophitia definitely has the mathematical advantage in that match up. I was just illustrating that even characters that are mostly gimmicks can still create mathematical advantages in their own unique ways, though the way this usually happens is unorthodox and not exactly in that characters favor, e.g. to get that particular Siegfried mix-up, I have to block TAS B, which, while safe, isn't something thrown out just because they feel like it - besides, if you've already conditioned your opponent to use TAS B when you KNOW you'll block it, you can pretty much substitute Grab/1B mixup with anything you want and it will still work.
Dr. Hates
Jerk.
This is actually slightly different from what I'm discussing, and it's a great illustration of why I just factor out the human element when examining a mixup qua mixup. You'll notice in my article that I say two players of equal skill will choose correctly 50% of the time in a given 50/50. My implication is that they're not necessarily choosing each of their options with 50% frequency, but that whatever option they choose is the righti choice, whatever that may be, about half the time.
There's some potentially more complex calculation that can come from weighing the risks and rewards of options against a likely distribution of how frequently a smart person picks said option, but at that level of complexity I just "eyeball" it.
Evaluating moves/scenarios outside of the context of players is relatively straightforward and useful. Attempting to do it within that context is all kinds of difficult. Figuring mathematical advantage will always be a guideline because there's no substitute for just reading somebody like a book. Everything's safe on hit.
Dr. Hates
Jerk.
Sorry for posting back to back, but...
What this really underscores is why Astaroth is so damn hard to balance. Barring characters with exceptional punishes, many of his crucial throw scenarios are basically just trade-downs. If you give him tools to zone, chip, and gain a marginal advantage before trading down, he becomes incredibly strong. If you give him nothing in that department, he basically becomes a great big coin flip (see: the difference in SC3 Asta vs. SC4 Asta).
What this really underscores is why Astaroth is so damn hard to balance. Barring characters with exceptional punishes, many of his crucial throw scenarios are basically just trade-downs. If you give him tools to zone, chip, and gain a marginal advantage before trading down, he becomes incredibly strong. If you give him nothing in that department, he basically becomes a great big coin flip (see: the difference in SC3 Asta vs. SC4 Asta).
In this post you delve quite a bit into game theory. While your comments on SC are generally spot on, there's some errors in how you treat game theory that actually have some important ramifications.
This is completely wrong. The players will absolutely not guess each option 50 percent of the time. You are assuming that each player picks each option 50% and that the two choices are independent. While the second assumption is valid (as you said, controlling for player skill), the first is absolutely not. Rather than crank through the math in this post (I can put the math in a follow up if people are interested), I'll give a very simple example of why this is wrong using your second scenario as the difference is much more profound.
In your outline, you make Cervantes choice duck/stand, and Asta's bullrush/grab. So bullrush is a safe option now. If Cervantes does the fancy damage option, you claim that he has mathematical advantage. Well, I would say your Asta player is very foolish to use grabs 50% of the time when they are so unsafe. He should clearly use bullrush much more often. If Astaroth uses bullrush 100% of the time, Cervantes should just block 100% of the time. So Astaroth cannot do any worse than break even damage wise. Optimally, Astaroth can mostly bullrush and very occasionally grab. Cervantes will then follow a strategy of usually blocking, and very rarely ducking The damage will then be in Astaroth's favor.
The way you look at it misses one of the most critical ideas in game theory as applied to SC: a mix-up with one safe option (like bullrush in your second example where Cervantes does not step) is ALWAYS favorable.
Signia touches on some of these points, but I think in fact I will do a follow up post where I work out the math. Nothing is needed beyond high school calculus.
This is completely wrong. The players will absolutely not guess each option 50 percent of the time. You are assuming that each player picks each option 50% and that the two choices are independent. While the second assumption is valid (as you said, controlling for player skill), the first is absolutely not. Rather than crank through the math in this post (I can put the math in a follow up if people are interested), I'll give a very simple example of why this is wrong using your second scenario as the difference is much more profound.
In your outline, you make Cervantes choice duck/stand, and Asta's bullrush/grab. So bullrush is a safe option now. If Cervantes does the fancy damage option, you claim that he has mathematical advantage. Well, I would say your Asta player is very foolish to use grabs 50% of the time when they are so unsafe. He should clearly use bullrush much more often. If Astaroth uses bullrush 100% of the time, Cervantes should just block 100% of the time. So Astaroth cannot do any worse than break even damage wise. Optimally, Astaroth can mostly bullrush and very occasionally grab. Cervantes will then follow a strategy of usually blocking, and very rarely ducking The damage will then be in Astaroth's favor.
The way you look at it misses one of the most critical ideas in game theory as applied to SC: a mix-up with one safe option (like bullrush in your second example where Cervantes does not step) is ALWAYS favorable.
Signia touches on some of these points, but I think in fact I will do a follow up post where I work out the math. Nothing is needed beyond high school calculus.