Hi this is ratxt1, you may remember deluks and my guide on geiger, where we got into specific range analysis using a nash equilibrium solver and assumed payoffs for TD turns ([Character Guide] Time Enough for Love: Thoughts on Geiger for reference). Over the years I have calculated numbers like these in a similar manner but those were the only ones I posted. Usually I will try to calculate in spots that are “interesting” or I don’t feel I have a good grasp of what is going on.
I have decided to post more of these publicly on an “as I feel like it basis”. The format for the posts will be split into three sections; Description of the specific yomi situation (MU, constraints), rationale for payoffs (valuing intangibles), and resulting NE.
Here is Arg vs Troq in neutral to start us off.
Arg vs Troq, neutral
Arg: slow attack, throw, block.
Troq: fast attack, throw, block.
omissions: Arg Q (I like it less than most in this MU). hidden Arg AA (I think bubble is better early)
Troq attack win
Q is 9. slow J is 10. subtract a little for J clashes. add a little for hidden aces.
Arg attack win
low end 2Q =11+3-2=12.
11 for damage +3 for card off top. -2 per combo card. (card off top is worth significantly more than card in hand since pair, triple, ace, and joker draw odds).
high end 6KJ =19+3-4=18
19 for damage +3 for card off top. -2 per combo card.
high end 456=15+3-4+4(A)=18.
15 for damage. +3 for card off top. +4 for ace. -2 per combo card
You shouldn’t be playing options that lose to K since you have counter (counter backup cost is also negligible).
Troq block win
+3 for card off top. (I would like to point out that Arg K is an often undervalued combat option in this MU due to defensive mastery skewing valuation and chip being 100% relevant. Don’t go too far the other direction though)
Arg block win
Bubble shield is so hard to evaluate I’m not going to do it. I think it’s like 15+? About 30-40% of your blocks should be bubble shield if hidden (You have to block more often than you have it in your hand and you should still normal block sometimes when you have it for the value trap). Always play it over normal block if it is not hidden. Normal block is only worth 5 (+3 for card off top. +2 for keeping block). So on no known aces turns I could see the value of this being closer to 10.
Troq throw win
K is 15. Normal throws do about 16-18 but -2 for the combat card.
Arg throw win
12 is avg damage (6+5/6/7). -2 for combo card.
Some variations based on different valuations of bubble shield
Comment on payoff valuations
You probably disagree with my valuations of payoff options and I encourage you to post your reasonings. However, there is a pretty large margin for error when it comes to these (I would say 5 EV or more), so I am not going to do anything like re-run the NE or edit my post even if I agree with you. What will change the analysis is if you think I am forgetting to account for an option that is +EV and a character has available to them. This often changes things significantly and I might redo it because of that (or explain why I am not accounting for it).
You might wonder why I even go into so much detail on the valuations if the margin of error is so large. And the reason is that I have found that coming up with conclusions around the value of intangibles has provided as much, if not more value than the NE numbers.
Comments on accuracy
I would say that 4 out of 5 times I have done these the results have been obvious and match intuitions. 1 out of 10 times the results are flawed in some way, or not possible due to constraints on analysis (for example if you try to make oni numbers it always tells you to play T some impossible amount). 1 out of 10 times there is some insight. I would not read too far into anything.
(strategic game. select “by simplicial subdivision” so that you get decimals).