Kazumi's db+3 is +2 on hit and forces crouch, which is a small but notable advantage.
The question is, how should we press this advantage? How do we determine which options should be used, and how often? How do we rule out options as too risky or not worth using? To what degree should we adapt our strategy to our opponent's behaviour? And what are some rules of thumb we can use to answer these questions quickly and on-the-fly so that we can apply them to other situations?
Building a strategy
To keep things relatively simple, we're going to focus on a single matchup. So let's just pick a random character, say, Armor King.
One place to start at is to assume the opponent is just gonna block and throw out our best mid/low mixup, which for Kazumi is f,F+4 with db+4. And with the db+4 we're gonna do f,db+4 instead to make it harder to fuzzy guard and low parry.
| b | d | |
|---|---|---|
| f,F+4 | -2 | 75 |
| f,db+4 | 19 | -22 |
Obviously this is really good for us, and our opponent isn't gonna play along. One strong option here is ws2, which will counter hit launch both of our attacking options.
| b | d | ws2 | |
|---|---|---|---|
| f,F+4 | -2 | 75 | -75 |
| f,db+4 | 19 | -22 | -75 |
Now this is terrible for us. He can do ws2 every time and we just die, so we need to find something that deals with that.
There are a lot of candidates. We could get a counter hit launch with 4. We could interrupt with a poke like df+1 or 2,1. Or we could make it whiff with a backdash or a sidestep. It's hard to say which we should choose because they all have their own strengths and weakness.
I'm gonna choose sidestep left, but we'll revisit this decision later.
With a sidestep we need to decide what we'll whiff punish with. Since we're only worried about ws2 for now we can safely go with u/f+4 for a launch.
| b | d | ws2 | |
|---|---|---|---|
| f,F+4 | -2 | 75 | -75 |
| f,db+4 | 19 | 22 | -75 |
| ssl | 0 | 0 | 62 |
Now it looks good for us again, and our opponent needs to find an answer.
Instead of relying solely on ws2, which has poor tracking, they could also use ws4 to challenge, which hits us doing ssl.
| b | d | ws2 | ws4 | |
|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 |
| f,db+4 | 19 | -22 | -75 | -26 |
| ssl | 0 | 0 | 62 | -26 |
This once again looks troublesome, because ws4 wins every time. But we can step right instead of left to deal with that. Since ws2 loses to both steps there isn't any tradeoff here in switching.
But now there's some trouble with the whiff punisher we're using. While ws2 is a big enough whiff to use u/f+4, ws4 recovers much faster. Theoretically we could react to which move whiffs and act accordingly, but this is really hard in practice. So to make easier we'll use d/f+1,2 as our whiff punisher instead.
Payoff on ssr vs ws4 is worse than vs ws2 because of chance that d/f+1,2 whiff punisher is too slow.
| b | d | ws2 | ws4 | |
|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 |
| f,db+4 | 19 | -22 | -75 | -26 |
| ssr | 0 | 0 | 33 | 28 |
Now ssr is dominating. One thing Armor King can try here is ws1, which beats ssr and is also fast enough to interrupt the original mixup.
| b | d | ws2 | ws4 | ws1 | |
|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 |
| ssr | 0 | 0 | 33 | 28 | -71 |
That's surprisingly scary. Now, we could add a new option to deal with this, but if possible it's better to improve our existing options. The ws1 is much slower than the other challenges, so we can actually block it and step the other options with a step block. This is both a tricky timing which requires some practice and makes our whiff punishment more difficult. To make the whiff punishing easier, we'll use 1,1,2 instead.
Although the timing on a step block is pretty strict, this timing should be the same in every matchup after d/b+3, because you're usually trying to block launchers that start around i15.
Payoff on ssr,b vs ws2 is better than other options because of chance that P1 reacts and whiff punishes with u/f+4 instead.
| b | d | ws2 | ws4 | ws1 | |
|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 |
| ssr,b | 0 | 0 | 35 | 29 | 29 |
Now ssr,b is dominating. For a lot of opponents you could stop here because the only thing they challenge with are while standing attacks. You shutdown the challenges with ssr,b and then otherwise go for the big mixup.
If they're aware of it, however, FC.d+4 is an option that poses a lot of trouble.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | |
|---|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 |
This highlights the strength of generic d+4 in general: it beats movement, and it's fast enough that it's hard to challenge too. The full crouch version also does more damage, although at the cost of frames. We could deal with this by ducking or by challenging with a faster move. Since ducking loses to the various mid challenges, we'll try and avoid that. And since ws2 is pretty scary, we need an i13 or faster attack, so the only options are d/f+1, d+3+4, or dickjabs. Since d/f+1 has the best payoff we'll start with that, and we'll use d+3+4 as well to be robust against fuzzy guards.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | |
|---|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 |
Things are looking good again. Armor King still hasn't forced us to duck yet, so he's gonna have to pull out the dickjab. It beats or trades with all of our attacks, and it's pretty safe against our sidestep since we're committed to whiff punishing with 1,1,2. Although there is some risk that it'd get whiff punished with d/f+1,2, it's pretty marginal compared to the benefit of shutting down all the attacks.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | |
|---|---|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 |
With the dickjab added, we really do need to duck. A low parry can punish it and FC.d+4 with a big enough payoff to justify exposing ourselves to the mid options more.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | |
|---|---|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 |
At this point things are looking grim for Armor King. The only options that beat df+1 are FC.d+1 and ws4, and if he were to stick to using those exclusively we could change up our ssr,b whiff punishment strategy to use d/f+1,2 instead, punishing the dickjab harder.
One ray of hope for him is that df+1 is weak to ssr, so if he's on P2 he could replace b with a step right. Not only does this make df+1 a lot scarier to use, it also causes trouble for the original mixup's f,F+4.
In fact, right now we aren't doing any mids that track left, so rather than a step block he can opt for ssr into SS.2,1 i.e. ssr~2,1, which punishes our mid options hard. This is stronger than something like ssr hopkick because he can stop at the first hit if there wasn't any whiff, making it safer. However, since it's still unsafe on block, we'll add it as an extra option rather than replacing b with it entirely.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | |
|---|---|---|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | -75 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 22 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 |
To deal with ssr~2,1 a bit better, we can alter the timing of our original mixup. The main idea here is that since this mixup loses to challenges anyway, it's worth taking a bit of extra time to do a little dash to re-align and make it robust against steps.
The exact timing to use here isn't important. In fact it should be varied somewhat to keep things unclear. If it's too fast or too slow it can lose to ssr~2,1 done on a timing to match.
Payoff of f,f~f+4 vs ssr~2,1 is unclear since winner depends on timing, but it generally favours P1. There's also some chance that f,f,d/b+4 is delayed too much and loses.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | |
|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 |
At this point, both strategies are fairly complete. Neither player could add an option that robustly beats the entire strategy, nor can any option be changed to be strictly better. If Armor King tried to low parry instead of a simple crouching guard, it's a bit awkward since d+3+4 is much faster than db+4, especially now that the latter is being delayed.
To make any significant improvements, we need to figure out not just which options look good but how good they are. It's possible that, for example, ws2 is too risky, and we don't need to be that scared of it, or that the f,f,db+4 mixup is too risky and we need to add a faster one.
Estimating a good strategy
While we could calculate the optimal strategy for both players given we have this nice payoff table already finished, this doesn't help us come to an intuitive understanding of how those strategies are constructed.
So going back to the original mixup between f,F+4 and db+4, how often should each be used?
| b | d | |
|---|---|---|
| f,F+4 | -2 | 75 |
| f,db+4 | 19 | -22 |
For a simple mid/low mixup, you can estimate the optimal strategy on-the-fly. Add up all the payoffs to get the denominator. Then add up the payoffs of the low to get the numerator for how often you do the mid. So for this mixup, f,F+4 is done (19+22)/(75+2+19+22) of the time, or about 1 in 3. Then the low is done the other 2 of 3 times, twice as much as the mid.
(If you can't ballpark these numbers in your head, you should probably skip this section.)
Using the low twice as much as the mid sounds a little crazy. Shouldn't you use the mid more because it's safer and more rewarding? This counter-intuitive result is because you need to give your opponent a reason to duck. If you don't use the low enough, they're better off tanking it, because the mid is that scary.
Another counter-intuitive result is that if your low does less damage, you want to use it even more. For example, if we use d+3+4 for our low instead with a payoff of 6, then we'd use the mid about (6+22)/(75+2+6+22) of the time, or about 14. Again, the idea is the same: You need to give your opponent a reason to duck. If the low does less damage, then you need to use it more before they're gonna care.
Of course, if the low does less damage, then the payoff of the mixup is also worse. But we only need to know the payoffs if we're deciding between two different mixups, and that decision is pretty easy: The best mid is whichever safe one does the most damage, and the best low is whichever one does the most damage.
Now that we know we do the low about twice as much as the mid, we can figure out how often we need to step block to deal with the mid challenges.
Payoff on ssr,b vs ws2 is better than other options because of chance that P1 reacts and whiff punishes with u/f+4 instead.
| b | d | ws2 | ws4 | ws1 | |
|---|---|---|---|---|---|
| f,F+4 | -2 | 75 | -75 | -26 | -74 |
| f,db+4 | 19 | -22 | -75 | -26 | -74 |
| ssr,b | 0 | 0 | 35 | 29 | 29 |
The first thing to figure out is which of these challenges, if any, is dominant. We can discard ws4 right away since the payoff on hit is much worse. And since ws1 is safer than ws2, we can discard ws2.
From there, we can reduce the 3x3 matrix to a 2x2 if we know the payoff of the original mixup. To get that, we need to know what the defender's strategy is too. The calculation is the same, but using the payoff of the columns instead. So, for example, b is done (75+22)/(75+2+19+22) of the time, or about 4 in 5. So the payoff for f,F+4 is about 45*(-2) + 15*(75) ≈ 13.
| Block | ws1 | |
|---|---|---|
| Mixup | 13 | -74 |
| ssr,b | 0 | 29 |
With this we can determine how often to use ssr,b by dividing the payoffs of the mixup by the total of all the payoffs. That's (13+74)/(13+74+29), or about 3 in 4. So we only go for a mixup about 1 in 4 times, and in that mixup we go low 2 in 3 times.
If this seems a little outrageous too, that's because it kind of is. Slow mixups are dangerous, and lacking any faster moves in our strategy means we need to use movement much more than we do in a complete strategy. But it's also not entirely ridiculous. Movement is really strong as long as your whiff punishment is on point.
Beyond this point, quickly estimating the optimal strategies doesn't really cut it. The estimations are already off by a decent amount.
Unsafe strings
The same process of reducing a 2x2 to a single option is done to estimate that ssr,b vs ssr~2,1 has a payoff of 8 damage. This is a typical situation where the blocked hit (SS.2) is punishable but a punisher can be interrupted by finishing the string.
| SS.2,1 | b | |
|---|---|---|
| 1,1,2 | -67 | 29 |
| b | 37 | 2 |
Determine how often AK does SS.2,1 by dividing the payoffs against b by the total payoffs. That's (29+2)/(67+29+37+2)[1] or about 3 in 14. So the payoff for 1,1,2 is about 3/14*(-67) + 11/14*(29) ≈ -14 + 22 ≈ 8. We're off by a bit (real payoff is 1207/131 ≈ 9.21), but it's close enough.
Optimizing a calculated strategy
With a well-defined payoff table, we can compute the optimal strategy and look for weaknesses. So starting with where we were at earlier.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | |
|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 |
Nash equilibrium with payoff 1.62
- f,f~f+4
- 0.1
- ssr,b
- 0.43
- df+1
- 0.07
- d+3+4
- 0.3
- df
- 0.09
- b
- 0.46
- d
- 0.17
- ws1
- 0.11
- FC.d+4
- 0.2
- ssr~2,1
- 0.06
Payoff for dominated options
- f,f,db+4
- -5.18
- ws2
- -9.1
- ws4
- -9.22
- FC.d+1
- -6.03
One weakness in Kazumi's strategy is that f,f~f+4 is used but f,f,db+4 isn't. So there's no mixup on the slow moves and Armor King could improve his strategy by adding a fuzzy guard.
And one weakness in Armor King's strategy is that he isn't using any of his fastest challenges. The fastest challenge he's doing is FC.d+4. So Kazumi could improve her strategy by adding df+4, which has a better payoff on hit than df+1 and beats ssr.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | d,b | b,d | |
|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -22 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -22 | 6 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 | 0 | 0 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 |
Nash equilibrium with payoff 1.85
- f,f~f+4
- 0.04
- f,f,db+4
- 0.08
- ssr,b
- 0.51
- df+1
- 0.08
- d+3+4
- 0.09
- df
- 0.11
- df+4
- 0.09
- b
- 0.62
- d
- 0.14
- ws2
- 0.05
- ws1
- 0.04
- FC.d+4
- 0.11
- ssr~2,1
- 0.04
- d,b
- 0.02
Payoff for dominated options
- ws4
- -6.57
- FC.d+1
- -5.77
- b,d
- -1.85
Now we could note that ws4 isn't being used at all. The initial reason we went with ssr instead of ssl was that ws4 beats ssl, but if that's not being used then it's a strong option. Counter-intuitively, the fact that ssl loses to ws4 actually makes it stronger in one way: because the only moves we're stepping with ssl are ws1 and ws2, we can commit to whiff punish with u/f+4 instead of 1,1,2.
Payoff of ssl based on commitment to whiff punish with u/f+4 as it loses to ws4 anyway and other options have slower recovery. As with 1,1,2 whiff punishment, reacting to a dickjab whiff is still necessary.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | d,b | b,d | |
|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -22 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -22 | 6 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 | 0 | 0 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 |
Nash equilibrium with payoff 2.02
- f,f~f+4
- 0.05
- f,f,db+4
- 0.09
- ssr,b
- 0.42
- df+1
- 0.08
- d+3+4
- 0.09
- df
- 0.12
- df+4
- 0.09
- ssl
- 0.07
- b
- 0.61
- d
- 0.13
- ws2
- 0.03
- ws4
- 0.04
- ws1
- 0.03
- FC.d+4
- 0.12
- ssr~2,1
- 0.02
- d,b
- 0.02
Payoff for dominated options
- FC.d+1
- -5.9
- b,d
- -2.02
At this point it's worth revisiting Armor King's movement options. While ssr~2,1 looked good initially, it's lost its lustre a bit now that we've included or modified so many options besides df+1 that beat it incidentally, so it's probably worth considering a step block now instead.
Ideally, ssr,b would step df+1 and block df+4 with the same option. However, being the defender this is a much harder task, because the defender's timing depends on the opponent's blockstun. To step block effectively, Armor King must be familiar with the timing of Kazumi's db+3 hitstun, making it a matchup specific technique. On the other hand, Kazumi only needs to be familiar with the recovery of her own move. So the payoff of those outcomes is heavily dependent on the player in question.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | d,b | b,d | ssr,b | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 | -2 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -22 | 19 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 | 0 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 | -3 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -22 | 6 | 6 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 | 0 | 0 | 0 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 | 3 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 | 0 |
Nash equilibrium with payoff 2.02
- f,f~f+4
- 0.05
- f,f,db+4
- 0.09
- ssr,b
- 0.42
- df+1
- 0.08
- d+3+4
- 0.09
- df
- 0.12
- df+4
- 0.09
- ssl
- 0.07
- b
- 0.61
- d
- 0.13
- ws2
- 0.03
- ws4
- 0.04
- ws1
- 0.03
- FC.d+4
- 0.12
- ssr~2,1
- 0.02
- d,b
- 0.02
Payoff for dominated options
- FC.d+1
- -5.9
- b,d
- -2.02
- ssr,b
- -2.15
Whether or not ssr,b is even a credible strategy here depends entirely on the payoffs vs df+1, df+4, and d+3+4. The latter is done often, and stepping into low parry isn't a viable option (you either don't get the parry or don't step the df+1). A whiffed df+1 can't really be punished on reaction, but it's still a good frame advantage. A blocked df+4 is a decent frame advantage, but with the pushback it's hard to get much out of it. Messing up the step block even 1 every 5 times is enough to make the payoff there in P1's favor. Given that the execution required to make it work is a bit much, and even then it doesn't improve things significantly, we're just gonna drop it.
Another thing that could be tried is f,hcf+1 (Giant Swing) and FC.db,d,db+1+2 (Pile Driver). The Giant Swing is i10, so it'll interrupt all of our mid options. Pretty scary! But the trouble with this is that both of our steps are going to punish it, and the step left being committed to a hopkick is going to punish it super hard. (It's convenient we're doing a committed sidestep left instead of a step block, because a step block left gets hit by the giant swing sometimes.) Moreover, although the Giant Swing is i10, the Pile Driver is i12, so if df+1 is interrupted by a throw there's no mixup on the break. So the only options this beats are df+4 and the big mixup. But those options are only done about 1 in 4 times, and against the other options the throws lose pretty hard.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | d,b | b,d | f,hcf+1 | FC.db,d,db+1+2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 | -25 | -25 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -22 | -25 | -25 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 | 29 | 29 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 | 0 | 12 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -22 | 6 | 7 | 6 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 | 0 | 0 | 37 | 37 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 | -25 | -25 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 | 62 | 62 |
Nash equilibrium with payoff 2.02
- f,f~f+4
- 0.05
- f,f,db+4
- 0.09
- ssr,b
- 0.42
- df+1
- 0.08
- d+3+4
- 0.09
- df
- 0.12
- df+4
- 0.09
- ssl
- 0.07
- b
- 0.61
- d
- 0.13
- ws2
- 0.03
- ws4
- 0.04
- ws1
- 0.03
- FC.d+4
- 0.12
- ssr~2,1
- 0.02
- d,b
- 0.02
Payoff for dominated options
- FC.d+1
- -5.9
- b,d
- -2.02
- f,hcf+1
- -15.94
- FC.db,d,db+1+2
- -16.78
So that's no good. Perhaps FC.df+2 is a good try? It'll launch our slow mixup, and it's safe against ssr,b.
Payoff of df vs FC.df+2 assumes P1 can react in time to block most of the time, but sometimes gets hit.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | d,b | b,d | FC.df+2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 | -82 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -22 | -82 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 | 1 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 | 14 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -22 | 6 | 7 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 | 0 | 0 | -20 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 | 17 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 | 62 |
Nash equilibrium with payoff 1.73
- f,f~f+4
- 0.03
- f,f,db+4
- 0.06
- ssr,b
- 0.39
- df+1
- 0.09
- d+3+4
- 0.14
- df
- 0.06
- df+4
- 0.15
- ssl
- 0.08
- b
- 0.61
- d
- 0.14
- ws2
- 0.02
- ws4
- 0.06
- FC.d+4
- 0.09
- ssr~2,1
- 0.02
- d,b
- 0.02
- FC.df+2
- 0.04
Payoff for dominated options
- ws1
- -10.85
- FC.d+1
- -2.81
- b,d
- -1.73
Surprisingly effective, even if we're generous with our ability to block it when going for a low parry. It's almost a straight upgrade over ws1 since despite being slower it's actually safer.
It might be worth revisiting the low parry options, now. For df, this would be better off as a fuzzy, since there aren't any slow lows to worry about. For Armor King it's a bit trickier, because if we turned d into df it'd now lose to f,f,db+4. But turning d,b into df,b and b,d into b,df is almost a strict upgrade.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | df,b | b,df | FC.df+2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 | -82 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -55 | -82 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 | 1 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 | 14 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -55 | 6 | 7 |
| df | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 0 | 0 | 0 | -20 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 | 17 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 | 62 |
Nash equilibrium with payoff 1.14
- f,f~f+4
- 0.05
- f,f,db+4
- 0.05
- ssr,b
- 0.42
- df+1
- 0.1
- d+3+4
- 0.07
- df
- 0.06
- df+4
- 0.16
- ssl
- 0.09
- b
- 0.62
- ws2
- 0.01
- ws4
- 0.05
- FC.d+4
- 0.07
- ssr~2,1
- 0.01
- df,b
- 0.08
- b,df
- 0.11
- FC.df+2
- 0.04
Payoff for dominated options
- d
- -5.1
- ws1
- -11.09
- FC.d+1
- -2.62
Now that's a dramatic shift. Low parries and fuzzy guards are pretty crazy. But they aren't without a weakness.
Dealing with fuzzy guard low parry requires us to exploit the fact that there's going to be some time where it's vulnerable. You can't go from df to b in an instant. But right now we're not getting inside that timing. So let's take our big mixup and put a non-delayed version back in.
Payoff for non-delayed big mixup against low parry fuzzy guards assumes that P1 gets inside the fuzzy about half the time, and that it's otherwise a toss up. For b,d/f this means getting hit by the low 3 times every time it gets a parry, and getting hit by the mid half the time. For d/f,b this means getting hit by both options 3 in 4 times.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | df,b | b,df | FC.df+2 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 | -82 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -55 | -82 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 | 1 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 | 14 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -55 | 6 | 7 |
| df,b | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 8 | 0 | 0 | 1 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 | 17 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 | 62 |
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | -75 | 57 | 32 | 79 |
| db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 22 | 2 | 2 | 22 |
Nash equilibrium with payoff 2.04
- f,f~f+4
- 0.03
- ssr,b
- 0.46
- df+1
- 0.1
- d+3+4
- 0.02
- df,b
- 0.12
- df+4
- 0.1
- ssl
- 0.06
- db+4
- 0.11
- b
- 0.62
- d
- 0.14
- ws2
- 0.03
- ws4
- 0.04
- ws1
- 0.03
- FC.d+4
- 0.12
- ssr~2,1
- 0.02
- df,b
- 0.01
Payoff for dominated options
- f,f,db+4
- 1.91
- f,F+4
- 0.34
- FC.d+1
- -6.01
- b,df
- -2.19
- FC.df+2
- -8.05
Now that that's dealt with the fuzzy parries, we need to bring the regular fuzzy guard back.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | df,b | b,df | FC.df+2 | d,b | b,d | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 | -82 | -2 | 75 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -55 | -82 | 19 | -22 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 | 1 | 0 | 0 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 | 14 | 12 | 0 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -55 | 6 | 7 | -22 | 6 |
| df,b | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 8 | 0 | 0 | 1 | 0 | 0 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 | 17 | 17 | -1 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 | 62 | 0 | 0 |
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | -75 | 57 | 32 | 79 | -2 | 75 |
| db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 22 | 2 | 2 | 22 | 19 | -22 |
Nash equilibrium with payoff 1.86
- f,f,db+4
- 0
- ssr,b
- 0.44
- df+1
- 0.05
- d+3+4
- 0.06
- df,b
- 0.13
- df+4
- 0.1
- ssl
- 0.08
- f,F+4
- 0.05
- db+4
- 0.09
- b
- 0.57
- ws2
- 0.02
- ws4
- 0.04
- ws1
- 0.05
- FC.d+4
- 0.13
- ssr~2,1
- 0.02
- df,b
- 0.07
- b,df
- 0.02
- b,d
- 0.09
Payoff for dominated options
- f,f~f+4
- -0.13
- d
- -2.55
- FC.d+1
- -6.75
- FC.df+2
- -14.06
- d,b
- -2.55
At this point, it's a bit suspicious that we aren't using the delayed mixup anymore. The reason is that that mixup is soft to step blocks, but P2 isn't doing any of those. So let's put those in.
| b | d | ws2 | ws4 | ws1 | FC.d+4 | FC.d+1 | ssr~2,1 | df,b | b,df | FC.df+2 | d,b | b,d | ssr,b | ssr,df | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| f,f~f+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | 15 | -2 | 75 | -82 | -2 | 75 | -2 | 75 |
| f,f,db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 12 | 19 | -55 | -82 | 19 | -22 | 19 | -55 |
| ssr,b | 0 | 0 | 35 | 29 | 29 | -11 | 5 | 8 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| df+1 | 0 | 12 | 14 | -12 | 14 | 14 | -8 | -75 | 12 | 0 | 14 | 12 | 0 | -3 | -3 |
| d+3+4 | 6 | -22 | 7 | 7 | 7 | 7 | 2 | 6 | -55 | 6 | 7 | -22 | 6 | 6 | 6 |
| df,b | 0 | 0 | -18 | -22 | -71 | 49 | 49 | 8 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| df+4 | -1 | 17 | -75 | -26 | 20 | 20 | -8 | 18 | 17 | -1 | 17 | 17 | -1 | 3 | 17 |
| ssl | 0 | 0 | 62 | -22 | 62 | -11 | 5 | 8 | 0 | 0 | 62 | 0 | 0 | 0 | 0 |
| f,F+4 | -2 | 75 | -75 | -26 | -74 | -13 | -8 | -75 | 57 | 32 | 79 | -2 | 75 | -60 | -60 |
| db+4 | 19 | -22 | -75 | -26 | -74 | -13 | -8 | 22 | 2 | 2 | 22 | 19 | -22 | 19 | -55 |
Nash equilibrium with payoff 1.57
- f,f~f+4
- 0.06
- f,f,db+4
- 0.03
- ssr,b
- 0.44
- df+1
- 0.1
- d+3+4
- 0.03
- df,b
- 0.11
- df+4
- 0.09
- ssl
- 0.07
- db+4
- 0.05
- b
- 0.64
- ws2
- 0.03
- ws4
- 0.04
- ws1
- 0.01
- FC.d+4
- 0.07
- ssr~2,1
- 0
- df,b
- 0.08
- FC.df+2
- 0.01
- ssr,df
- 0.12
Payoff for dominated options
- f,F+4
- -8.1
- d
- -4.99
- FC.d+1
- -5.52
- b,df
- -3.3
- d,b
- -3.54
- b,d
- -3.02
- ssr,b
- -1.62
With this, we aren't using f,F+4 but are using db+4. This might seem a little fake, but Armor King is a little overloaded on fuzzies by now.
We could keep going, but at this point the strategies are already far more complicated than any real player would use in practice.
Adapting
A key property of the optimal strategies is that they're arrived at by ensuring the opponent is indifferent to which options they choose, i.e. the payoff for all of their credible options is the same.
This poses a bit of trouble for someone expecting to get some advantage out of this. If you stubbornly stick to the intricate, optimal mixed-strategy to the letter, perfectly randomizing your choices based on the correct probability distribution, executing all of the precise step blocks and accurate whiff punishment... if you do all that and your opponent just does ws4 every time, the payoff doesn't change at all.
To get any improvement on the optimal strategy over a weak opponent, you have to change your strategy too. But you have to be careful. What you think is adaptation your opponent might think is conditioning. You want to adapt in a way that won't fall prey to an opponent merely playing dumb.
Identifying weaknesses
There are manys ways in which an opponent could be weak:
- They use non-credible options
- They can't execute a credible option
- They aren't aware of a credible option
- They overuse a credible option
- They underuse a credible option
In the first case, adapting isn't really necessary. An opponent using non-credible options gets a worse payoff without you changing anything. Non-credible strategies are typically weak to movement, which is probably what you're doing half the time anyway. In any case, identifying it is super easy—seeing it even once is enough.
The second is pretty easy to identify. If the opponent tries to sidestep and whiff punish a certain move but fails, or they step but don't punish at all, or they duck a high but don't punish it, it's pretty safe to assume that's not a trick to throw you off.
The third can be identified not just from a particular opponent but from your experience generally. A few rounds is often not enough information to confidently decide your opponent isn't aware of a certain option (unless it's a particularly dominant one). However, if you have prior information that opponents generally don't make use of an option in this situation, you can use that as a starting point. For example, it's my experience that very few players use FC.d+4 after db+3, even though it's a powerful option. If I notice an opponent hasn't used it at all after 4 or 5 times and that they've challenged with other buttons, I'd start assuming they aren't aware of it.
The fourth can be identified by seeing a credible but rare option get used more than once. For example, if an opponent uses ws4 twice after db+3 in a single round, that's strong evidence they're overusing it as an option.
The fifth can be identified by rarely seeing a dominant option or not seeing it at all. For example, if an opponent challenges a lot despite being at a disadvantage and thus rarely uses options like b or d, that's a good signal they're a bit mash heavy and underusing movement.
Punishing weaknesses
Robustly punishing weaknesses requires understanding why you're using the options you're using.
From there, it's a simple matter of taking the options your opponent overuses, and using the options that beat them more, and the options that lose to them less. If your opponent underuses something, do the opposite. This adaptation should be done gradually to avoid overcorrecting.
There's a tendency for people to use whatever beats the opponent's last choice, which suggests you ought to use whatever beats the thing that beats your last option. But then if you did that, the opponent could instead go to use whatever beats the thing that beats the thing that beats the thing you last did. But if they did that...
One must accept at a certain point that guessing is all that can be done, and that sometimes you'll guess wrong. Rather than try to fight this, to become a divine oracle with perfect reads, energy might be better directed towards something more tangible like improving your execution or the robustness of your strategy.
Something to avoid is using new options that aren't credible against a strong opponent. It builds bad habits. It's very tempting to go for a delayed hopkick because dammit this guy's spamming dickjabs, but is that really necessary when a low parry or step block would do the job just as well?
In the case of an opponent with lacking execution, this can just be treated as if the option is underused, but it can also change the nature of the situation entirely, particularly if the missing link is something dominant like a step block. Unlike other weaknesses, it's not likely this one is a trick, so there's less risk of being conditioned.
That said, all of this should be understood in the context of the limitations of this kind of analysis. In particular, high risk options are more credible the further behind someone is, and you can't disregard the value of hard reads entirely.
Footnotes
- ↑ In the proper calculation you actually subtract the 2 because that outcome is in P1's favour and the mixed strategy algorithm is more complicated than I'm letting on here. But the difference is negligible enough that worrying about the sign is more trouble that it's worth given that we're just estimating. The outcome where we might mess up the sign is when the mid is blocked or both players do nothing, i.e. when the outcome has low payoffs, so messing up the sign on it isn't a big deal.