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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]].

{{Mixup|Kazumi-db3-ak-1.gbt}}

Obviously this is really good for us, and our opponent isn't gonna play along. One strong option here is {{P2|ws2}}, which will [[counter hit]] launch both of our attacking options.

{{Mixup|Kazumi-db3-ak-2.gbt}}

Now this is terrible for us. He can do {{P2|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 {{P1|4}}. We could interrupt with a [[poke]] like {{P1|df+1}} or {{P1|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 {{P2|ws2}} for now we can safely go with u/f+4 for a launch.

{{Mixup|Kazumi-db3-ak-3.gbt}}

Now it looks good for us again, and our opponent needs to find an answer.

Instead of relying solely on {{P2|ws2}}, which has poor tracking, they could also use {{P2|ws4}} to challenge, which hits us doing ssl.

{{Mixup|Kazumi-db3-ak-4.gbt}}

This once again looks troublesome, because ws4 wins every time. But we can step right instead of left to deal with that. Since {{P2|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 {{P2|ws2}} is a big enough whiff to use u/f+4, {{P2|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.

{{Mixup|Kazumi-db3-ak-5.gbt}}

Now {{P1|ssr}} is dominating. One thing {{P2|Armor King}} can try here is {{P2|ws1}}, which beats {{P1|ssr}} and is also fast enough to interrupt the original mixup.

{{Mixup|Kazumi-db3-ak-6.gbt}}

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 {{P2|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.

{{Mixup|Kazumi-db3-ak-7.gbt}}

Now {{P1|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 {{P1|ssr,b}} and then otherwise go for the big mixup.

If they're aware of it, however, {{P2|FC.d+4}} is an option that poses a lot of trouble.

{{Mixup|Kazumi-db3-ak-8.gbt}}

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 guard]]s.

{{Mixup|Kazumi-db3-ak-9.gbt}}

Things are looking good again. {{P2|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.

{{Mixup|Kazumi-db3-ak-10.gbt}}

With the dickjab added, we really do need to duck. A [[low parry]] can punish it and {{P2|FC.d+4}} with a big enough payoff to justify exposing ourselves to the mid options more.

{{Mixup|Kazumi-db3-ak-11.gbt}}

At this point things are looking grim for {{P2|Armor King}}. The only options that beat {{P1|df+1}} are {{P2|FC.d+1}} and {{P2|ws4}}, and if he were to stick to using those exclusively we could change up our {{P1|ssr,b}} whiff punishment strategy to use d/f+1,2 instead, punishing the dickjab harder.

One ray of hope for him is that {{P1|df+1}} is weak to ssr, so if he's on P2 he could replace {{P2|b}} with a step right. Not only does this make {{P1|df+1}} a lot scarier to use, it also causes trouble for the original mixup's {{P1|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. {{P2|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 {{P2|b}} with it entirely.

{{Mixup|Kazumi-db3-ak-12.gbt}}

To deal with {{P2|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 {{P2|ssr~2,1}} done on a timing to match.

{{Mixup|Kazumi-db3-ak-13.gbt}}

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 {{P2|Armor King}} tried to [[low parry]] instead of a simple crouching [[guard]], it's a bit awkward since {{P1|d+3+4}} is much faster than {{P1|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, {{P2|ws2}} is too risky, and we don't need to be that scared of it, or that the {{P1|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 {{P1|f,F+4}} and {{P1|db+4}}, how often should each be used?

{{Mixup|Kazumi-db3-ak-1.gbt}}

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, {{P1|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.

{{Mixup|Kazumi-db3-ak-7.gbt}}

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, {{P2|b}} is done (75+22)/(75+2+19+22) of the time, or about 4 in 5. So the payoff for {{P1|f,F+4}} is about 45*(-2) + 15*(75) ≈ 13.

{{Mixup|Kazumi-db3-ak-7a.gbt}}

With this we can determine how often to use {{P1|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 {{P1|ssr,b}} vs {{P2|ssr~2,1}} has a payoff of 8 damage. This is a typical situation where the blocked hit ({{P2|SS.2}}) is punishable but a punisher can be interrupted by finishing the string.

{{Mixup|AK-ss2-ob.gt}}

Determine how often AK does {{P2|SS.2,1}} by dividing the payoffs against {{P2|b}} by the total payoffs. That's (29+2)/(67+29+37+2)<ref>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.</ref> or about 3 in 14. So the payoff for {{P1|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.

{{Mixup|Kazumi-db3-ak-13a.gbt}}

One weakness in {{P1|Kazumi}}'s strategy is that {{P1|f,f~f+4}} is used but {{P1|f,f,db+4}} isn't. So there's no mixup on the slow moves and {{P2|Armor King}} could improve his strategy by adding a [[fuzzy guard]].

And one weakness in {{P2|Armor King}}'s strategy is that he isn't using any of his fastest challenges. The fastest challenge he's doing is {{P2|FC.d+4}}. So {{P1|Kazumi}} could improve her strategy by adding {{P1|df+4}}, which has a better payoff on hit than {{P1|df+1}} and beats {{P2|ssr}}.

{{Mixup|Kazumi-db3-ak-14.gbt}}

Now we could note that {{P2|ws4}} isn't being used at all. The initial reason we went with {{P1|ssr}} instead of {{P1|ssl}} was that ws4 beats {{P1|ssl}}, but if that's not being used then it's a strong option. Counter-intuitively, the fact that {{P1|ssl}} ''loses'' to {{P2|ws4}} actually makes it stronger in one way: because the only moves we're stepping with {{P1|ssl}} are {{P2|ws1}} and {{P2|ws2}}, we can commit to whiff punish with u/f+4 instead of 1,1,2.

{{Mixup|Kazumi-db3-ak-15.gbt}}

At this point it's worth revisiting {{P2|Armor King}}'s movement options. While {{P2|ssr~2,1}} looked good initially, it's lost its lustre a bit now that we've included or modified so many options besides {{P1|df+1}} that beat it incidentally, so it's probably worth considering a step block now instead.

Ideally, {{P2|ssr,b}} would step {{P1|df+1}} and block {{P1|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, {{P2|Armor King}} must be familiar with the timing of Kazumi's db+3 hitstun, making it a matchup specific technique. On the other hand, {{P1|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.

{{Mixup|Kazumi-db3-ak-16.gbt}}

Whether or not {{P2|ssr,b}} is even a credible strategy here depends entirely on the payoffs vs {{P1|df+1}}, {{P1|df+4}}, and {{P1|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 {{P1|df+1}}). A whiffed {{P1|df+1}} can't really be punished on reaction, but it's still a good [[frame advantage]]. A blocked {{P1|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 {{P2|f,hcf+1}} (Giant Swing) and {{P2|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 {{P1|df+1}} is interrupted by a throw there's no mixup on the break. So the only options this beats are {{P1|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.

{{Mixup|Kazumi-db3-ak-16a.gbt}}

So that's no good. Perhaps {{P2|FC.df+2}} is a good try? It'll launch our slow mixup, and it's safe against {{P1|ssr,b}}.

{{Mixup|Kazumi-db3-ak-16b.gbt}}

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 {{P2|ws1}} since despite being slower it's actually safer.

It might be worth revisiting the low parry options, now. For {{P1|df}}, this would be better off as a fuzzy, since there aren't any slow lows to worry about. For {{P2|Armor King}} it's a bit trickier, because if we turned {{P2|d}} into {{P2|df}} it'd now lose to {{P1|f,f,db+4}}. But turning {{P2|d,b}} into {{P2|df,b}} and {{P2|b,d}} into {{P2|b,df}} is almost a strict upgrade.

{{Mixup|Kazumi-db3-ak-17.gbt}}

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.

{{Mixup|Kazumi-db3-ak-18.gbt}}

Now that that's dealt with the fuzzy parries, we need to bring the regular fuzzy guard back.

{{Mixup|Kazumi-db3-ak-19.gbt}}

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.

{{Mixup|Kazumi-db3-ak-20.gbt}}

With this, we aren't using {{P1|f,F+4}} but are using {{P1|db+4}}. This might seem a little fake, but {{P2|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 {{P2|FC.d+4}} after {{P1|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 {{P2|ws4}} twice after {{P1|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 {{P2|b}} or {{P2|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.

[[File:wifom.jpg|thumb|250px|But it's so simple! All I have to do is divine from what I know of you... Are you the sort of man who would do three hellsweeps in a row, or only two?]]

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 [[Template:Mixup#Limitations|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 ==

<references/>