FE Heroes: Lynja team class vs Emblem Ike

Lynjas. Or the duo unit Ninja Lyn. She has been my favourite unit in clearing stuffs and apparently it has attracted some interests among friends and servers. Why am I using her and how do I use her in clearing stages? I decided to start posting my Lynja solutions to GHB/LHB maps to my Youtube channel and this blog post serves as an introduction.

FE Heroes has entered the stage where any PVE content is essentially trivial for any veteran players with deep enough bench. The only challenges they can post are the Grand/Legendary Hero Battles(GHB/LHBs) with the newest units but inflated with all the disgusting mobs around. Yet players find it easy to clear even just with the most F2P units -- just those free units from stories.

To some it's easier to crush the stage with their newest toys. They can always create synergies that attacks the weakness of those challenging stages. Some players however, sticks to the same team over and over again and makes dazzling clears. Some heavily invests onto a single unit and perform turn 1 or true solo clears but I don't have units like that. Additionally given how quick the meta shifts, I hardly see the same unit true-soloing GHB/LHBs for an extended period. So like many others, I tried to clear the stages using the same team/idea over and over again.

In the early years, I used refined Celica plus 3 dancers. The idea is clear: fury Celica enters desperation and WoM range so that she can consecutively be danced. Savage on C to ensure chipping and AoE special if further chipping is needed.

Problem eventually arises though: you can only kill 4 units in a turn, often less than that in turn 1 because you need positioning. But there are 6 enemies at start and 3 extra every turn, meaning that you will be dealing with 4-5 enemies (including the 'boss unit' most likely). Maneuvering is hard when the dancers plus Celica are all vulnerable. At first dancers can tank a single hit with triangle adapt and stacked def/res, but that very soon failed due to inflated stats and passives.

Another problem is the need for diversified roles. To become an WoM anchor you need fury on A and possibly on S. But then you lose 2 slots to strengthen the unit. In order to chip, savage blow on C (and S) is used, or even an AoE special. But you could have used joint hone/drive otherwise. Finally there are vantage units forcing the use on hardy on S! There are so many desirable passives to use, many deemed essential. Celica eventually got overwhelmed and become impractical of clearing these stages.

It is clear that better action economy and diversified roles are needed in the team, and Lynja is the perfect solution with her duo skills. Adaptive damage, CD-1, post battle stat penalties and rein is so good when it comes to the need in firepower. But what's better than 4 Lynjas? 3 Lynjas plus a dancer. Dancer is more flexible as it allows extra action without needing to attack first which helps a lot on turn 1. With so many new game breaking dancers available now it's hard to say who's the best, but my choice has been the same -- duo peony as she has the duo skill that gives one further action, meaning that the maximum action in a turn is 8 with merely 4 units!

Here is the team:

1) Fury Lynja

Fury 4/Desperation/Savage Blow/Reposition

Speical is flexible (damage-type special or AoE)

S: Fury/Savage Blow/...

-HP with no merges or flowers would yield 36HP that fury 4 twice (instead of fury 7) is enough for her to enter WoM range. You don't want her to attack 3 times on turn 1 -- that makes retreating very hard.

2) Lynja2

Base kit + WoM + Repo + Hardy

Special is flexible but I used Lethality

Just in case there are vantage units but can be morphed into another nuker.

3) Lynja3

Base kit + WoM + Repo + Blade Session

Special is flexible but I used Blue flame (for diversity)

This is usually the unit that delivers the heaviest blow.

4) D!Peony

Base kit + WoM

C usually joint drive atk, S usually drive atk but both flexible

Pure support unit, support with Lynja gives free stat.

Notice that I have not fully optimize the kit. Most investments are cheap except the units themselves. I am sure they will be much stronger with better A and C skills! Other than Lynjas, Ninjorrin and Ninja Laegjarn would fit similar roles albeit not able to fly.

The team did well even in AR-O before save tanks becoming too tough, but for GHB/LHBs they should clear pretty easily. I also use the team to clear most chain battles. The key has always been positioning both in turn 1 and later turns, but I can't really exhaust all positioning techniques in one go. It is just easier for me to demonstrate them bit by bit in the videos. Below is my first in the series -- against Emblem Ike which is the toughest in a long time. Ike made a grave mistake: he became arrogant and didn't bring a healer. As a result multiple savage blow and AoE chipping put him down. This is a typical approach towards omnitank just like the maps against legendary Alears. I hope you enjoy the walkthrough and find it useful!

FE Heroes theoretical Grand Conquest gameplay(?)

Rare sight of an uncontested knocked out area. Third round grand conquest is always a wild one.

It has been while since I wrote anything about FE Heroes as I have no interest in covering metas and crying about how many times I ended up with 20798 lifts in Aether Raids. The most recent one was about voting gauntlet written in 2021 but just like the last AHR we had, people just don't care as much anymore. So today let's look at another mode where theoretical behavior differs so much from reality.

Grand conquest.

In the past infernal difficulty is almost impossible with the warps. As time goes by, the difficulty goes up by including more inflated units into the pool. That however, does not take account into the facts that (1) old units are still there meaning that the average opponent strength is not inflating as quick and (2) recent units also enables more disgusting combos with such potential inflating faster than pure unit strength. As a result, those 'top difficulties' became much easier. Similar phenomenon happens in most PVE modes. Remember 10th Stratum in 2016, or Veronica as final boss in the first Tempest trial?

For inferal difficulty with warps, my solution is to use units with multiple actions so that I can overwhelm a certain front constantly in a single turn so that opponent can't warp. Summer Edelgard, Lynja, Ninjorrin and many more disgusting units would do the job well as long as terrain allows early aggression. 

But I am not going into that in detail. My question is, how would grand conquest looks like in an ideal play? Here are the assumptions and simplifications:

Assume that players would score 2000 per sword consumed. Assume that teams consist of equal number of players who will play at all time and waste zero resources. WLOG assume that scores do not flow to neighboring area (because you can adjust number of times you participate in those areas to achieve the same score regardless) and ignore the 'help out' function because that help would be of negligible effect when everyone scores so much (that will be an interesting random perturbation under a perfect game from both though). Ignore also the mechanism that scores multiply with players participated in the area because I believe it's worthy to invest at least an epsilon in every area or otherwise opponent is always happy to take the free area. 

This is now the game where each player starts with K units of resources in the reserve (which do not recover, resembles the swords). In each turn the teams take turns to assign resources onto contested area (say, teams take turns to assign 1 unit every time). Each turn players can distribute at most N (= 4 x head count) plus arbitrary amount left in the reserve into those contested areas. At the end of each turn, area with opponent spending more onto it would have the ownership flipped. The score calculation would be the same as in FEH: summation of [area hold/5] plus area count at the end. 

How would the game look like then?

...the more I think about the possibilities the more complicated it could be like, that at a point I simply give up.

We simplify by thinking of a game of two players (maybe with 20 areas). At first it's of course the concept of choke points and defending the choke points, so you want to reduce the number of points that you are defending to increase the average resource that can be put in one area. You may also think of going into an equilibrium where it's not worthy to take any more lands except for the last turn, and the examination can go much longer.

However all these become useless with the extra resources K assigned to each team at the beginning because they can then breakthrough the defense with much higher firepower. This is now a game of distributing proper resources in each turn to balance between offence and defense.

Similar problems occur in real life, quite commonly actually. One practical example is to participate an auction with limited amount of money. Assuming that each participant has equal amount of money and each auctioned item has a fixed and transparent intrinsic value, how do you maximize profit in the auction? 

Going into these 'games' would be extremely complicated and far beyond what we want to discuss here, so I decided to cheat a bit.

What if teams are allowed to react against opponent's resource distribution bit by bit within the same turn? Say, when a team is to assign 1 unit of resource onto an area then the other team can assign 1 unit after the first assignment. 

Well then this will be a draw as long as the team with the second move replicates everything. Zermelo then tells us that since player has a forced draw strategy, there will be no winning strategy.

Everything is going well on a two player game as this is the classical setup. What about a three player game then? 

All classical tools broke down here and I have absolutely zero intention to head into an active research  field. But my guess is that it depends on the maps. In a two players game, the contested area is always symmetrical to both, hence the draw. In a three players game this is sometimes not the case, especially when two teams combined always overwhelm the third one.

We can generate perfectly symmetrical map (like the star graph if you like) where by symmetry will end up in a forced draw. There are also one-sided maps like three teams based in the three vertices of a V-shaped map where the two teams will simply squeeze the middle team to death.

There are configurations/states where forced draws will happen from there, which we call that an equilibrium. Equilibrium may occur with unequal scores like 9:10:11 or 5:9:16, as it depends on the contested areas only.

There will be maps with asymmetry that a team will start with negative maximum possible expectation, meaning that they are going to lose somewhere they had at the beginning. Since trading (between two teams) is a waste of resources, the team would cleanly lose that area and fight for an equilibrium afterwards. Similar strategy will be adopted by the team who are supposed to gain that piece of land who will quickly take that and go for the equilibrium from there. 

The last paragraph is surely the most shady argument/guess. One immediate question is: is it possible for an oscillation to happen? The answer is yes and obvious if you set K=0 and resources available to 3 (instead of 4) then by parity there will be exchange each turn. If we take cyclic states as an equilibrium as well, then I ultimate guess is that given enough rounds, all maps will end up in an equilibrium (a 2:14:14 in the V-shape map is also an equilibrium!).

***

I think I have my time wasted in writing all these because grand conquest will never be played in such an ideal/competitive way. It is still more fun to play the mode as it is, rather than giving the team a chatroom probably temporary discord server as well with players monitoring and reacting 44 hours nonstop.

FEH is really declining with less groundbreaking updates, lower reaction against new units due to saturated barracks, less votes in popularity contests like CYL and AHR, PVP modes completely scaring away most players and so on. I would still support the game till the end, but please give me a premium unit that is +10-worthy both in terms of art and competitiveness. Not now, but when I have enough orbs...

Thoughts on Three Hopes: a fast food game(?)

3 routes in 100 hours.

This is the third switch game that I played on screen via capture card and surprisingly all three are action games. It is almost miracalous that I didn't rage over the serious latency and even managed to clear the hidden boss in Neo TWEWY.

How is it possible to play games on a monitor with 300ms delay?

I got myself a new monitor this time and the difference is hell and heaven. Battles went much smoother...only then my Internet broke down that I have to fall back to pre-recording my gameplay videos which were then uploaded separately. You can find those videos here.

So how do I rate the game? Well in short, not exactly what I expected. This is the review from someone who had their first taste of the Warrior series.

It took me 47 hours to clear the Azure line on normal, then another 18 to clear Scarlet on hard. 35 hours on maddening, including many retries to S everything but I then realized 100% achievement is too hard for me so I stopped doing that at some point.

*spoiler below*

Plot

What did I expect in the demo review? Shez as a proxy on the opposite side of Sothis to find a solution between the two civilizations, and a solution between the three countries.

Is it the good end I have been looking for? Absolutely not. Does it make sense? Yes somehow. It turns out that Agarthans/Epimenedes/Arval is never supported by another alien entity that matches Sothis(at least Thinis didn't show up).

Without a matching opponent you won't expect the conflict to resolve without brutality. So either you killed Byleth (altogether with Sothis), or you recruited Byleth which could be a time bomb when Sothis threatened that she can takeover at anytime. 

On the other side, who can tell if in another thousand years the remanant at the underground would compose another plan of revenge? Even without central church and Rhea, anyone could well be the target as indicated from the shadow library as they hold the "blood of the beasts" regardless of the crests. Three Hopes basically made no attempt to iterate such conflict other than them being foes suddenly hop into the battlefield and become your final boss.

It is also kind of disappointing to see all three routes being extremely similar in structure both from the countries and the growth of Shez. The routes started with uprises in their respective countries (which coincidentally occurred at the same time), when things slowly get resolved they turn their eye into other countries or the church, and finally the TWSITD comes out as the final boss. The only difference is who's on your side and who's not (remember there are 4C2/2 = 3 ways to divide 4 items into 2 groups of 2). Dialogues are very similar if not identical (mainly those with Arval) and so as the plot which makes it in overall more repeated and less rich in content.

There are a hell lot that could potentially be covered should extra chapters be inserted. I would definitely love to see minimal developments in the academy. That would have slowed down the pace by a lot instead of "just joining the academy and the next moment you are on the battlefield". In a similar way chapters can be inserted along the solidification of the house leaders' power, and also at the end to discuss further the relation against TWSITD/the church (then again there was no church route here). 

Well I guess it's my expectation that is unrealistic in the first place...many details that I mentioned above were based on what we found in the shadow library which is DLC content after all. We didn't see super in-depth stories in Three Houses main routes either, but at least the routes in Three Houses explained the big pictures in full.

A smug and arrogant Byleth(/Sothis) is absolutely one of the things that shocked me the most.

Oh well.

While Three Hopes is so disappointing in its overall structure, I think IS did a great job writing stories around individual characters this time.

This time the story is not limited to the academy students (plus a few academy  staffs) anymore. We got the parents/relatives of the students and all the nobles of the countries. They were merely a random name mentioned in Three Houses, but here we can find loads of conversations between them and the students. From here it is much easier to hear from the  students talking beyond their academy/daily life. 

Most students got sections dedicated to themselves. They are no longer puppets under their respective House leaders. Instead they lead their own noble troops and act on behalf of their family interest. It is much easier to draw out their personality in that way. We thought Ferdinand is only someone who shout "von aegir" and Sylvain is a playboy, but in Three Houses their defend their countries like a true leader; we also observe interactions between students and their relatives like Hilda and his brother and Caspar/Felix and his father. All these arrangements allow us to understand the world in much different perspectives.

The Ashen wolves are no longer locked behind DLC and they join our troops for free. They are the characters that I liked to use the most because they are always recruitable unlike the other students (that you don't have to start from level 1 which is painful in higher difficulty -- how can you protect a lv15 Holst from enemies of lv120?). IS gave us a heavy dose of the wolves in the game. Though not appearing in main story conversations they get loads of paralogues not just only about the story of the wolves, but also with other students. It shows that the wolves are not just isolated weirdos, but students equally colorful as those in the other Houses.

And of course the lords. Even though the routes and outcomes are so similar, they clearly distinguished themselves from each other. The strong emperor Edelgard, the kind king Dimitri and the schemer Claude -- they really picked up their power and responsibility (cf. the Dimitri who wanted to kill the last one in Three Houses), and their characters are really well expressed.

If only they put more support conversations into the game...

Why do you do that IS...I want to use my lovely Sylvain in all three routes...

Mechanics

There are two main parts that composed the game, the overworld and the battles. Let us talk about the overworld first.

This is an adoption of Fire Emblem into the Warrior series, in particular mimicking Three Houses. It is easy to find many familiar systems from weapon ranks, classes to factilies are all heavy in Three Houses. 

They made a few changes from the Three Houses system like splitting training and activity points (plus the sucessive training system saves all the time to put characters into pairs), removing fishing (which took me 5+ hours in Three Houses no joking) and jotting down options that does not work in tea party (or else you check walkthroughs anyway). These are nice little adjustments to have.

The overworld map is also smaller this time. Loading the map is much faster than loading Garreg Mach. They distinguished different camp locations with flag colours and various backgrounds which is a nice little detail. Funny though the camp sometimes managed to have stone structures albeit being temporary(?).

Overworld netvigation now allows fast travel not only to locations but also to characters and functional NPCs. I also like the design of putting supply master at the bottom even it seems to be incidental (because it appears the last), but I indeed visit her the most and that saves time. 

Reducing repetitive overworld routines, fast nativigation plus (much) faster loading time really boosted gaming fluency. These are almost essential in an era where people always want to clear a game quick.

In terms of resource management Three Hopes is also quite close to Three Houses. You can barely upgrade the facilities to the max in the first playthrough if you gather every last bit of resource. There are quite some room for further upgrades via tactics instructor, levelling up or weapon forging but they are all locked behind a single currency -- gold. It eliminates further redundant currencies as all excessive materials in post-game can easily be exchanged into gold for these upgrades. 

The only game breaking non-NG+ mechanism is the meals (recall in Three Houses the effect of having meals is much more reasonable). Acclerating the warrior gauge really turns the game into spamming warrior specials. Also, Byleth mentioned in the support conversation that he/she does eat a lot. That explained how was it possible for him/her to have multiple meals with the students but now Shez is doing the same. (Another notable thing is that ingredients are quite rare in Three Houses but in Three Hopes you basically have 50 of each by doing nothing...)

Battles

Cutting opponents like weeds is definitely cool, but I found myself enjoying some characters/classes more than others.

The core idea is to aim accurately. It is quite hard to aim the opponents for some classes after some regular moves: pegasus in the air, cavalries after dashing, Yuri with his ring equipped...too much mobility is often a problem in actual fights. I found Yuri much easier to control without his ring actually, and I have to use specific combos for pegasus knights or cavalries to aim properly. For example Bow knights give an all round shooting with the combo XXXXXY which is far more better than the combo XXXXXXY, not only because the latter dashes which is so hard to use, the circling shot also breaks defense very efficiently.

Another consideration is attacking speed. While trying not to dodge (which slows you down and waste time) you always want to hit fast and break opponents' defense before they hit hard (which almost cost you the S rank in maddening). Dexterous classes are so much better in that sense. For example I found trickster much than mortal servants which swing their swords chop by chop. Gregmory is another class the casts so slow that I never thought of using those. Are they useless? Not really, just don't control them by yourself, they are doing well on their own.

The reason that you want to optimize your character so much is because your performance is almost solely decided by your technique instead of everything else including weapon ranks, skills, abilities, buffs...as long as you know how to fight and the weapon is minimally strengthened the maps are just as easy. This is hugely different from traditional Fire Emblem where resources are very carefully distributed and all the moves are catiously delivered.

Another problem with such design is that the difficulty curve becomes flat. Even at maddening, you don't find later chapters much harder than the earlier ones. In terms of one-on-one combats, dodging a soilder's attack is no different than doing the same against a swordmaster or mortal servant. The only difference is that you are in a much deeper trouble if you get hit by the later but as long as if you don't you will always be healthy, and this is quite easy to do so. In terms of general tactics early maps are as complex as the later ones, and reinforcements do not come more intensely in later maps anyway. This is a game of sweeping strongholds one by one...and it easily gets repetitive.

If we look at Dynasty Warriors, people are happy with the content even when the battles are more or less similar because those battles correspond to actual historic battles where contexts could be put into including who's appearing and saying what. You don't have that in Three Hopes. They tried to make some description to each of the auxiliary battles, but the contents are almost the same: sweeping bandits (or whatever opponents with no specific name) or battling beasts. It is very hard not to feel repetitive in that way. As I suggested above, expanding number of chapters would see such problem greatly repaired.

Artwork

Now you start to wonder after so bashing, how did the game ended with mostly positive feedback? Well, I have to say that the game looked very solid at the very least, and artwork is a crucial factor for that.

This is a job very well done.

They have updated the students' designs, and the designs fit them well at the age of around 19. The 3D models are so much better than those in Three Houses as you don't see pixels anymore. They also put a lot of effort in modelling each of the classes to make them look so different from each other. My favourite is of course trickers' finger gun when casting magic, especially when Yuri's wind magic actually one shots the armored units :)

Two comments on the design though: one is Shez's bright purple hair is a bit too unnatural -- I guess many have critized when the very first trailer came out already. Another is Dimitri's academy phase hairstyle in 3D...I guess it's easier to show here directly :/

The OST matches the high bar of that in Three Houses as well. My favourite is Melody of Clarity which is again the track for golder route final boss fight. Still I prefer the Three Houses ost just a slight tad more, perhaps just because how they mix the Fire Emblem melody into the credit song (A Star in the Morning Sky 2:40).

Rare to see Dimitri in academy phase but...

Conclusion

I can understand why the general reputation is so nice because it is inherited with what makes Three Houses success. It also delivered the other side of the game, the Warrior series properly. 

Many of my disappointment including mistreatment of stories, repetition and the lack of difficulty curve, occurring only from my second playthrough. Perhaps it is just my expectation that is unrealistic in the first place: the Warrior series is meant to be brainless chopping but not high precision action games, and the Three Houses story wasn't supposed to be that deep, with documents in the shadow library being no more than some teaser for those story maniacs.

In overall I had a mixed experience on the game...but others may have different opinions.

FEH VG predictor continued: wave pattern and early estimation

Building a model for VG is something that I wanted to do for a long time. In the previous article I wrote about the basics of a VG model and the article concluded with the chart below:

The perfect wave in the first 12 hours caught my eyes -- is that a coincidence or is that a general phenomenon? The aim of this article is to look into further patterns that help us to build the model. Before we start recall the terms that I used in the previous article -- please refer to the previous article for further details.

- Three examples all extracted from VG June 2021. Please refer to the previous article for further details. You can extract the raw data from the Japanese predictor made by @rammtiger_n. 

Example 1: Final (Popularity ratio >4)

Example 2: Quarterfinal 4 (Popularity ratio 1~2)

Example 3: Semifinal 2 (Popularity ratio close to 1)

- Parameter $k$: the parameter so that the accumulated score is of order $O(t^{2+k})$, or that the team's activity is of order $O(t^{1+k})$. To be more precise, for team i (i = 1,2) define $c_i(t)$ to be the constant factor which scales upon team size, and switch between three values according to the state of the hour, and $f_i(t)$ is the corresponding hour multiplier (which can either be $1.05+0.05t$ or $3.2+0.2t$). Ignoring intraday variation we assume that the team activity $A_i(t)$ is approximated by $c_i(t) f_i(t)^{1+k}$.

One should note that this parameter for the two teams are not necessarily the same, but they are close enough for most of the time. Let us assume that parameter $k$ is uniform across the two teams first.

*

The chart showed at the beginning is what happened in example 3. The curves are easily spotted because it is a perfect ping-pong where activity of the two teams are almost equal. At the same time when a team is in the excited state the other must be in the post-excitement state as it is exhausted due to bonus multiplier at the previous hour. As a result we find two perfect curves with alternating dots, one for the activity at excited state, another one for the activity at post-excitement state.

We do not have a perfect ping-pong most of the time, so are there any ways to extract such trend if it exists? One approach is to assign a factor to the three states: we may assume that the normalized activity in the excited state is 10 times the normal activity and 100 times of the post-excitement activity. Although we can explain this by the fact that flags comes in a multiplier of 100, such ratio is still affected by the parameter $k$, which we do not want to fix. 

There is a smarter way to get around this: observe that the state of the two teams are almost always excited + post-excitement or normal + normal. On rare occasions it could be normal + excited or normal + post-excitement but they always cancel out. Therefore we can simply take the (geometric) average of the (normalized) activity to retrieve the trend!

Mathematically, we first guessed that the parameter to be $k_0$. We then normalize the activity by considering $A_i(t)/(f_i(t))^{1+k_0}$. By taking the geometric mean we have that

$GM = (c_1(t)c_2(t))^{1/2}(f_1(t)f_2(t))^{(k-k_0)/2}$.

If we are either in the excited + post-excitement or normal + normal states, then $\sqrt{c_1(t)c_2(t)} = c_S$ is a constant. Since $f_1(t)f_2(t)$ is always $\Theta (t^2)$, we know that the geometric mean is constant (or regressed to be constant) if and only if $k=k_0$, i.e., if the estimated parameter $k_0$ meets the true parameter. We take log GM instead of GM to even out the impact of normal + excited states against normal + post-excitement states.

As a demonstration we calculate the log-geometric mean team activity for example 1 we get the following chart (with the guess of $k=1$):

We can see a downward trend starting from hour number 8, indicating that $k=1$ is an overestimate here. 

Again we retrieved the same early wavy pattern as in the first chart. It has a simple explanation: in FEH there are quests to clear. You need to clear these simple quests to get the (maximum number of) flags. The quests are mostly "clear VG with red/blue/green/colorless unit", but they require you to enter VG actually. On the other hand, you start the event with zero vote so you cannot do these quests right away. Most people do these quests with votes almost fully restored, which is exactly 4-8 hours into the event. 

Now we can estimate $k$ by removing the first 4 hours as outliers and search for $k_0$ such that the linear regression returns a zero slope. Since the regressed slope is strictly decreasing with $k_0$ we can always find such $k_0$.

If we apply that on example 1 we estimate $k$ to be 0.85: 

And if we apply that on example 2 we estimate $k$ to be 1.17:

The wavy pattern seems to be very consistent among all situations: we always observe two peaks, one at hour number 4 (which corresponds to 8 hours into the event since we removed the first four) and another one at hour number 12 (16 hours into the game). We may interpret these as the activity peak from players in different part of the world. Computationally the peak and troughs helps us greatly in the sense that we can do the same linear regression using the first two peaks and troughs, i.e., the data of the first 20 hours, and the result is highly correlated to the estimate using all 44 hours of data.

Example 1: $k$ estimated to be 0.8 with the data of hour number 5~20 vs 0.8 on global data

Example 2: $k$ estimated to be 0.92 with the data of hour number 5~20 vs 0.92 on global data

It seems that such estimation is always an underestimate due to (out-of-correlation) increased activity at the far end, but we can always add a little bit to our estimate. 

*

So, what can we do with the predictor now? This is a purposed way of creating a prediction:

- Use the early data to estimate the constant factor for teams' activity with $k_0=1$

- Predict by combining team activity and states guessing

- Analyze team composition by wave decomposition at hour number 20 and modify $c_i(t)$ accordingly

- Update $k_0$ by linear regression every time before iterating through the prediction after hour number 12 or 20

- ???

- Feathers!

As much as the above being a big and serious discussion, I still prefer participating the event in a simple way by guessing frequency of the bonus hours linearly. A 99% accurate predictor? Sure but no thanks if I am the one to write the codes. Not to mention that it is actually quite hard to measure the error in a dynamic system and we just can't tell in a mathematically rigorously way that how accurate our predictor could be...

You can find the raw data that I used here. 

The charts were not properly imported onto google drive, but you can plot them easily. Column L-N are time-normalized difference and bonus boundaries with $k=1$. Column T is the log-geometric mean of team activities. You can change $k$ as you like at W4 and W5, but the $k$ for the two teams are by default equal. The three labels are SF2, F and QF4 which correspond to examples 3, 1 and 2 respectively.

Some optimization on the FEH VG predictors

Voting Gauntlets in FEH is always controversial in many ways. In terms of outcome some hates to see popular characters always triumph over ordinary characters while the rest complains how the result is unpredictable and favors the chasing side by so much. In terms of reward some players are unhappy about the lack of rewards -- well actually 12 orbs is a lot, but the feathers are also very friendly to new players (and even me back in the days). In terms of difficulty, some found that playing with 3 random characters is quite fun, but some say they have terrible luck and facing 3 fallen Edgelord is bullshit.

But today I want to talk about mathematics and not the game mode itself. How can we predict the outcome given the first few/12/24 hours of data? Certainly there are a few attempts already: on Reddit there are a few predictors on the West and also one from Japan. I found that the interface of the Japan predictor is pretty nice, despite that the prediction is sometimes off. 

In the past I have talked about VG in the sense of a multiplayer game -- in the game theory sense, but this article is doing the complete opposite. We assume that the reaction is fixed under some unknown parameters, and the goal is to build a model out of that.

I do not plan to build a predictor by myself. It takes lots of time and does not benefit one so much ingame: in terms of ranks it makes no difference if the bonus hour shifts as everyone has the same bonus time. You can almost always get the highest reward by not missing the bonus hours in the last 20-24 hours, which can be done using VG bots. The prediction for the last few games where final result matters, can be predicted fairly accurately by most models anyway. 

The reason I wanted to write this is because there are a few things that I spotted that are relevant but they were not accounted in existing models, so it serves more as an investigation.

For starters, these are what you need to know: (FEH and negligible details are cropped, just to give a sufficient model here)

- Two teams undergo a head-to-head battle over 44 hours.

- Every player has a voting gauge which recovers by 1 vote per hour and is capped by 8. 

- Every player has 2000 flags which they can spend over the battles. One may spend a maximum of 100 flags per vote that they applied. With N flags applied the score is multiplied by N. For example if one spends 8 votes with 800 flags then the score is multiplied by 800. If no flags were spent the multiplier is 1 per vote.

- There are two multipliers: the normal multiplier starts from 1.1x and increase by 0.05x per hour. The bonus multiplier starts from 3.4x and increase by 0.2x per hour.

- The score is updated every hour. If a team is 1% more than the other, bonus multiplier will be triggered for the weaker team during the hour. 

- The team with higher score at the end wins.

Score normalization

First of all, we know that the score is not growing linearly and we need a way to normalize them for a time-invariant comparison. A clear choice would be the direct score ratio between the two teams. This is a very intuitive choice which also hooks with the bonus trigger, but the accumulated score certainly affects the velocity of this indicator over time.

Another choice is to divide the score by the multiplier, whether it's the ordinary or bonus multiplier does not matter too much because that is just a constant scaling (almost). The problem is that player's VG activity isn't constant either: higher multipliers are expected at the end so they prefer to spend flags towards the end. With flags around the score obtained by not spending flag is basically negligible. We need to capture when people spend flags.

With everything being non-linear it is so hard to decide the right exponent, so I decided to look at the accumulated score instead. It is natural to assume that players' activity is non-decreasing in general, then their points gained per hour, after enlarged by the linearly growing multiplier, is at least linear. As a result, the accumulated points are at least quadratic, i.e., $\Omega (t^2)$. 

Assume that the players' activity -- or the teams' activity as a whole, is of order $O(t^{1+k})$ then the accumulated score will be of order $O(t^{2+k})$. It is not hard to find that the accumulated score is indeed at the order $O(t^{2+k})$ for some small $k$ -- so let us just divide everything by $t^2$ before we look into the parameter $k$. 

Here are the two typical examples taken from VG 2021 June.

Example 1: VG final (F!Corrin vs Klein)

Example 2: VG quarterfinal 4

These are two typical matches in VG: example 1 is when the popularity of one clearly overwhelms the other, while example 2 happens when a team is of significantly higher popularly but not as extreme as example 1.

All the charts are time-normalized by $t^2$ where $t$ is the average of the two multipliers.

In the first chart, the orange and yellow line indicates the time-normalized boundary for bonus multipliers, while the blue line shows the normalized score difference. The second chart indicates the normalized score activity of the first team (a positive score difference means that the first team is leading). 

We expect the normalized player activity should be of order $O(t^{k-1})$, and from here we can estimate $k$. The spikes are when bonus multiplier happens.

We can see that the parameter $k$ clearly varies in different situation. We can assume that $k$ is close to 1 in example 1 while $k$ is clearly much smaller than 1 in example 2. In fact, $k=0.2$ is a pretty good estimate. The $k$ value can also be verified by checking the growth rate of the bonus boundary curve.

We can explain the correlation by how player anticipate the battle towards the end instead of casually spending their flags in the middle. Very interestingly the parameter $k$ seems to be independent of the ratio of player base size: the dominant a team is, the more bonus hours the opposite team will get. So in theory if the parameter is decided by the frequency of bonus hours, then the parameter for the two teams should be different, but that is not the case here. If we plot the activity of both teams on the same chart for example 1, we can see that the parameter for the two teams are more or less equal.

Calculating the parameter $k$ would be extremely helpful because we can then get a normalized data. (And we will cover that in the sequel of this article!)

The three states of players

With the above graph we see that the activity of the players divide into three categories, or three states that we call.

A team is in an excited state if it receives a long-waited bonus hour, or a bonus hours that shoots them to the leading position. The activity clearly spikes for this hour.

A team is in a post-excitement state if the bonus hour in excited state shoots them into leading position with bonus triggered on the opponent then the team enters the post-excitement state where activity is abnormally low because they run out of votes and flags.

A team is in a normal state otherwise. There are more fluctuation within this state depending on the score situation. 

We can plot the same for example 2 which is a lot more chaotic, but the activity is still clearly divided into the three states as described.

The pattern shows that most players aren't playing to optimize the chance to win as a team. Rushing to overtake the opponent early has little to no effect on the final result but looks good in a team sport, while the increased activity when a team enters bonus multiplier is natural as it maximizes score gain (for those who urgently need to spend flags).

I am actually quite surprised that this was not taken into account by most predictors, as it plays an important role at the end where people react to the hourly updated results vigorously. For example the JP predictor predicted a constant downward ping-pong at the end for example 1 (i.e., bonus for second team for 1 hour + no bonus for both teams for 1 hour alternately and these two together results in favor of the second team), but the reaction from the second team at hour 42 should be much more violent as it sends the team into leading position -- and of course the first team hit them back with 10x the power. This is the nature of VG predictor: players react to score but not team result.

Daily variation on player activity

Clearly players do not stay awake 24/7 for these shitty reward (well even if orbs are worth its monetary cost that is merely a burger meal, so it's not worth the time to stay awake overnight), so they stop playing when they are asleep. But people over the world situates in different time zone and they sleep over different time. More importantly, the taste from different part of the world seems to be different. As a result, we may observe higher activity from one team during daytime then higher activity from the other team during nighttime (which could then be daytime for that part of the world).

Assuming that the main division would be Japanese (or Asian) players vs the West, we can divide the players into 3 groups: time-invariant players, Asian players and Western players. We estimate the portion of the three and how supportive they are to each team. This is taken as a scaling factor when we predict the future outcomes. 

And how do we do that? Well this is simple linear algebra -- these three groups of players can be modelled into 3 kinds of waves: constant, sine and cosine waves, orthogonal to each other. We can then apply orthogonal projection to estimate the portion from each of the three. 

*

I really believe that the three factors together with what we already have around, builds a very accurate VG predictor, but surely no one would waste the time doing that.

To conclude this article let me show the graph plotted for the same VG but semifinal 2, which is ping-pong all the way. I stacked (apology for the poor stacking) the two graphs together so that you can observe the interaction more clearly. Since it's a perfect ping-pong first the first 20 hours or so, you can see that the activities alternates from excited and post-excitement states but not the normal state. Although the waving pattern in the first 20 hours which in fact, also occurred in the first two examples, seems to raise more questions from here...

(To be continued)

Acknowledgements: raw data extracted from the Japanese predictor by @rammtiger_n

On three houses (3): Cindered Shadows

DLC 4 is the last scheduled expansion of Three Houses and is also the largest expansion. A completely new side story alongside with new characters, quests and activities that provides further clues about the main story.

Having new characters and activities means you need to play side story plus a complete rundown in the main story to experience everything -- which is too much for a player who have already completed the game 5 times. Below are my thoughts after completing the side story with a taste of main story with the presence of the new contents.

Part I: on game mechanics

Part II: maddening and more

*spoilers alert*

Side story

Did it in hard classic and it does not disappoint me. Enemies have config slightly above the "main story" hard, but with limited resources (though not "lacking resources") and being inaccessible to auxiliary battles it could be pretty hard. The way the game works here is pretty close to that in classic Fire Emblem (like Blazing Blade), so as the difficulty.

The side story consists of 6 unique battles. Enemies are compactly packed that does not allow the slightest bit of excessive training.

I personally like the third battle the most -- the two possible routes gives flexibility on how you can play the stage. Actually I figured that it is the safest to use both of them.

The final boss is also interesting given its gimmicky special attack. I found however, the fight would still be possible without the post-AOE weakening. That would be a lot more interesting as well as pushing the difficulty up to the maddening bar.

Story-wise, there is not a lot that you can do in a 7 chapter span where the second half are all about consecutive battles. Someone data-mined that there will be 13 chapters and a more detailed stories can be delivered in such length.

With the introduction of Abyss, I expect them to focus on interaction among underground students and residents because those residents are reasons the student were there. But with 7 chapters only IS did enough to introduce the students. The interactions are left for support conversations, which are also nicely written.

New classes

Yes that is a great solution to what I pointed out before. The new classes aimed to provide full flexibility between magic accessibility and melee potential of the characters.

Dark fliers is the long awaited class, fliers that can use magic. Even with sacrificed growth the class completely worth it given how overpowered fliers can be in the game.

Valkyries seem to clash with holy/dark knight at the master class, but it bridges well between the mage class and the magic knight classes since the lance requirement is gone. It's range+1 also allows long range magic snipers other than Lorenz.

Tricksters and war monks are adjustments to melee-magical units without the problem of mortal servants where growth were split 50/50 that doesn't really work on characters that fit. These two classes are primarily for melee based (trickster for dex based and war monk for vit/def based) characters who also wants to use heal at times.

Trickster is also a bridge between sword users and mortal servants, if one trains reason and faith simultaneously. However this is really a class taylor made for Yuri with his growth distribution especially with his unique combat art, the foul play. In side story I would made him MVP as he and Edelgard combined are capable to take all physical attacks. And while Edelgard slashes back for 35 damage, Yuri simply goes for 15+45 critical...

In side story, the two magical units are very fragile due to its limited movement (compared to master classes), the abundance of stairs (for valkyries) and team composition that couldn't protect them well. The war monk is kind of balanced -- he can sweep but you do not want to put him up front too often. Yuri of course survives anywhere on the map.

If we are to use these classes in the main story with proper team setup, it is expected that dark fliers will be used as a final form. Valkyrie might be a bridge to magic knight but it may also be used as a final form if one wants to do long range snips. Trickster is probably reserved for Yuri or at most Felix. War monk...is still awkward for me.

New region and activities

That I do not have full experience of. But new area's new area. They fill the area with new NPCs and new dialogues that consolidates the story further and this is never a bad thing.

Scraps may be useful for maddening or players who really lack resources. Altar is useful for New Game+ players who wants to get specific item where they didn't get because they skipped some game elements, and that's also good.

The idea of mysterious teacher is nice although I still haven't got a full picture on how it works, but it looks interesting. And for the rest, I am probably won't have the time to explore since it will take me another 15-20 hours to go through the game again...

Cindered Shadows

4 new well-crafted characters and they fit well in Abyss.

Hapi the anti-social who disbeliefs the church. Constance a fallen noble with Schizophrenia. Balthus the bold, the gambler and the alcoholic. Though nothing too surprising you have got to say these settings do work.

And of course Yuri. As a house leader (kind of) he completes the weapon cycle among the leaders, and he also completes the personality quadrants among them. He is charismatic but disbeliefs in the church unlike Claude. His charm and wise fits with his trickster class, but what surrounds him does not give him free will after all. He is the classic Japanese RPG protagonist, and a fitting last piece to this Fire Emblem sequel.

I wish that the support between Yuri and Byleth(s) could have been more romantic -- Yuri can flirt Ingrid without backfiring (just look at Sylvain), but he seems to be so clueless against us...

Conclusion

So, what should I grade Fire Emblem Three Houses for now?

School system that attracts everyone except hardcore classic players. New class system that is pretty much complete upon DLC. Multiple difficulties that can be completed with or without extra battles. Up to 40 characters with thousands of support conversations.

...all in one game. This is Fire Emblem Three Houses.

I would give 7.8/10 after writing (1). But with DLC the game probably worths a score of 8.5/10. A masterpiece that is for everybody, whether you are hardcore SRPG player or not.

On Three Houses (2): Serious gameplay

Maddening accomplished, with NG of course. It took me about 100 hours, and the file shows 85 hours. That means I spent 15 hours retrying the courses. I took a very conservative approach both on the battlefield and in the academy exhausting all resources every step. I know I can go a lot faster but I didn't want to because I do not want to take the risk of retrying the whole game when I get stuck.

This, is my thought about the game from the perspective of maddening playthrough, the true difficulty for Fire Emblem fans.

- Story and plots - 

I chose Golden Deer this time as my final route for the game. It really is a "true end" to me -- not only that the story is complete, informative and less painful, the final fight is also a grand one -- that is the only final stage where you do not fight layer by layer but as a whole. You are also pressurized by the frontline enemies at turn one. The collaboration among the distant artillery units are terrifying. The boss is tiny yet hard to deal with. Not to mention the opera styled BGM -- everything is perfectly set to be the final fight.

After playing all four routes the overall plot is pretty clear. Crimson flower route need some further refine on its own, which will probably happen in update 3. The other routes are pretty complete.

Some may look for further information about the distant past...I hoped for the same but you know, these kind of supplement information is never enough. Perhaps they will publish a fanbook in the future?

- Team and formation - 

Due to limited resources I only recruited Doro, Sylvain, Mercedes and Ingrid this run. Doro became my dancer, Sylvain is a free recruit as well as a powerful axe wyvern (although everyone went to shoot arrows anyway), and Ingrid should be a dexterous falcon knight...except that her strength growth is horribly low in my run that she never became more than a chipping unit. Mercedes for her fortify, of course.

With the 4 recruits that completes my team of 12+1 for the final fight, where I usually drop Leonie because her dexterity never get to the point where she can steadily kill. For most battles in front where you can only use 10 units, the 3 lowest leveled units will follow the healers as adjuncts and absorb exp points from them.

I tried to exhaust the healing capabilities a bit. Marianne, Lys, Doro, Mercedes and even Lorenz and Byleth are overleveled due to constant healing. That also left the rest of the units enough opponents to kill. At the end, the mages are around level 60+, Lorenz and Byleth are around level 55, and the physical units are about the recommended level (42-44).

- Tactics - 

Everyone use bows and curved shots. Fliers may use close range weapons but really they just utilize curved bows and the canto ability to hit back and forth. In maddening you cannot really afford to go deep into the danger radius because everything doubles you, even with weapon breaker disadvantage.

But what hurts the most (other than Lys bomber) is the two 5-range units: Ignatz and Lorenz. Ignatz's hit+20 inherited skill allow us to build him in a super offensive way so that he can crit at will while still having a reliable accuracy even against assassins. Lorenz meanwhile, can fire up to 40-50 spells 5 grids away. This is perfect when you want to take down a particular unit in the opponent formation that will trigger the rest. 5 range attack also penetrates most walls so that allows you to do lots of unintended attacks.

In the Shamblala map, my team got stuck in the left-bottom corner when the 3 or 4 titans were trying to go through the gates. I stopped them by placing Raphael (but he still get critted twice for 15x2 at a crit rate of 15%) and ingrid up front, but these two are not good enough to handle 400 HP+ titans. What I did is to use curved shots to break a barrier on the titans, then Ignatz-Doro combo will produce 200+ damage on their own, every turn.

I did the same for Lorenz and even Marianne (as a holy knight), but Marianne is more like a magical tank - she easily take doubles with the white magic that heals upon damaging the opponent.

Lys and Byleth, can of course kill enemies at will, but I tend not to use them unless it's necessary. I enjoyed defeating the opponent without using these two too much. Although I defeated almost every non-generic characters by Lys (except for Nemesis), including Death Knights of course.

- Difficulty -

Maddening is for those who carve for a challenge -- the sentence accurately described the difficulty of maddening. It is challenging. It requires you to think and execute carefully every step, as well as hoping for reasonable luck in order to proceed.

Regardless of your endgame plans, the gameplay is similar for everyone at least in the first 6 chapters where you only have 1 battle points and very limited activity points. These chapters are really tricky and every reinforcement will catch you off guard.

I started to get frustrated on the second encounter with death knight. I used to finish the stage nice and slow but we have a 25 turn restriction this time. That forces you do be aggressive against opponents that are far stronger than you. Mages on avo floor is really a pain when your entire team missed hitting them. But this stage is also the time when Ignatz started to shine. His 4-range shots accurately clears the DK room and prevents the bloodleash.

After that everything changed because I know have 2 battle points. I started taking bandits after bandits, and finally I can clear the main quests in an easier way.

But not the reunion at dawn.

I didn't train Byleth seriously before time-skip, so that stage took me forever even with enough speed...It's Claude's gambit saved me, but I would be more pleased if he didn't take me out to do the battle with just 2 units.

In general, the exp mod forces you to really focus on units that barely forms a team. Further exp penalty causes most physical units to be of level similar to the recommened one, and at that level, fighting is really challenging due to hit rate and speed. It's more painful in the beginning because opponents having no specific classes means they are better than you all-roundedly. Later in the game the enemies are diversified meaning that you can kill them with proper tactics.

The two extra skills - pass and poison strike are good additionals to the difficulty. They require some extra thoughts to deal with in a reasonable way. Pass forces you to create compact formation retaining a correct distance from the opponent. It is less of a threat late in the game because you can utilize gambits and fliers to avoid having a solid frontline, so being able to pass do not create any harm. Poison strike on the other hand is still a threat late in the game, because that means you cannot tank infinitely many units by a single armor unit anymore. You will need to be careful when placing your tank by such.

- Mechanics in higher difficulty -

Looking back on what I said after playing normal and hard, it's time to review whether these comments hold anymore in maddening.

1) Weapon triangle: weapon breaker skills is essentially a weak weapon triangle, so weak to the point that does not affect your choice of weapons. Think about how you deal with those endgame physical units:

Sword - thieves and assassins. Due to their pass skills, you are forced to hold your line and kill them using multiple units. Lance units with swordbreaker may increase the accuracy a bit, but at close range mage and archers would work better.

Lance - well, where are all the cavalry units?

Axe - those are simply free kills. With enough dexterity most units are capable of dealing with them.

With everyone using their bows more than any other close range weapons, the discrepancies among the three weapons are weaker than ever.

2) Class meta: The class meta shifted further to distant attackers since you get doubled for every close combat, and dexterous units does not create enough damage (like my poor Ingrid). Ineffective classes remains ineffective, except for mage knights equipped with extra range tools. But for the rest like war master and dark mages...we just can't afford to choose those.

3) Maddening+: so...what should we expect in the fourth difficulty? There is no further news about this difficulty yet. Something looks like that appears in the fourth DLC but it's a side quest. Stat boosts on the enemy as well as the exp penalty is already harsh enough so that it's hard to expect further modification on this part.

Instead, changes should be made on the finest details -- so that players would optimizes themselves to the finest as well. These may include:
- a different AI that takes a mixed strategy between being stationary and aggressive, cares more on formation and harder to be baited
- restriction to physic and fortify uses
- reduce level cap to 50

After playing all 4 routes, I believe 50 is sufficient for everyone. We can modify the exp curve - lift the penalty below the recommended level and increase the penalty above the recommended level. By removing the unpenalized exp gain from dance and healing, the game become less grindy -- we can do less auxiliary battles and fish less (although Flayn would be sad), but you can utilize a team up to a certain level in the main quest without much effort. And that "certain level" is the intended strength of the team in which the developer wants you to clear the stage with.

But well, I am not going to do the highest difficulty if it ever comes out, with New Game. And not even New Game+, because it has taken too much time from me. I would rather play harvest moon in October. If I come back for Three Houses again, it is probably for Sauna, new stories and new characters...

- Elements missed -

I may not write anything further about the game (because it would have to be something related to the plots, but I am not ready to sort out the whole story. So I would like to conclude my review with a list of traditional FE elements that is missed in three houses:

- weapon triangle, of course.
- fixed but more diversified grow path
- advanced class with less movement restriction
- more talk options and ability to talk/recruit enemies
- villages and villagers
- pair up and rescue options
- ...

I know some of them does not fir into this game, but still I am hoping for something similar in the next franchise.

Thoughts on Fire Emblem Three Houses (1): core mechanics

I decided to use this picture so as not to post any endgame spoilers. But it seems like this picture is also kind of a spoiler...

Three Houses for FEH fans, of course. Clearly FEH gives great attention as well as financial support to the development of the game. Before even going into the game you can tell that the game is a sincere one. I had no choice but to start playing since July 26 and as a result I almost abandoned FEH, stopped daily bonus streak in neopets...but that's totally worth it. I am satisfied with the game, the first mainline FE franchise I played since the three GBA-era games.

I finished 3 of the 4 routes and that takes me 145 hours -- 60 for the first route, 30 for the second route (that branched from the first halfway through), and 55 for the third route (via new game+). The first route is done in normal casual and that is really, really easy in FE standard. The third route done in hard classic is more of the expected normal difficulty, and is very fun to play.

Fire Emblem has evolved from a pure RPG-battle game into a game with huge amount of character interaction in various forms -- support system, academy, gifts and tea party and so on. The ~20 main quests should take a good FE player no more than 15 hours of gameplay, but the extra auxillary battles and the school exploration time takes a large portion of gameplay as well. If you skip everything and purely focus on numeric battles one can possibly finish the game in 25 hours, but that would be a huge waste because everything is well-designed to enrich the world of Three Houses.

And because of the vast amount of material that I can talk about the game I want to be kind of selective: I want to compare what I used to (old FE, FEH) and Three Houses since this is not covered in mainstream reviews (which is for everyone). Somewhere in the future I may also write something general about the game: plots, arts, characters and so on.

But before discussing any game mechanism, I want to stress that the importance of a certain mechanism is not absolute -- it depends on the difficulty of the game. The easier the game is, the larger flexibility players are given to not optimize things. In higher difficulties some mechanism may become crucial or even become the meta because if you do not do a certain action the rest of the game would be much more difficult. One example is having the glass cannon Lysithea in the game -- her unique set of black magic plus monster-effective white magic is such a nuke weapon in the game.

Similar argument simply applies to FEH as well. In arena we care about merges because it's the one or two points difference that determines the winner. I do not believe that -- I always believe that wise movements are more important except that characters with higher stats actually yield a higher score. Another example is the Legendary Hero Battles: in lower difficulty you can bring in your favourite team but for abyssal difficulty you have to either bring a well discussed meta team, an extremely specifically designed team on walkthrough, or something really spectacular to pass the stage. The over-inflated stats and skills leave basically no space for someone to experiment with.

The term flexibility sometimes does not only apply to strategical flexibility, but also flexibility in terms of space. The maps in three houses are in general very big comparing to the past. Not only that allows greater leniency for players to give commands, but that also lowers the difficulty quite a lot. (Think about the 2x3 hidden rooms in the final fights in blazing blade!) That accounts partially to why three houses is easy in FE standard.

But enough talking. Let's start with mechanism that are changed in three houses.

- Weapon triangle and class system -

The removal of the triangle is certainly a big change -- it lowers the complexity of matchup consideration so that the game is more accessible to new gamers. And of course, it allows characters to yield their favourite weapons, which is cool after all.

But for hardcore FE players, decision making became straightforward and less interesting because of the changes. The most significant change is that, the choice of weapon is now heavily dependent on the choice of the moving type.

Unlike 2-steps class system in the past, there are now 5 steps: "class-less" (commoner and noble), beginner (lv 5), intermediate (lv 10), advanced (lv 20) and master (lv 30). Since master classes the highest stat growth bonuses we shall assume characters are trained for at least one master class.

But that's where the problem is: the choice of weapon is then heavily relying on the moving type.

With the removal of the weapon triangle the melee weapons became more or less the same. We train a particular kind of melee weapon just because it suits the career path that we planned.

Just think about how we characterize the three weapons:

Sword: high crit, speed, pegasus or mortal servant
Lance: balanced, knight and fliers
Axe: high atk, armored or wyvern

But...without the triangle but with the master class restrictions, specializing in the right weapon seemed to be more important than what they are actually good at, because that is not going to make a great difference.

The only consideration is crit rate because the crit rate for swordmasters and snipers are terribly high so I have a tendency to push everyone to use sword, and those who are not compatible with sword will go into the lance path -- fliers or knights. And for axe? We don't need warriors and war masters thank you. There are a few characters that go well with armored knights, but they ended up using lances anyway because they received knight training anyway...

On the melee side weapons can be freely used given the proficiency rank, but this is another story on the magic side. There are only a few classes who can use magic even if units already learned such magic -- this is so weird. Are there anything stopping them from casting magic while wearing as a non-magician?

With such restriction naturally magicians really focus on magic and melee units should not bother about magic at all. Unfortunately master classes force you to do a mixed training. Just...why? Such requirement raises the difficulty of breeding a unit into master class and that seemed to contradict with the overall idea to make the game more accessible, or are they treat master classes as something not to be reached by new players? It's already hard enough to train a magical unit into holy/dark knight, but it's even harder to train a sword unit into mortal servant because their magic are of limited use even at the later stage. 8/8 fire plus 4/4 thoron means you can only train your reason rank 12 times before you have to go back to melee weapons.

I should also mention that the anima-holy-dark triangle is also gone. Given that dark and anima are merged into reason class anyway the removal is not very surprising. It's not even impactful because it is much less often that we have magical duels in three houses anyway. Just a small observation to put here.

- Non-infantry units -

There are three non-infantry movement types: armored, fliers and cavalries. There aren't many master classes available:

Cavalry: Bow/holy/dark knight, (great knight)
Armored: Great knight
Flier: Pegasus, Wyvern

Despite the the lack of magical classes for fliers, these master classes are quite strong and provides great tactical flexibility. Fliers (both pegasus and wyvern) are already the best classes around. The three ranged cavalry classes, in particular bow knights, are really good at producing damages without getting hit. Great knights meanwhile, well, are really strong in close combat.

In three houses we can no longer rescue other units but cavalry and flier units can now unmount to mock as infantry units, but that provides little or no tactical variety after all.

In practice we almost never unmount fliers because fliers receive no movement penalties, but at the same time they do not receive tile bonuses which is alright -- they can avoid lethal damages by canto skill anyway.

Calvary movement is seriously affected by desert and forest tiles. Most main battles happened in cities so that cavalries are not affected anyway. There are desert and forest based maps for auxiliary battles but since these are of lower difficulty it won't cause much problem especially with the help of divine pulses.

Perhaps the only reason for me to unmount is to cooperate with auto-battle, where cavalry and flier units often advance too far ahead and get defeated. By unmounting them we can make sure units are moving at a similar pace, so that they can fight effectively as a pack.

If they are to develop more on auto-battle strategies, they should really add another option where units advance and attack in a way they are still united. This is even less aggressive than 'focus' but still an attacking one.

- Divine Pulse and difficulty-

That's of course a quality of life improvement - it saves you from resetting the game that you already spent 45 minutes just ruined by an unexpected crit or AI movement beyond the static danger area. It allows players to experiment to slightly more aggressive tactics without having to push towards the limit bit by bit.

We all know from FEH that auto battle is unreliable at times, this is even more of a problem in three houses due to the difference in range of movement. Even with the 'focus' auto battle option, we often found our cavalry healer rushing onto the front line...and pathetically defeated. With divine pulse we can always go back and manually fix the decision made by these headless units then proceed to auto battle again. That compresses the time required for auxiliary battles to just a few minutes.

We have so many distinctive features for players to explore in the game, and spending time repeating the same fight is not the most interesting one -- going through battles at maximum speed really hurts your thumb (the second most tedious thing in the game, next to fishing). So allowing players to skip that part of the game is not bad after all. The game alone is already a 200+ hours masterpiece already -- we don't need something excessive to buff the time needed to clear the game further.

Some say that three houses is easier just because of divine pulse, but this is not entirely true. We can easily list a few difference between three houses and the old FE games showing that the game was made easier:

- extra auxiliary battles to grind the levels
- fewer opponent with a `commander' level stat, in particular those generic commander enemies
- fewer forced time constraints
- flexible mount/unmount option
- charges for physics and fortify resets every battle
- less compact maps
- ineffective level cap
- higher weapons easily accessible at unlimited quantity
- legendary weapons made in mass, and the crests...

Level cap is perhaps one of the biggest concern in the past. You have to breed your characters properly before level 40 (20+20) so that the stat growth will not go to waste.

In three houses the level cap is 99...which is totally out of my surprise. When I completed my first lap with Ed (which is the shortest route), I was expecting the level cap to be 40...but no. I was allowed to keep leveling. When I then proceed to Dimitri route I was expecting the level cap to be 50, but that's again not the case.

Level cap is playing a vital role in FE because it prevents overpowered units by pouring most resources onto one or a few units. It forces you to think about growth rate and skill combos, which is the deepest FE theory in some sense. Without the level cap one may just tank everything by creating an over-leveled unit, and this is not interesting.

But well, since we admitted that their normal is actually the `FE easy' and their hard is `FE hard', shall we expect a more cruel ruleset in Maddening(lunatic+)? There is no need to give distant counter to every unit and make disgusting skill combos like FEH legendary hero battles...just cap the level at 40 and I am sure players will be crying at later stages.

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At the end I should again stress that comments on the mechanism might change vastly against different difficulties. I look forward to the updates for lunatic and maddening difficulties, so that I can complete Claude route as well, before Harvest Moon comes out...

Fire Emblem: Three Houses and Rokkr Sieges

Back to something casual...Fire Emblem. Surely quite a lot happened since last time I wrote about FE and now it is a good time to talk about that again, since Three Houses is coming soon.

Well what should I expect? Unfortunately it's very hard for me to make a fair comment because I have not played the main franchise since the GBA era, a time where skills did not exist and information was sacrce because you didn't know Japanese back in the days...But FEH players should beware of the vast difference between playing FEH and the main franchise.

In FEH the key word is competitiveness. We keep facing stronger and stronger metas and we need to use the same team to work around it (unless you spend heavily). When you use more or less the same team against the opponent, what brings you victories is either the tiny bit of stat difference, or a well-desgined tactic which after all tricks the AI.

In the main franchise it is a totally different story. You are not really fighting in the fair setup -- instead of a 4v4 battle you are doing a 15v50 battle in a well designed stage where you are expected to solve the puzzle bit by bit. Restrictions are kind of loosened but you often ended up putting soft restirctions on yourself: units can be "killed" without failing the stage, but you want to unlock all stories. Time limit is less of a problem but you want to get all secret items and recruit hidden characters...the flexibility is much higher but the difficulty can be no less than what we have met in FEH. The most important bit is, you need to know how to work with a complete army, instread of your precious 4 units.

But yeah I can't wait further for the game. And I am going for Edgelord. Based on the official tease and FEH unit intro she's gotta have an interesting story behind.

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Back to FEH we now have two more game modes which I also want to talk about.

- Alligence battle -

Interesting concept, but competitiveness forces the highest difficulty and hence very tense and allows very limited unit choices. It's also very luck based when you are not using a DC/CC based team, then you will have to play multiple times to get a high enough score.

But the reward is kind of reasonable - taking 900 as the threshold, the effort required to climb above 900 is hard but not very rewarding, while scoring a 860 is of moderate difficulty. I believe a large portion of the players are settled to the casually playing state on this mode.

- Rokkr Siege -

The opposite of the alligence battle. Fun, promotes casual play and allows huge flexibility. The three difficulty means you can score quite a lot without getting into trouble, and the score cap means you do not need to strike for the optimal. For sure the reward is not the most attractive but 10k feather is still 10k feather and I will take it.

In the discord channel we have seen many different setups, but today I want to talk about my setup.

Three features about the dynamax (taking a lesson from the shitty pokemon sword&shield -- that's another story for another day) boss:
1) Swaps upon special proc
2) AOE damage upon special proc
3) Always counterattack creating non-zero damage

If you are taking lower difficulties, damage is not a problem and you can deploy simple means of recovery to overcome the damage like recover 3, or breath of life. In advanced however, you will either need to stop special from processing, or use a strong means of healing, like using a staff or heal based moves.

Swapping means your defense tiles will then be occupied by the boss, or that the boss will escape from your lineup. In lower difficulty, it is hard to hit the score cap just because the multiplier is too low, so stragety that adapts swapping is essential if we want to hit the score cap, especially if we are fighting cavalries.

With that being said, to tackle lower difficulties steadily you would like to:
- mobility to tackle swapping
- minimum healing power

And to tackle the advanced difficulty you would like to:
- much stronger healing
- ability to take down generic enemies
- not necessary to keep a full team to the end; in fact it would be easier to finish the battle within 5 or 6 turns with some units defeated

Some like to use tank units with guard and healing special to lock down the boss, but without enough merging it is hard to hit the score cap. Don't forget that special fighter and guard are both premium skills and quite costly to inherit (if you do not use to do that).

Another problem with guard is the 70% HP requirement which is hard to maintain during enemy phase. My brave sword guard DC Ayra strategy failed miserably -- not to mention that such build is so impractical in PVP battles.

So with my newly merged +10 Catria, I had an idea. A lesson taken from my Cherche.

The setup is basically dancer + flying healer (witchy hand) + 2 fliers

Dancer - Partial tank, need to tank attacks with triangle disadvantage

Olivia in my case
A - Atk/Def Bond 3
B - Wings of Mercy 3
C - Hone Atk 4 [flexible C-skill or depends on your flier performance]
S - Atk/Def Bond 3

L!Azura is of course a perfect choice for fliers, but she cannot tank physical attacks and you may not have enough Iote shields.

Flying healer - putting guard effect on enemy

HS!Sakura [with H!Mia inherited]
A - Iote shield [use something else if you have it on the S-slot]
B - Live to serve 3
C - Hone fliers [spur buffs are also preferred, since the units may move around]
S - Breath of life 3

Fliers - to block boss on one quadrant and DPS
Units depends on the color of enemy but they should be brave based with galeforce. Without galeforce we can steadily hit the cap in 5 turns. It is suggested to bring at least one galeforce flier. If you do not have galeforce, sol is a temporary solution.

Standard builds:
Weapon - Brave weapon [or amiti / whitewing weapons]
Special - Galeforce / Sol
A - Iote shield / Swift sparrow / Death blow / Life and death
B - Seal atk / seal def
C - Ward fliers
S - Iote shield / defensive based seals

We start by blocking the boss on one of the quadrant - attacking is of second priority because we have enough time. It is important to keep the right formation to keep things predictable.
(1): Cherche to destory the wall
(2): Sakura to attack so as to reset the special cooldown
(3): Catria attacks [quad attack due to whitewing effect] 3 times [galeforce + dancing]

If we are fighting close attack bosses then it's not going to move but otherwise the boss may move by a grid, then we have to reform. We first move the unit to facilitate Sakura - remember that when you are using Brave weapons, a second attack would trigger boss' special so we must use Sakura before the second attack.

Here Sonya moved up a grid.
(1): Cherche moved up and attack [galeforce activated so that she looks active again]
(2): Sakura goes up to attack
(3): Catria and Olivia go up accordingly

It is important to deal with other generic enemies. That's the advantage of using galeforce -- we wait until they approach the fliers and attack, within the attack range the two fliers can kill the enemy then going back to the original position without further dancing. The dancer is also expected to be capable to kill most non-armor enemy by floating around.

It is relatively easy to lock the boss using this strategy, unless it's cavalry distant boss -- then we will need to carefully corner her.

The theoretical limit is 6.5 mil points. I somehow used 2 crests in the first round, so this is a pretty good score. It's definitely not a very rewarding act, yet this is a fun mode to play.

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Oh and the Three Houses banner is out. Bitybroken by Chrom I spent 400 orbs to get Edgelord and Byleth. Now I am not prepared for Ayra revival...