Shadow Tactics Analysis: Mugen
To no one's surprise, Mugen is internally labeled 'samurai'.
Mugen is the second party member to be seen in gameplay, helping Hayato from fairly early in the first mission, but then is not present in the second mission and takes a good chunk to show up in the third mission. As the first mission is primarily a tutorial, I tend to think of him as the third character to join 'properly'. He's also one of two characters (out of five) to not have the ninja mobility profile, so his early presence makes Hayato's mobility seem more exceptional than it actually is relative to the overall party mobility: it's not that Hayato is hyper-mobile, it's that Mugen is below-standard for your cast!
More specifically, Mugen cannot perform jumps of any kind, cannot swim, cannot use ninja hooks, cannot climb ivy, and cannot walk tightropes. (This last point is only properly visible in Aiko's Choice: in the base game, tightropes are always placed so Mugen can't reach them in the first place)
This isn't to say Mugen is all-disadvantage when it comes to moving about:

Carry Behavior
Mugen may carry up to two bodies at once, and may even run while doing so, but is always considered to be standing during a carry. Additionally, Mugen may pick up mission-specific 'heavy objects' that other characters cannot interact with, though he cannot do so simultaneously to carrying one or more bodies. He's still able to run when carrying a heavy object.
Notice that this is 100% superior to Hayato's carry behavior. Indeed, Mugen is king of rapidly clearing bodies before a patrol comes back and the like. I quite enjoy this, as it's a very sensible and distinctive way to make 'big strong guy of the team' work as a stealth concept. Or, well, it would be if Shadow Tactics was prone to setting it up so you have cases of wanting to kill two people and rapidly haul their bodies out of sight before a patrol comes back or the like; in practice Mugen's ability to handle two bodies at a time tends to be more like an unimportant nicety, where you spend less time and clicks on cleaning up bodies but it wasn't actually important. But I do like it in theory and can see how this design could potentially make it work with refinement.

Throw Sake Bottle
Range: 5
Mugen throws a sake bottle at a chosen location nearby. The first Guard or Civilian that spots the bottle will break from their post or patrol route, wandering over to pick up the bottle, with their viewcone essentially completely stable for the duration. Mugen has only the one bottle, and will need to retrieve it to be able to throw again, so if a Guard or Civilian picks it up you'll need to take them out to get it back. Note that Guards that are patrolling together or talking to each other will all move to investigate the sake bottle if any of them notices it. Strawhats and Samurai will be briefly distracted by the sight of the bottle one time per throw, but will not approach it unless patrolling with one or more Guards who notice the bottle.
"Have a drink, friend."
Carry Behavior
Mugen may carry up to two bodies at once, and may even run while doing so, but is always considered to be standing during a carry. Additionally, Mugen may pick up mission-specific 'heavy objects' that other characters cannot interact with, though he cannot do so simultaneously to carrying one or more bodies. He's still able to run when carrying a heavy object.
Notice that this is 100% superior to Hayato's carry behavior. Indeed, Mugen is king of rapidly clearing bodies before a patrol comes back and the like. I quite enjoy this, as it's a very sensible and distinctive way to make 'big strong guy of the team' work as a stealth concept. Or, well, it would be if Shadow Tactics was prone to setting it up so you have cases of wanting to kill two people and rapidly haul their bodies out of sight before a patrol comes back or the like; in practice Mugen's ability to handle two bodies at a time tends to be more like an unimportant nicety, where you spend less time and clicks on cleaning up bodies but it wasn't actually important. But I do like it in theory and can see how this design could potentially make it work with refinement.
Also, note that while Mugen is your fastest character at carrying bodies, his base running speed is actually a little lower than most of the other characters. It's a small enough difference it doesn't really matter, but if you order Mugen plus Hayato, Yuki, or Aiko to run to a location, you will see Mugen slowly fall behind. This, oddly, is specific to running; when walking, all your characters travel at the same speed, and same for when moving while crouched. (Which is slower than walking while standing)
But wait! There's more!

Throw
Range: 4
Mugen may throw anything he is carrying, including heavy objects and bodies. If he is carrying two bodies, he will throw both of them, and they will land slightly to each side of where you targeted instead of dead-on.
Something worth noting is that Mugen lacks some of the contextual body-throwing behavior of other characters; you can't just hover your cursor at the bottom of a cliff to get a prompt to throw the body down the cliff. You must instead manually use Mugen's unique throw ability to perform such. As the game doesn't properly tutorial you on the idea that Mugen can throw bodies, I imagine there's a decent number of players who never realized Mugen totally can throw bodies down cliffs and whatnot. Fortunately, for stuff like throwing bodies down bottomless pits, you'll still get the contextual prompt.
Notably, he can throw bodies up cliffs, which is completely unique and potentially quite useful. The most straightforward use of this is hiding bodies, such as if a clifftop is closer than any bushes or buildings to stash the body, since enemies are generally completely unable to find bodies stashed atop roofs and so on. A less obvious use is getting bodies to locations only your ninja can reach (ie Hayato, Yuki, and Aiko) so they can do whatever you want them to do with bodies.
On the face of it, that might sound a bit pointless, but there's two non-obvious points that apply here. The first of these is that thrown bodies knock unconscious enemies they land on; that right there gives a lot of creative utility to Mugen's ability to throw bodies, but the other big factor here is that your ninja can take advantage of this themselves. No, they can't throw bodies freely the way Mugen can, but if you use a contextual throw-down-cliff input on a ninja character, and the body ends up landing on someone's head? They're unconscious. As such, you can potentially kill someone, have Mugen toss them up to some place only ninja can access, and then have a ninja toss the body down to knock another enemy unconscious.
What's particularly important here is that Samurai aren't immune. In missions Mugen is actually on, this isn't too important, since Mugen can often handle the job himself, but if Mugen isn't around being able to drop bodies on Samurai is a way to kill them without spending bullets or one of Takuma's grenades. Knock them unconscious, drop down, finish them: Samurai are only protected from most attacks so long as they remain standing!
Also interesting is that hurling an unconscious enemy atop a roof is a weird way of nonlethally getting them out of your way. If they can't find a way back to their post, they'll wake up, wander around looking for their tormentor for a bit, and eventually stop and sit down. Depending on where you dump them off and what direction they end up facing, they can end up permanently irrelevant. Hilariously, thrown bodies are completely silent, so you can actually hurl multiple people up into the same general area and so long as you're not dumping them in the line of sight of the previous victims nobody will raise an alarm over the fact that a bunch of people are ending up trapped on roofs.
In practice the utility of this is very limited, as normal play encourages lethality and even the Badges that require nonlethal play are less restrictive than you might expect. Sure, stuffing an unconscious soldier into a building is only a temporary solution... but, surprisingly, shoving enemies down a well is a permanent solution that the game doesn't consider to be lethal, never mind that realistically they're dead by drowning. Trapping an enemy on a rooftop is funny, but you should first check if you can dispose of bodies permanently without voiding the Badge before bothering. Since carried enemies never wake up on their own, even if the mission has very few such locations this merely means that disposing of unconscious enemies will take a while, not that it's impossible or risky or even particularly complicated.
If you do mess around with storing enemies on rooftops, something to keep in mind is that enemies can be reshuffled through investigation-triggering effects like causing them to see footprints in snow. So if you do store someone on a roof and end up unhappy with their facing, you don't necessarily need to reload.
Anyway, the main thing the game does draw your attention to regarding Mugen's throw is 'heavy objects': map-specific contextual objects like large rocks. These are actually pretty uncommon, and in practice are a bit of a nuisance to leverage, because Mugen is always considered standing when carrying anything and his throw range is much shorter than enemy viewcones. He basically has to throw over a wall or down a cliff, and with a cliff it must be the case that no enemy is facing the cliff. The main reason this isn't completely useless is because enemies killed by throwing rocks or the like on them are flagged as having an 'accidental death' and so other enemies won't formally raise the alarm if they spot such bodies -even if they witnessed the rocks launch over a wall and really ought to know that this is murder. This can allow you to kill enemies watched by other enemies without issue: if it weren't for this, you'd just... have a ninja drop-attack in or the like. (Mugen is never fully alone, nor does he ever deploy with just Takuma: he always has a ninja partner present)
Throw
Range: 4
Mugen may throw anything he is carrying, including heavy objects and bodies. If he is carrying two bodies, he will throw both of them, and they will land slightly to each side of where you targeted instead of dead-on.
Something worth noting is that Mugen lacks some of the contextual body-throwing behavior of other characters; you can't just hover your cursor at the bottom of a cliff to get a prompt to throw the body down the cliff. You must instead manually use Mugen's unique throw ability to perform such. As the game doesn't properly tutorial you on the idea that Mugen can throw bodies, I imagine there's a decent number of players who never realized Mugen totally can throw bodies down cliffs and whatnot. Fortunately, for stuff like throwing bodies down bottomless pits, you'll still get the contextual prompt.
Notably, he can throw bodies up cliffs, which is completely unique and potentially quite useful. The most straightforward use of this is hiding bodies, such as if a clifftop is closer than any bushes or buildings to stash the body, since enemies are generally completely unable to find bodies stashed atop roofs and so on. A less obvious use is getting bodies to locations only your ninja can reach (ie Hayato, Yuki, and Aiko) so they can do whatever you want them to do with bodies.
On the face of it, that might sound a bit pointless, but there's two non-obvious points that apply here. The first of these is that thrown bodies knock unconscious enemies they land on; that right there gives a lot of creative utility to Mugen's ability to throw bodies, but the other big factor here is that your ninja can take advantage of this themselves. No, they can't throw bodies freely the way Mugen can, but if you use a contextual throw-down-cliff input on a ninja character, and the body ends up landing on someone's head? They're unconscious. As such, you can potentially kill someone, have Mugen toss them up to some place only ninja can access, and then have a ninja toss the body down to knock another enemy unconscious.
What's particularly important here is that Samurai aren't immune. In missions Mugen is actually on, this isn't too important, since Mugen can often handle the job himself, but if Mugen isn't around being able to drop bodies on Samurai is a way to kill them without spending bullets or one of Takuma's grenades. Knock them unconscious, drop down, finish them: Samurai are only protected from most attacks so long as they remain standing!
Also interesting is that hurling an unconscious enemy atop a roof is a weird way of nonlethally getting them out of your way. If they can't find a way back to their post, they'll wake up, wander around looking for their tormentor for a bit, and eventually stop and sit down. Depending on where you dump them off and what direction they end up facing, they can end up permanently irrelevant. Hilariously, thrown bodies are completely silent, so you can actually hurl multiple people up into the same general area and so long as you're not dumping them in the line of sight of the previous victims nobody will raise an alarm over the fact that a bunch of people are ending up trapped on roofs.
In practice the utility of this is very limited, as normal play encourages lethality and even the Badges that require nonlethal play are less restrictive than you might expect. Sure, stuffing an unconscious soldier into a building is only a temporary solution... but, surprisingly, shoving enemies down a well is a permanent solution that the game doesn't consider to be lethal, never mind that realistically they're dead by drowning. Trapping an enemy on a rooftop is funny, but you should first check if you can dispose of bodies permanently without voiding the Badge before bothering. Since carried enemies never wake up on their own, even if the mission has very few such locations this merely means that disposing of unconscious enemies will take a while, not that it's impossible or risky or even particularly complicated.
If you do mess around with storing enemies on rooftops, something to keep in mind is that enemies can be reshuffled through investigation-triggering effects like causing them to see footprints in snow. So if you do store someone on a roof and end up unhappy with their facing, you don't necessarily need to reload.
Anyway, the main thing the game does draw your attention to regarding Mugen's throw is 'heavy objects': map-specific contextual objects like large rocks. These are actually pretty uncommon, and in practice are a bit of a nuisance to leverage, because Mugen is always considered standing when carrying anything and his throw range is much shorter than enemy viewcones. He basically has to throw over a wall or down a cliff, and with a cliff it must be the case that no enemy is facing the cliff. The main reason this isn't completely useless is because enemies killed by throwing rocks or the like on them are flagged as having an 'accidental death' and so other enemies won't formally raise the alarm if they spot such bodies -even if they witnessed the rocks launch over a wall and really ought to know that this is murder. This can allow you to kill enemies watched by other enemies without issue: if it weren't for this, you'd just... have a ninja drop-attack in or the like. (Mugen is never fully alone, nor does he ever deploy with just Takuma: he always has a ninja partner present)
The game's introduction to such heavy objects is also odd in that it's a mechanic that's used only one other time in the game: delivering an explosive barrel to a designated location, so you can blow up a plot-objective for plot purposes. Any other time a heavy object shows up, it's an optional way to murder people that won't be recognized as murder. Which is design-awkward since the game can also do that with objects any character can interact with: pushing rocks off a cliff works the same, just with less control but more of an assurance that the devs made sure it's useful to do so.
The potential for creativity with throwing around bodies is neat, at least.
Do note that tossing bodies has a friendly-fire risk! This applies not only to Mugen's unique throwing action, but also to the contextual throw-down-edge action available to Hayato, Yuki, and Aiko. This rarely has reason to come up, but can be an unpleasant surprise if you're trying to pass a body down to someone else to then move it elsewhere. This crops up as a problem especially readily if you're going for one of the non-lethal Badges, where it might give an unconscious enemy time to wake up!

Katana
Death Duration: 1.4 seconds.
Noise: 3
Mugen kills a single enemy in melee. Works on Samurai.
"My blade for the shogun."
Mugen is your only character who can freely kill Samurai. Everyone else who tries to use an unlimited-use attack will either have it fail to hurt them (eg Yuki's trap) or will be killed for their effort. (When performing a melee attack) Having someone die is, yet again, a Game Over. So don't do that.
Also note that having Mugen kill an at-the-ready Samurai takes longer than when having Mugen kill other enemies: instead of Mugen simply killing an unwary target, the Samurai notices him coming, they clash blades briefly, and then Mugen wins the duel. The game unfortunately doesn't list this alternate death duration explicitly, but it's somewhere around twice as long as when killing a non-Samurai. As such, trying to kill a Samurai in a brief window when no one is looking is not nearly as plausible as doing so to other enemies.
Outside Samurai, Mugen is only very slightly slower than Hayato at melee kills, making him your other character who can potentially drop an enemy when other enemies are briefly glancing away and not get caught. For various reasons (eg his slower running speed) he's not as preferred for doing this as you might expect, but it's good to keep in mind when eg he's partnered with Yuki or Aiko, with Hayato not present.

Unarmed
'Dying' Duration: 1.4 seconds.
Noise: 3
Mugen knocks the target unconscious temporarily. Works on Samurai.
"I can spare a life today."
Normally, there's little cause to KO a Samurai when you could just have Mugen kill them, but there's some Badges that you'll miss out on if you're going lethal all the time. If nothing else, you'll want to consider the nonlethal angle if you try to earn those Badges.
There's also a mission where Mugen is initially unarmed, but is still able to perform his unarmed melee attack. It can be easier to untangle that mission if you're aware Mugen can just walk up to a Samurai and KO them, since an unconscious Samurai can then be stabbed by another character in complete safety, thus allowing you to kill a Samurai without spending limited resources even though Mugen lacks his tools for killing Samurai himself.
Katana
Death Duration: 1.4 seconds.
Noise: 3
Mugen kills a single enemy in melee. Works on Samurai.
"My blade for the shogun."
Mugen is your only character who can freely kill Samurai. Everyone else who tries to use an unlimited-use attack will either have it fail to hurt them (eg Yuki's trap) or will be killed for their effort. (When performing a melee attack) Having someone die is, yet again, a Game Over. So don't do that.
Also note that having Mugen kill an at-the-ready Samurai takes longer than when having Mugen kill other enemies: instead of Mugen simply killing an unwary target, the Samurai notices him coming, they clash blades briefly, and then Mugen wins the duel. The game unfortunately doesn't list this alternate death duration explicitly, but it's somewhere around twice as long as when killing a non-Samurai. As such, trying to kill a Samurai in a brief window when no one is looking is not nearly as plausible as doing so to other enemies.
Outside Samurai, Mugen is only very slightly slower than Hayato at melee kills, making him your other character who can potentially drop an enemy when other enemies are briefly glancing away and not get caught. For various reasons (eg his slower running speed) he's not as preferred for doing this as you might expect, but it's good to keep in mind when eg he's partnered with Yuki or Aiko, with Hayato not present.
Unarmed
'Dying' Duration: 1.4 seconds.
Noise: 3
Mugen knocks the target unconscious temporarily. Works on Samurai.
"I can spare a life today."
Normally, there's little cause to KO a Samurai when you could just have Mugen kill them, but there's some Badges that you'll miss out on if you're going lethal all the time. If nothing else, you'll want to consider the nonlethal angle if you try to earn those Badges.
There's also a mission where Mugen is initially unarmed, but is still able to perform his unarmed melee attack. It can be easier to untangle that mission if you're aware Mugen can just walk up to a Samurai and KO them, since an unconscious Samurai can then be stabbed by another character in complete safety, thus allowing you to kill a Samurai without spending limited resources even though Mugen lacks his tools for killing Samurai himself.
Also, just like his kill animation on Samurai, Mugen's animation for KOing an at-the-ready Samurai is noticeably longer than when KOing other targets: instead of just bashing them over the head, once again the Samurai notices Mugen coming, attempts to attack, but Mugen catches the blade with his bare hands (This is a thing with a basis in reality, surprisingly) and then successfully closes the distance and KOs them. It's a really nicely-done animation!... that I suspect 90% of players have no idea exists, possibly not even noticing it happening if they do go for a KO on a Samurai.

Sword Wind
'Blast' Radius: 3
Noise: 6
Cooldown: 18
Mugen, once he is within the targeted area, kills every enemy in the radius... excepting Samurai, who are unaffected. Enemies killed by Sword Wind take a long time to die, but if they're in the radius when Mugen initiates the attack they will have no chance to raise the alarm, even if the animation makes it seem like they should have the chance. Mugen himself is mechanically invisible until the animation completes.
"One death, many cuts."
Note that while Mugen attacks from the center, the game is very generous and has the attack considered to be initiated the instant Mugen has entered the very edge of the targeted radius, rather than waiting until he starts the sword-swinging portion of the animation. Mugen thus doesn't need nearly as large a window as you might expect to sneak up on enemies, and can also target it in the middle of a group of enemies without any risk of them raising the alarm so long as they don't see him approaching the edge target zone. This also means you can and should try to set the radius with a focus to minimizing Mugen's travel distance, rather than putting it in the dead center of the group you're targeting. It also means there's edge cases where you can use Sword Wind as essentially a ranged attack, albeit short-ranged, to land kills in situations a regular melee attack wouldn't quite let you make the kill undetected due to a precise intersection of terrain, patrol routes, etc.
Sword Wind
'Blast' Radius: 3
Noise: 6
Cooldown: 18
Mugen, once he is within the targeted area, kills every enemy in the radius... excepting Samurai, who are unaffected. Enemies killed by Sword Wind take a long time to die, but if they're in the radius when Mugen initiates the attack they will have no chance to raise the alarm, even if the animation makes it seem like they should have the chance. Mugen himself is mechanically invisible until the animation completes.
"One death, many cuts."
Note that while Mugen attacks from the center, the game is very generous and has the attack considered to be initiated the instant Mugen has entered the very edge of the targeted radius, rather than waiting until he starts the sword-swinging portion of the animation. Mugen thus doesn't need nearly as large a window as you might expect to sneak up on enemies, and can also target it in the middle of a group of enemies without any risk of them raising the alarm so long as they don't see him approaching the edge target zone. This also means you can and should try to set the radius with a focus to minimizing Mugen's travel distance, rather than putting it in the dead center of the group you're targeting. It also means there's edge cases where you can use Sword Wind as essentially a ranged attack, albeit short-ranged, to land kills in situations a regular melee attack wouldn't quite let you make the kill undetected due to a precise intersection of terrain, patrol routes, etc.
Also note that Sword Wind, unexpectedly, kills unconscious bodies on the ground. This can be useful to know if you're doing something esoteric, like throwing bodies down at a couple enemies to KO them and having Mugen run a long way to reach them, where he might not have the time available to execute them with his regular melee attack one at a time. It can also just save clicks after having Takuma use his poison bomb to KO a bunch of enemies. It's mostly just a weird bit of trivia, though.
The cooldown on Sword Wind is very nearly a technicality. It matters, inasmuch as it means you can't just have Mugen hop from one cluster of enemies to the next and completely trivialize eg enemies coming to investigate an alarm, but the fact that it's much longer than any other cooldown in the game is very misleading as it's pretty rare in actual play for you to be meaningfully affected by the cooldown, between how long Sword Wind's animation is and how enemies don't tend to be set up as multiple close-together clumps in the first place.
The cooldown on Sword Wind is very nearly a technicality. It matters, inasmuch as it means you can't just have Mugen hop from one cluster of enemies to the next and completely trivialize eg enemies coming to investigate an alarm, but the fact that it's much longer than any other cooldown in the game is very misleading as it's pretty rare in actual play for you to be meaningfully affected by the cooldown, between how long Sword Wind's animation is and how enemies don't tend to be set up as multiple close-together clumps in the first place.
Sword Wind's value as a skill is a bit odd to discuss. It's very much a powerful skill, but the mission design makes it seem more powerful than it really is, and in fact its value is actually surprisingly low once you've mastered the game sufficiently, far below its apparent potential. The basics of the point are that the missions Mugen is present for are prone to setting up enemy batches so Sword Wind is either not particularly helpful (Enemies spread out too much to catch multiple at once, or a Samurai mixed in who will survive and raise the alarm) or single-handedly solves the situation. (eg three Guards patrolling, with poor coverage from other enemies) Those latter cases make Sword Wind seem downright essential when first playing, but as you master character skillsets, particularly coordinating them, it becomes increasingly plausible to do things like kill a three-Guard patrol with just two characters, neither of whom is Mugen.
There's one mission in the game where one of its Badges requires not using Mugen at all where it is genuinely challenging to take apart some of the multi-Guard patrols on the map without using Sword Wind, but overall it's more a nice-to-have than anything else.
I do like Sword Wind on a conceptual design level, though: Mugen is your 'bruiser' character, the least sneaky of your sneaky characters, and Sword Wind does a pretty good job of selling that, in that Mugen has more ability to 'brute-force' solve situations like multi-Guard patrols with a minimum of actual stealth. Just hide in a bush, and burst out and shred everyone too quickly for them to realize they're under attack. It's a little unfortunate the design isn't so great at giving it a strong place in your arsenal as your skill rises.... though not too bad for reasons I'll talk more about in a bit.
Throw Sake Bottle
Range: 5
Mugen throws a sake bottle at a chosen location nearby. The first Guard or Civilian that spots the bottle will break from their post or patrol route, wandering over to pick up the bottle, with their viewcone essentially completely stable for the duration. Mugen has only the one bottle, and will need to retrieve it to be able to throw again, so if a Guard or Civilian picks it up you'll need to take them out to get it back. Note that Guards that are patrolling together or talking to each other will all move to investigate the sake bottle if any of them notices it. Strawhats and Samurai will be briefly distracted by the sight of the bottle one time per throw, but will not approach it unless patrolling with one or more Guards who notice the bottle.
"Have a drink, friend."
Note that the game is perfectly happy to let you toss the bottle somewhere Mugen can't retrieve it from. Don't do that; the game won't let some other character retrieve the bottle for Mugen.
Also note that the sake bottle's visibility is equivalent to a crouching character's: it's not enough to have it in their viewcone at all, it needs to be in the inner part that's fully filled in. This includes that enemies won't notice the bottle if you toss it in a bush unless they happen to walk basically right on top of it anyway. By a similar token, elevation differences will usually make the bottle invisible, which is another reason to not throw it up a cliff.
Also note that the sake bottle's visibility is equivalent to a crouching character's: it's not enough to have it in their viewcone at all, it needs to be in the inner part that's fully filled in. This includes that enemies won't notice the bottle if you toss it in a bush unless they happen to walk basically right on top of it anyway. By a similar token, elevation differences will usually make the bottle invisible, which is another reason to not throw it up a cliff.
Further note that some enemies are considered a special form of busy that will be only briefly distracted by the bottle. Civilians visibly carrying something, for example, will generally briefly pause in their routine to look at the bottle the first time their viewcone catches it, and then ignore it forevermore. (Until you pick it up and throw it down again) The vast majority of Guards and Civilians can be pulled by the bottle, but the exceptions can really trip you up if you're not expecting it.
The bottle itself is visibly tracked with an icon once picked up, and is not 'dropped' by a target when they die. This is mostly not important, since of course a body being spotted normally results in the alarm being raised, but can come up if you use the bottle to set an enemy up for an 'accidental' death: if they grab the bottle before dying, other enemies won't try to take the bottle off their body. Mugen automatically retrieves the bottle if he passes close to such a body, same as Hayato retrieving his Shuriken or Yuki retrieving her Little Trap, whereas if the bottle never gets picked up by an enemy you have to directly order Mugen to pick it up.
Do note that the bottle is not actually attached to the corpse, though. Say you have Mugen toss the bottle up to a high point, then Hayato kills the Guard that picks it up: if you have Hayato throw the body down to Mugen, the bottle icon will remain where that Guard died. I was very serious when I said other characters can't help Mugen retrieve his bottle.
An important piece of the sake bottle's utility that's easy to overlook and very important to keep in mind if you're attempting to get the speedrun Badges is just manipulating the victim's viewcone is surprisingly useful. You don't necessarily need to wait for the enemy to actually approach the bottle: you can do stuff like toss the bottle out one side of a barrier Mugen is hiding behind, and then once the enemy notices the sake bottle have him immediately run out the other side and stab them before they've even halfway to the bottle.
The sake bottle itself is very appreciated when first learning the game, but is another case of an ability tending to drop in value as your skill rises. Mission 3 provides one of the clearer examples, in that it's a snow mission, and having a character walk through snow can substantially replicate the sake bottle's utility in terms of drawing an enemy to a desired point. There's a lot of stuff like this, where the sake bottle is easy to understand how to use it, but as your mastery rises you'll realize there's lots of other tools available for replicating its functionality at pulling enemy attention to where you want it.
An important piece of the sake bottle's utility that's easy to overlook and very important to keep in mind if you're attempting to get the speedrun Badges is just manipulating the victim's viewcone is surprisingly useful. You don't necessarily need to wait for the enemy to actually approach the bottle: you can do stuff like toss the bottle out one side of a barrier Mugen is hiding behind, and then once the enemy notices the sake bottle have him immediately run out the other side and stab them before they've even halfway to the bottle.
The sake bottle itself is very appreciated when first learning the game, but is another case of an ability tending to drop in value as your skill rises. Mission 3 provides one of the clearer examples, in that it's a snow mission, and having a character walk through snow can substantially replicate the sake bottle's utility in terms of drawing an enemy to a desired point. There's a lot of stuff like this, where the sake bottle is easy to understand how to use it, but as your mastery rises you'll realize there's lots of other tools available for replicating its functionality at pulling enemy attention to where you want it.
It was a nice surprise when Desperados III brought back the concept and tried to buff it. I don't think the buff was very successful, unfortunately, but still.

Hand Cannon
Range: 14
Noise: 8
Death Duration: 1 seconds.
Cooldown: 3 seconds.
Mugen kills an enemy with his hand cannon. This even kills Samurai in one hit. Mugen only ever starts with 1 or 2 ammo, and cannot get more.
"
Just like Hayato's Matchlock, the first few missions you have Mugen he doesn't actually have the Hand Cannon, as it's locked behind a specific plotpoint. Also just like the Matchlock, Mugen is temporarily treated as standing after firing, though this is a little less important since there's nothing equivalent to the Matchlock-Samurai interaction.
Hand Cannon
Range: 14
Noise: 8
Death Duration: 1 seconds.
Cooldown: 3 seconds.
Mugen kills an enemy with his hand cannon. This even kills Samurai in one hit. Mugen only ever starts with 1 or 2 ammo, and cannot get more.
"
Just like Hayato's Matchlock, the first few missions you have Mugen he doesn't actually have the Hand Cannon, as it's locked behind a specific plotpoint. Also just like the Matchlock, Mugen is temporarily treated as standing after firing, though this is a little less important since there's nothing equivalent to the Matchlock-Samurai interaction.
The Hand Cannon really seems like something that should be an amazing tool, but unfortunately the game constructs itself so it never really has a chance to shine. The obvious ideal use-case for it would be to sneak up on a pair of Samurai and kill them without raising the alarm, by virtue of shooting one and immediately meleeing the other, but while such paired Samurai happen, the game is loathe to have them happen in a mission where you have Mugen and he has access to the Hand Cannon.
The other ideal use case for it would be to shoot a Samurai in a brief window where they're not observed by anyone, whether by patrolling briefly into a blind spot or by a viewcone being perpetually broadly aimed their way but with them in the outer portion and even that portion spending a second or so not covering them... but again, this doesn't really happen in missions Mugen is present and has the Hand Cannon. In fact, this doesn't really happen in general; Samurai tend to be either well-covered such that an instant kill would send up the alarm regardless, or so poorly-covered that arranging to shoot and then stab is possible to do without bothering to take out anyone else in the area, regardless of whether Mugen is present or not.
This isn't a terribly surprising oversight, as you just don't get that many missions with Mugen having the Hand Cannon; less than 25% of the game's missions give you the opportunity to use the Hand Cannon.
It gets a little more of a chance to shine in Aiko's Choice, thankfully: in the base game, you could be forgiven for not even realizing Mugen has it instead of another Matchlock.

Heal
Mugen restores up to 3 missing HP to himself or a single adjacent ally. One charge per mission, with any overhealing wasted.
"A well-earned scar."
If you are accepting mistakes and whatnot, Mugen is your best meatshield and thus best recipient of damage, having 8 HP on Normal difficulty and 5 on Hardcore as opposed to the 4 and 3 other characters have. This allows you to use Heal's full value without having to get a character riding up to the edge of death on Normal, and on Hardcore lets you use the full value of Heal at all.
Heal
Mugen restores up to 3 missing HP to himself or a single adjacent ally. One charge per mission, with any overhealing wasted.
"A well-earned scar."
If you are accepting mistakes and whatnot, Mugen is your best meatshield and thus best recipient of damage, having 8 HP on Normal difficulty and 5 on Hardcore as opposed to the 4 and 3 other characters have. This allows you to use Heal's full value without having to get a character riding up to the edge of death on Normal, and on Hardcore lets you use the full value of Heal at all.
Mugen's superior HP meter is itself one of those things that makes me think that at some point the game design was more oriented toward accepting mistakes. In the current version, it's harmlessly irrelevant for supporting 'Mugen is your bruiser character', where in a version in which accepting hits was intended to happen at times, it would more concretely tie into making his playstyle more brute-force.
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Once again, from hereon there will be unmarked serious spoilers. Maybe come back later if you haven't beaten the game yourself.
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In terms of the writing, to my surprise Mugen is possibly my favorite character of your party. To a certain extent this can be put to a way in which he is a rarity in video games: a middle-aged individual who is treated as middle-aged. (As opposed to being presented as a doddering fossil that will topple into the grave any second now) This right there makes him stand out from the crowd, so to speak; if I want to see a calmly mature adult who is written as being such and actually gets a lot of focal attention from the writing, I can't just go digging in a bargain bin and expect the resulting game(s) to have such an example.
But even aside that point, Mugen is just written well, and has great interactions with the rest of the party, where these interactions are consistent with each other, yet clearly show different elements of Mugen's character, and tend to reveal that there's more to Mugen than you might first expect without suggesting the first impression is a lie. That's an impressive balancing act by any metric.
Part of what's nice is how often Mugen's interactions with the rest of the party pull 'double duty' -oftentimes in fiction of any sort, a given interaction between two characters is primarily there to convey to the audience something about only one of the two characters. The main character has a scene with the story's primary antagonist, and the scene only really serves to paint a picture of said antagonist, with any qualities the protagonist shows in the scene being things the audience has already seen in prior scenes; that kind of thing.
Mugen's early interactions with Yuki are probably the best example, as they simultaneously start conveying to the player that Yuki is a thief who talks about animals a lot because she hasn't had a helpful adult in her life since sometime in her childhood and was presumably stealing to feed herself and so is basically half-feral, but also start showing that Mugen is a pretty unconventional samurai. Which makes a lot of sense: he's a party member in a video game all about stealth, so he's certainly not going to be someone who sneers at subterfuge and exalts open combat. Indeed, Mugen is actually the person who forms and heads this unit: the 'Blades of the Shogun' in the title is a reference to your party, and your party acting in this capacity is all down to Mugen.
This itself touches on part of what's interesting about Mugen: I commented in Hayato's post on how the earliest portion of the game (Plus some meta signals) point to him as the Main Character of this story and then this falls away overall, and Mugen is something of the flipside to this. In the first mission, he's just some guy Hayato meets on a mission who helps Hayato complete his mission, a Side Character within that framework, but by the end of the game he's a lot more central to the plot than Hayato: Mugen is the one who forms the unit, the one who sets mission goals overall (eg mission 2 doesn't have Mugen playable in it, but the mission itself is Mugen's idea, not Hayato's), the one with an ideological commitment to the cause (By contrast, Hayato is a mercenary, Yuki starts out just being happy to help without necessarily understanding or caring about the larger context, and Takuma and Aiko don't seem strongly loyal to the shogun per se), and when he dies, his death is what decides the course of the other party members: avenging Mugen by slaying the man who prompted his suicide. You could swap out Hayato for a pretty different character without necessarily impacting the plot much. You couldn't do the same with Mugen.
This is particularly striking given that a common failing of pop culture that has any kind of Main Character is that such a Main Character often has immunity from death. (And indeed often gets immunity to many lesser consequences as well) Mugen being arguably the main character of Shadow Tactics and having a major part of his contribution be his death is very unusual!
His death itself is also pretty convenient for the game design, actually. The game clearly struggles with making Samurai be meaningfully a greater obstacle than Strawhats without being outright unreasonable anytime Mugen is on the team: since Mugen doesn't find a Samurai any harder to kill than a Strawhat (Aside the often-irrelevant detail that killing a Samurai has a longer animation), and Strawhats and Samurai are equally resistant to distractions, the only avenue the game has for making Samurai harder than Strawhats when Mugen is around is to rely on creating conditions that make it harder to deliver Mugen to a Samurai undetected. (More specifically, to put them and Strawhats in conditions where eg Hayato can jump off a building to instant-kill a Strawhat, and can't solve a Samurai the same way)
Once Mugen is out of your party for good, this problem fades away: now Samurai are more of a problem pretty reliably ('accidental' deaths being the main potential qualifier), requiring two party members working together to take them down safely and consuming limited resources you might otherwise spend on non-Samurai. (That is, the game is reliably generous enough with ammo that saving Matchlock bullets exclusively for Samurai leaves you with bullets to spare even if you kill literally every enemy on the map, but maybe you have a half dozen cases where shooting some non-Samurai would simplify things, but shooting all of them cuts into your ability to kill Samurai)
Aiko's Choice, incidentally, revisits this topic with a bit more deftness; for example, it has a mission that involves swimming to islands, which does include some Samurai on those islands. Since Mugen can't swim, he can't get to those islands, so those Samurai are meaningfully more of a challenge than Strawhats. This is still an imperfect solution, mind, but the main of my point is that the devs clearly recognized the issue and worked to correct it. (Honestly, I've wondered if killing off Mugen late in the plot was done because of these mission design issues)
Anyway, returning to Mugen as a narrative piece: when discussing Yuki I commented on how she is a surprisingly good depiction of a person from disadvantaged circumstances, and of course that wasn't just about how Yuki herself was written, it's tied into how other characters are written. Mugen is particularly stand-out here, as he pretty clearly is reacting to her life circumstances with a desire to help, but is shockingly reliable about approaching the topic with circumspection and respect: I'm not sure Mugen ever directly asks Yuki about her history (It's Takuma who talks to her about Kanazawa Town and her mother, for example), preferring to talk around the edges of the topic. When he offers to help, it's usually presented as or functionally is more of a trade: he offers to speak to Hayato on Yuki's behalf about the whole 'apprentice ninja' thing, for example, but of course Yuki is also a Blade of the Shogun and so improving her skills in such ways will be repaid by her being better at executing missions.
He's quick to offer praise for her good ideas -presumably trying to offset her self-esteem problems, where she tends to call herself 'stupid' a lot if she feels she made a mistake- but he's good about it not being empty praise. This is particularly helped by the voice acting: I mentioned in Yuki's post that in mission 2 Yuki suggests a distraction and Mugen comments that he's tempted to try it, and the voice acting does a great job of communicating that Mugen isn't saying that (just) to be nice, but is in fact kind of excited by the idea!
Which itself is another example of Mugen being successfully sold as an Unusual Samurai who fits into this stealth game: it's actually a recurring thing that Mugen's response to unusual ideas is to go, essentially, "Interesting! I wouldn't have thought of that, but now I can't wait to try it!" Which for one thing is what the gameplay is often trying to evoke from the player, making it especially obvious and fitting.
About the only part of Mugen's writing that doesn't sit entirely well with me is when he commits seppuku: seppuku was historically performed to avoid falling into enemy hands and being tortured, or to undo shame/restore honor as a more public ritual. There have been cases of people committing seppuku in isolation because the actual point is to die and they don't necessarily care if anyone else knows how it happened, but seppuku was not really a thing samurai did in this way. Indeed, a samurai historically required permission to be allowed to commit seppuku! So I'd expect Mugen to go to his shogun, explain his failing that he feels can only be compensated for with suicide, and then commit seppuku in front of his shogun...
... but for one thing Shadow Tactics' story is all supposed to be 'shadow war' stuff where most people are unaware of major elements of what is going on around them. Mugen committing seppuku in a highly public ritual to atone for things going wrong in his black ops unit's mission wouldn't exactly make sense. Either his reason for shame would be kept secret and witnesses would be confused as to why this is happening, or these things the narrative intends to be secret would... not be secret.
So even on this one thing that bothers me, I'm not sure Shadow Tactics could have actually done better at handling it.
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Next time we wrap up characters with Takuma.
See you then.
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