In video games, the difference in power between different characters can usually be accurately gauged by comparing their physical and skill statistics and the qualities of their equipment. Even so, antagonists will usually be unable to size up the protagonists and determine that the latter are at a massive advantage. Even though there is nothing compelling them to attack, they will usually express their belief in their own superiority, attack and promptly get slaughtered.
Sometimes a result of non-linear gameplay; a group of enemies that would be a good match for you when you're low level, are missing half your party and can't use magic without being arrested, for example, has exactly the same scripted response as when you're able to beat up demigods for sport. Other times, there's simply no explaining why the enemy mooks just don't flee before the One-Man Army, the character who's on a New Game+, or the epic-level character party.
Some games do try to avert this by having lower level enemies run away after a round or two. This may be justified in a story as a case of Mugging the Monster if the protagonist doesn't seem formidable because they are Weak, but Skilled or are a Pintsized Powerhouse in a setting where Muscles Are Meaningless. May be due to Spiteful A.I.. See also Leeroy Jenkins and Artificial Stupidity.
NOTE: This trope deals exclusively with video game situations where the computer is clearly outmatched but is unable to do anything but mindlessly attack; a number of perfectly good tropes, such as Attack! Attack! Attack! and Bullying a Dragon, exist for characters in other media who perform acts like this.
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First Person Shooter
The worst offender is likely The Darkness, where the player has demonic, flesh-eating tentacles growing out of him. Despite this, the enemies all don't seem that worried. Interestingly, whipping out your tentacles during battle DOES scare foes, but not arriving to a fight with them already equipped. It's the startle factor. When a empowered human charges across the room to you with Combat Tentacles, you start shooting. When the guy you thought was a easy target suddenly sprouts a pair of extra arms and charges, you might get a bit unnerved.
Justified in BioShock for most of the game; the Splicers will continue to leap out and attack you because they are clearly being driven insane by their mind breaking addiction to a chemical that allows for genetic engineering, which they can get a hit of in your blood. However, averted after you disguise yourself as a Big Daddy, unless you are protecting a Little Sister, the splicers will avoid you.
Deus Ex. A terrorist with a knife will happily engage a security bot powerful enough to take down a hundred punks like him at the same time.
Vampire: The Masquerade – Bloodlines: Your character never looks very powerful at first glance, but not even the lowest mook seems to back down even if they know beforehand you're on the level of an Elder, or even if they've witnessed you punching a few of their friends through nearby walls, equipped a Desert Eagle, or made a few of them explode by boiling all the blood in their bodies.
Anyone in Half-Life 2 who attacks GordonFreeman and expects to live. Big Creepy-Crawlies, Personal Space Invaders, Combine soliders, even heavily-armed aircraft and walking tanks (which at least have a small chance of succeeding), none of them ever consider this to be a Bad Idea. By about halfway through the game the player can even hear announcements by the Combine Overwatch (which sounds suspiciously similar to GLaDOS) that anyone who fails to complete their mission will receive "permanent off-world assignment" among other punishments, indicating this trope may be part of Combine official policy.
Left 4 Dead and Left 4 Dead 2 is like this at time for the special infected. While common infected are portrayed as being blood lust and crazy, justifying their mindless attacks, special infected are implied to be quite a bit more intelligent, which explains how they can set up ambushes. However, there's nothing that can justify why a Smoker would jump out of hiding and try to entangle a survivor when there's 3 other survivors ready to save their friend and blast the Smoker or why a Jockey would run straight at the survivors when they are so close together.
In Shogo: Mobile Armor Division's mecha levels it's common to find enemy human soldiers around. While they can present a sizable threat in groups they never act tactically, resulting in things like lone riflemen firing their peashooters at your Humongous Mecha, apparently firmly convinced they're dealing significant damage even as said mecha effortlessly shrugs the bullets off. Needless to say, lots of stomping usually ensues.
In the first game, an aggressive AI player can cause its own demise due to the way it's programmed. "We hate you! We declare war!" Cue Curb-Stomp Battle. "Uhh...we surrender! Here, have one of our cities." A few turns later: "We hate you! We declare war!" "Uh, we surrender. Here, have a city." "The [Insert Name Here] Civilization has been destroyed." Later games in the series avert this by allowing the AI to capitulate, which makes them a vassal of your civilization and adds their victory score to your own. Also, the AI will only initiate battles where it calculates a decent chance of winning, meaning lone spearmen won't mindlessly assault your tanks anymore.
In Civilization IV, the AI generally avoids suicidal moves, but since the enemy AI only looks at military strength, ignoring industrial and financial capabilities, it's possible to provoke a militarily stronger enemy and win by turning cities into industrial powerhouses and rapidly producing a larger army.
Montezuma's flavours in Civilization V often (depending on how some key flavours are rolled) cause him to manufacture practically nothing but Jaguars (the Aztec equivalent of the weakest unit in the game) and declare war on anyone nearby as soon as he has "enough" of them. This is effectively a Zerg Rush, but the earliness and general trouble the AI has fighting makes it a suicidal move most of the time.
Sid Meier's Alpha Centauri: Factions considerably weaker than their rivals will nevertheless declare war on them at the drop of a hat, and will often break their truces after they've been beaten into submission.
Deadlock: Enemy races will attack super-defended fortresslike cities belonging to a player several tech-levels higher than their own, with attack forces so puny they can't even scratch the paint on the automatic defense turrets. Races owning two or three cities will declare war (with angry-sounding messages from their representatives) against players owning the rest of the world. The representatives of enemy races will even just occasionally pop up and randomly insult the player, uncaring that a mere twitch of the finger would be enough to send them and their entire civilization to extinction.
In Master of Orion, the AI players will eventually declare war on another empire (yours or an AI empire) with complete disregard for the strengths of the respective empires. Particularly in the second game, at higher difficulty levels NPC empires will refuse to surrender even if their empire consists of only one population point on a planet blockaded by a fleet of warships that can turn the world into a rubble pile and eliminate the offending empire entirely.
Ditto for the iOS port Starbase Orion. Artificial Stupidity means that the enemy AI will frequently sent a single destroyer against your fleet consisting of a mammoth, several titans, a dozen battleships, scores of cruisers and destroyers, and a hundred frigates. It's even worse when the AI does this with unarmed troop transports, sending one after another at a defended planet, meaning they are automatically destroyed. Slightly justified, as the developers have stated from the start that the game is meant for multiplayer. However, AI improvements have since been made. Also, the AI will keep declaring war only even if you have conquered all but one of their planets and their defenses are nonexistent.
Before the second expansion, planets under attack are forced to respond with bravado. Sure, you have a fleet with three dreadnoughts and over twenty cruisers in orbit over their heads. Sure, you've demolished the planet's defensive fleet and there will be no reinforcements ever, because your three other fleets are mopping the entire sector clean of enemy warships. Sure, you've got the firepower to turn the planet's surface into a network of finely-patterned antimatter craters in a single turn. They will still force you to engage, futilely launch their few remaining surface-to-space missiles at your ships, and make you finish the job because the game just doesn't have any planetary surrender feature.
The second expansion added a planetary surrender feature... but only if the attacker is the same species or have sufficiently researched the alien culture. Even then, they often end up insisting to be wiped out anyway, especially if the population is large. Considering the game still doesn't feature ground combat so the only way to reduce the population is orbital bombardment and biological weapons, they really should know better.
The sequel has a more developed diplomatic system that defaults to neutral rather than starting everyone out at war with each other. Nevertheless, the Artificial Stupidity will usually declare war if you appear displeasing enough to them for some vague reason, never mind that you are much more powerful than them. At times, even civilian colonies succumb to the stupidity virus.
A prime example of this trope is present in EverQuest. Monsters too weak compared to you won't attack you, usually, but if you sit down, they'll grow overconfident, and attack you. It's even worse than usual, since, with certain buffs, the monster attacking will kill himself just by touching the character, succeeding only in forcing the character to stand.
LotRO averts this - mostly, in the game world. Enemies 9 levels below your character, or lower, will not attack unless you attack first. Exceptions are some of the major instances, where everything aggros like normal. On top of this, as a method to keep low level characters from spending too much time in high level zones, mobs 20 levels or higher, above your character's level - will aggro from a much larger radius - including mobs that are normally neutral.
World of Warcraft gets hit with this, thanks to the rules of the AI's Conspicuously Selective Perception. Aggressive NPCs generally ignore you when you're much higher level than they are, but will still mindlessly attack once you get extremely close. You can't help but feel some pity when you come across level 8 bandits who think it's a great idea to attack the level 80 Tauren who's decked out in all kinds of shiny armor and riding Baron Rivendare's Deathcharger, all because he got too close. Even better, use a damage shield ability and you don't even have to attack them; they'll gladly beat themselves to death.
All but the most bloodthirsty/brave/stupid Humanoids will run away in fear when they get to about 20% or so health. This might seem smart, but they're really just looking for their friends. Upon finding some, or even worse, not finding some, they'll run right back so you can finish the job of killing them. Against evenly matched players, this can be deadly, but against much higher level players, it's like a lemming suicide rush.
Northrend Humanoids never run. None of them are apparently programmed to do so. It is unknown why this is, although one guess is that running away was more frustrating to players than its value in realism.
Taken to ridiculous extremes in the Death Knight starting areas, where you get a quest to kill hapless villagers. At low health, they start begging you to spare them, saying they have a sick grandma at home, or five kids that will die without them. This would normally be refreshing, but they keep attacking you while simultaneously asking you not to hurt them.
If this is true, they've changed it so that they'll say this the second they see you and cower.
Some of them will cower, the rest will attack you suicidally.
And let's not forget Gamon, a level 12 tauren NPC who is killable thanks to quest requirements. Usually a neutral character, when a Death Knight enters Orgrimar for the first time he'll rush towards him to attack. Death Knights arive at Orgrimar around level 58.
The mooks of City of Heroes not only won't attack if you're more than three levels above them, they'll act as if you don't exist until you attack them, perhaps in a vain hope you will go away.
Although there was a bug in certain missions that spawned "ambushes" from a given faction who not only would attack but would chase after you all over the map... sometimes the ambushes consisted of some rather lower-level mooks. Like Level 1. Keep an eye out for the group of players, levels 45+ , standing around having a conversation and pointedly ignoring the villains flailing uselessly at them.
Mooks who rank low enough not to attack will also flee much quicker if engaged. Some powers, such as sneak attacks, also have a chance to freak out nearby enemies and scare them into fleeing.
Once you reach a high enough level, lower level enemies that aggro will ignore you in Final Fantasy XI. That is, until you decide to rest near them, where even a level 5 goblin will think he can kill a level 75 character, who could kill said goblin in one hit.
Most enemies in Runescape that are aggressive are only aggressive until the character reaches a certain level. Others, on the other hand, can be this trope. Level 10 unarmed thugs think they can take down a level 120 character wearing full Dragon armor with an Abyssal Whip.
Kingdom of Loathing doesn't really have a mechanism for most enemies to run away or surrender before you kill them, but Ed the Undying deserves special mention because he keeps attacking you even after you've separated him from his left arm, both his legs, half his torso... He never actually gives up, he just eventually becomes incapable of doing anything other than groaning and cursing.
Real Time Strategy
Warhammer 40,000: Dawn of War has a Morale system, where Squads Broken take more damage and deal less, encouraging players to pull them out of combat. However, without player intervention, these units will continue fighting and being slaughtered. True, such an automated response would detract from the player's control, but still... There is at least one mod that has created a fallback system for squads that get their Morale drained.
In Company of Heroes (made by the same developers), infantry units without rocket launchers or anti-tank grenades literally do no damage to tank units, yet will still attack them if they get into range.
The troops you are commanding will comment on this, with US rifle squads asking whether you are high when you order them to attack tanks, and the airborne yelling "Fire your rifles, we can distract them at least!"
Both games encourage you retreat if there is no chance on winning, since in Dawn of War, a broken squad is really only good for running anyway (it actually gives them a movement speed boost). In Company of Heroes, all infantry have a button to make them retreat back to your base. Dawn of War's sequel used the same system as Company of Heroes. Both Company of Heroes and Dawn of War 2 have a suppression mechanic which will cause infantry squads to be suppressed and ineffective at firing back - so you should retreat them.
In the Total War series (Particularly Empire and earlier), especially on higher difficulty, the campaign AI is essentially rabid. Portugal will break its alliance with your continent-spanning empire, attack you despite no chance of success, and refuse virtually any sensible peace treaty, even after you've slain five kings and are besieging their last settlement.
In Shogun II this fine tradition carries on. Notably, making someone into your vassal is pretty much a guarantee that you'll be the first person they'll put their knife in.
Avoided, however, with the battle AI. There is a morale system that applies equally for both your troops and any enemies. If you pull a flanking maneuver and your opposition is overmatched, or even if they are not, they may scatter and rout. Your own troops are subjected to this too.
The battle AI would also occasionally order a tactical withdrawal, if the situation was clearly hopeless.
Warcraft 3 custom maps have this problem. At least in ladder normal units together are well able to bring down enemy Heroes. In custom maps where there are unlimited stat-increasing tomes for purchase, enemies will still attack even if the Hero target has health in the tens of thousands and over 1000 DPS. Then again, it is reasonable for maps where the enemy units also scale to equally horrific levels.
For example, in Custom Hero Line Wars, a typical melee hero will have several thousand armor, over 100k damage, and a maxed out attack speed. But at that point in the game, the available monsters have gotten so strong they can often one hit you anyway.
In Age of Empires, you can attack a computer player and destroy everything except their Town Center, then surround it with priests and convert every single villager they make, and they will keep on making villagers until they run out of food. Then, if you give them a tribute of food, they will declare 'Your petty offerings will not sway my determination to crush your empire!' and resume making villagers.
In Age of Empires III the AI gets somewhat more sensible. If you have trashed enough of a computer's economy and military they will offer to surrender.
Skeletons in Dungeon Keeper 2 are like this, as are, to a lesser extent, Dark Mistresses. Since Skeletons have literally no fear, one at level 1 will happy charge against 20 level 10 Dark Angels (whether you want it to or not). Most your other minions though are sensible enough to flee in terror if outnumbered, or up against something much tougher than themselves.
In Battalion Wars, enemies will move to engage you as soon as you attack them or get within their range. It doesn't matter if you're a Grunt, a Flame Vet, a Missile Vet, a large double-barreled tank, a Battlestation or a freaking Strato Destroyer. Hell, it doesn't matter if you're bearing down upon them with the might of the same Battalion who's owned the rest of the battlefield. Every single enemy unit will suicidally charge towards you without regards to enemy numbers or strength, with also no regard to chance of winning, and thus disregard of survival.
Supreme Commander is geared toward massive attacks with hundreds of units, for which the savvy player will prepare with walls of automated defenses. Such massive attacks do occasionally come, but they're all scripted - inbetween them the AI, left on its own, constantly sends small groups of medium-level units to smash harmlessly against your impenetrable base, again and again and again. Granted, the game has unlimited resources, but you'd still think the AI would at least try to stockpile units for bigger assaults.
In Europa Universalis III it's not uncommon to have tiny city states offer your world spanning superpower treaties that make Versailles look modest - in their favour. This usually only happens towards the start of a war and once you've actually defeated them you can usually dictate terms although sometimes they remain stupidly intransigent in the face of overwhelming odds until either their capital falls or they lose their last army
The freeware RoguelikeTranscendence has this to a murderous degree, given the game's nearly exponential leveling system. You can end up taking out entire space stations with a single shot—and any nearby enemies that aren't destroyed in the explosion and aren't taken out by the debris cloud will still try to hurt you. Even though most of the time they can't even beat your shield's regeneration rate. That doesn't mean you can just ignore them, though...
Role Playing Game
Tales of Symphonia features mooks that will attack you no matter what. Go back to Iselia at around level forty or fifty and see for yourself.
The Baldur's Gate series features this heavily. A scripted sequence in the second game parodied this kind of overconfidence of part of newbie players: The player encounters a party of inexperienced adventurers that can be sent off on an errand. When they return, the leader is certain that they can defeat the player and goads the others into attacking. They are promptly slaughtered, and they "rewind" the scene by means of reloading their game.
Not only that, but it's very common to have bandits with leather armor and daggers trying to shake you down when you have weapons and armor so powerful they have their own auras.
Seems to be lampshaded, too. Some low-level mooks can be heard boasting that they could "take Drizzt with both their hands tied behind their backs." (Of course, in Throne of Bhaal you'll eventually encounter mooks who almost could do this, but by that time you'll be beating armies and demigods yourself.) And one guard who's precisely as weak as all the rest of them will attack your party alone after declaring that "you've come to the wrong place, kiddos. I'm one mean son of a bitch, and I'm gonna give you a world of hurt."
The games do have a script for opponents panicking, but they can't surrender, only run away until their morale resets and they attack again.
Throne of Bhaal plays with this somewhat. While there are a few idiots who attack you, most also have no idea who you are or what you are capable of. Those who do know are openly terrified (including, among other things, high level vampires, a Lich, and several armies).
In Neverwinter Nights 2, the player and his/her adventuring party encounters a group of thugs harassing a shopkeeper. There are more adventurers than thugs, and the adventurers are decked out in magic everything, but the thugs attack anyway.
Later, a lower level group of adventurers tries to kill you for a reward and your magic items. Some of the party will leave if you point out a few of the much more imposing threats you've already defeated, at which point the rest attack and get effortlessly wiped out.
In Chrono Trigger, even the weakest enemies who can be beaten in 2 hits at Level 1 with just Chrono in your party will gladly attack your Level 99 party in a New Game+, even though the party has defeated an Eldritch Abomination. The only enemies that ever run away from you are Metal Slime-types that give very high rewards for killing them, and they do that regardless of your party's level.
In Planescape: Torment the seedier parts of Sigil included street thugs that initially were not hostile, but would become so if you stood still for a few second while in their line of sight. They would never relent even as the player's party killed them in single strikes.
They would, however, bolt if their assault didn't do anything. In other words, any still alive after about 15 seconds would break and run.
Though removed from the original release, a third party patch restores a situation where a spoiled, effete noble is travelling Sigil's slums, provoking the largely helpless residents into duels to the death. Should the player converse with him, the noble sneers at the group in a misguided effort to do the same. Should you accept, and unless the PCs are drastically underleveled for the point in which he appears, the noble is soundly crushed.
Lampshaded in Knights of the Old Republic: Returning to the academy on Korriban after the confrontation with the instructors, you encounter a few students who intend to attack you. You can point out that you have already bested the head instructors of the academy and they do not stand a chance against you. This only makes them hesitate slightly before attacking anyway.
In the sequel, your party ends up in holding cells without weapons or armor at one point. A bounty hunter intending to kill you enters the room and gets goaded into letting you out. It goes about as well as you'd think for him.
The original game also contains one of the most insane examples of this trope. In a certain quest, a Mandalorian previously under Canderous' command seeks revenge on him. He brings two mercenaries to the battle to back him up, both pretty weak against a Jedi. You can talk the Mandalorian out of seeking revenge, at which point he commits suicide, and despite the employer who hired them no longer paying them to do anything, the two mercenaries will then proceed to rush to their near instantaneous deaths for no reason whatsoever.
In Geneforge, if you incurred the wrath of a specific town in the first game, even UNARMED townspeople and merchants would attack you. In the later games this was changed, as "civilian" characters are constantly afflicted with "Terror", and flee, while only guard type characters will actually attack you.
Worth noting is that with the right preparation, you can literally punch three such schmucks to death in a single turn.
Towards the end of Fallout 1 and 2 your character is usually wearing Power Armor, carrying one of several endgame weapons that can either disintegrate enemies instantly or rip off their torsos. Despite this, crossing the desert will get you attacked by punks wearing leather (barely above going naked, armor-wise) and armed with small pistols (which can't even penetrate your armor, not that it'd matter with your hundreds of hit points), who can usually be taken out all at once with a single attack from your minigun. Not to mention the rats.
This also applies to your allies, who all too often insist on charging headlong into battles between you and other heavily armed—and armored—foes. The fact that your capability for taking on these powerhouses obviously does not extend to the rest of your party never seems to dampen their enthusiasm.
Fallout 3 does it as well, mostly. Raiders and Mercenaries will still attack you on sight, but if you do enough damage to them they'll sometimes yell, "Fuck this!" and try to run away. This won't stop Super Mutants and Enclave Soldiers from attacking you, since they do remain a credible threat throughout the game.
Fallout: New Vegas plays this trope straight. Every time you visit Freeside, expect to get attacked by a naked mugger with a pathetic melee weapon. Even late in the game, when you have powered armor, incredible weapons, and pair of lethal followers for backup, they still think its a good idea to try to take your lunch money. Of course, if someone's jumping at you naked in the desert, he's probably not playing with a full deck.
Worse, if you have a good reputation in Freeside the local gangbangers will also attack them often meaning they die before getting in sight of you. Not to mention ones who spawn within range of the armoured, heavily armed Securitrons who guard the entrance to the Strip...
Played straight in the Pokémon games. Generally, if another trainer sees you it's automatic battle, whether the other trainer is a good match or his Pokémon are 30 levels below yours. Also, wild Pokémon throw themselves at you with abandon, especially in caves, regardless of how leveled up you are. However, there are a few Pokémon that will run away from you instead of battling, such as Abra, which Teleport away. However, this isn't self-preservation - Teleport is literally the only thing they can do.
If a certain book in the Canalave Library in Diamond & Pearl is any indication, the main reason many Pokémon attack you is that they actually want you to train them and are trying to impress you. Even the cocoon Pokémon who only know how to Harden themselves at you.
In the case of trainers this is a largely Justified Trope as you're playing a kid whose army of all-powerful monsters stays safely hidden away in your Poké Balls until after the battle begins. The trope is in full force in HeartGold and SoulSilver, however, as you can now have one of your Olympus Mons follow behind you everywhere you go.
In Pokémon Black 2 and White 2, there are trainers who will challenge you every time they see you, no matter how many times you defeat them. Their Pokemon never get any better, although yours probably do. They seem to be doing this intentionally, as they're usually Breeders who care about raising and training Pokemon.
Mount & Blade's battlefield AI lacks any form of morale, enemies always fight to the death and a single half-naked man armed with nothing but a handful of stones and a rusty kitchen knife is perfectly willing to charge unflinchingly at an army numbering in the hundreds.
Made weird by the fact that on the campaign map, these weak armies do flee from yours. Once you catch up with them though, they forget all their fears. This also applies to their pre-battle banter, which will always be confident even though their army has been running from yours for the better part of an in-game day.
In Warband, enemies do run away from battle, even if it's 50 against one, but of course in the case where that one is mercilessly slaughtering a great deal of those 50. They are more likely to attempt to flee when you take down the leader.
Providing a page quote, Dragon Age: Origins mostly plays this entirely straight. Enemies never fall back once the battle has started, unless they're leading you into an ambush. This is actually used to make a scene creepier a few times, as one by one the Demonic Spiders step aside without attacking.
Subverted once in Dragon Age: Origins – Awakening, wherein the Player Character has to face down a group of kidnappers. While it is possible to fight them all, if the Player Character reveals his or her identity several of them flee the scene(including one who jumps off the edge of the cliff rather than fight the player)
There is a similar conversation near the start of Origins; it's possible to intimidate the bandits who accost you outside Lothering by pointing out that you're a Grey Warden.
Another option for threatening the Lothering bandits is pointing out that you're a mage, if that's your Origin.
This also works with Dwyn in Redcliffe. "I'm a mage. Care to rephrase that?" "In the interests of not having my face catch fire..."
Dragon Age II: At one point, Hawke and his/her companions can track down a bunch of blood mages, killing the worst of them and either convincing the rest to give up or helping them escape. Either way, their leader sees quite clearly what Hawke can do. Six years later, you come across the same woman again, who can kidnap your sister/brother (if you knew to save them) and intends on killing them to prove a point. Depending on your actions, a Templar and associate of this mage can both tell her what she's doing is foolish, but she says she will prove herself by killing the Hero of Kirkwall. Just to reiterate, she intends to kill a heavily-armored hardened hero who bested the leader of a foreign race and almost single-handedly stopped an invasion of Kirkwall three years before (and, at this point in the story, possibly killed a High Dragon, the toughest enemy in the game), and (depending on who you brought with you) several experienced companions who are all sporting similar armor and weapons, not to mention loyalty to Hawke. To say she's "suicidal" is an understatement.
Snarky!Hawke can respond to a comment on this made by Zevran during his cameo mission with "Believe me, it's a burden I bear on a daily basis."
Devil Survivor is terrible about this. A demon with one hit point and both of its "sidekicks" dead will almost always still attack you no matter what your situation is.
Every now and then, you'll see one run and try to hide in a corner. Still the exception, though.
The Elder Scrolls monsters rarely run away, especially in Arena and Daggerfall. They were more likely to move towards you even if they were a mage. In Morrowind creatures were more likely, though still rare, to flee, however that was temporary and the effect was used as a method of varying combat rather than calling retreat (they were still in combat mode and would charge right back towards you after a few meters).
In both Morrowind and Oblivion, enemies beaten unconscious will spring right back to battle as soon as they regain consciousness. Every single time. Even if they haven't yet landed a strike of their own.
In Skyrim, every time you bring a humanoid NPC to very low health, they fall to their knees and surrender or beg for their lives. When you do nothing and let them get back on their feet, they resume fighting. Low level enemies such as standard bandits also cheerfully ignore the fact that you may be equipped with Daedric armor and weapons despite the fact that you can kill them in one hit with a normal attack.
Skyrim is littered with NPCs who'll try to pick a fight with you, accepting which starts hand-to-hand combat. While all this is by no means unusual, said NPCs will pick fights with you even after it becomes known nationwide that you're the Dragonborn - which means you've killed at least one huge dangerous dragon. This doesn't seem to faze them.
This makes a certain crazy kind of sense - When they inevitably lose they can still say they were brave enough to go a few rounds with the Dragonborn
They will also cheerfully offer to fight Khajiit characters in unarmed combat, even though Khajiit have a huge advantage in "unarmed" combat due to their large claws.
Ladies and gentleman, Maurice Jondrelle. He's an optional NPC follower who may join you during "The Blessings of Nature" quest and if he's with you at the goal you get an alternate option for finishing it. But good luck getting him there alive without cheating. He is essentially a civilian monk, unarmed, unarmored, lacking in any of the control commands that normal followers have (i.e. "Wait here.") and utterly devoid of survival instincts or actual combat ability. None of this stops him from attempting to box anything that attacks the player: bears, sabre cats, giants, aforementioned huge dragons...
He'll also attack the player if he is told the purpose of the trip was to wound the sacred tree of Kynareth. May be justified in that he's a very devout follower and couldn't just watch you casually desecrate one of his goddess' creations, but it's still pretty suicidal of him.
In Final Fantasy XII every red enemy in the field will go after you, regardless of your level. Early in the game, your level 5 duo can get swarmed by level 16 Werewolves, but mostly it just means Mandragoras will keep pestering you whenever you return to grind for elements in the Sandsea.
Paper Mario. It eventually gets to the point where you will be running away from low-level enemies because fighting them takes too long and has too little pay-off.
Mass Effect, all games. Intimidate or persuade options can sometimes prevent a fight from breaking out, but this trope is in full effect for anyone already flagged as hostile. There's also numerous examples of barely armed civilians choosing to suicidally fight you rather than face arrest. In one mission in the second game, your party encounters a pair of mercenaries fleeing in panic from a horde of rampaging krogan. They immediately stop up to hose your heavily-armed party down with automatic fire even if you haven't done anything to them.
Exemplified during Miranda's loyalty mission in the sequel, at one point, Miranda and Shepard are stopped by an Eclipse lieutenant who brags that his men already have shots lined up, and explains that you should give up and walk away. The Renegade interrupt in this sequence has Shepard break the lieutenant's neck before s/he and Miranda (who immediately pulls out her weapon as soon as Shepard makes a move) take down several enemies by using environmental hazards, which leaves a lone salarian commando staring in shock at what just happened. He'll still open fire on you once the battle starts without any sign of retreat.
Honestly, ME 2 is one of the worst offenders in recent times. Everybody knows you - you are Commander motherf**king Shepard, a person who has personally mowed down armies of baddies and saved the entire galaxy from omnicide. Yet, random merc # 17001 is still convinced that he can kill you in a few shots. The only one Genre Savvy enough to notice this is Garrus:
Garrus: The Collectors managed to kill you once and all it did was piss you off. I can't imagine they'll stop you this time.
Justified in Mass Effect 3; every enemy, from Cerberus to the Geth to the Husks, is indoctrinated by the Reapers or The Illusive Man. The only enemies who aren't are the few Reaper Destroyers you fight and KaiLeng, and them attacking you is completely justified by their personalities; they're all very ignorant.
Kai Leng definitely fits the "over-confidence" part, considering himself far better than Shepard (he's good, but he's not that good) and he cheats like crazy when he does fight Shepard). His boss tells him not to underestimate Shepard but he may as well be talking to a brick wall. He even takes being compared to him/her as an insult to his skills.
Averted in the Exile series, where many low-level creatures will simply "run away" or "get scared" when they go to randomly attack you.
Everything in the Might and Magic series. Monsters may run away if their HP becomes low enough, but they'll start a fight with anything.
This is partly an exception, though, as even the most powerful foes will retreat if they run low on HP. Also, magic users of any kind will always fire their magic while running (even dragons don't stay in one place while they fire, but rather move in a circle around you).
Averted and played straight in Dragon Quest IX in that enemies are programmed to flee from you if your party is significantly more powerful than them, but the strength difference that they finally start fleeing from you at is so high that many monsters will still be charging you down long after you can likely kill them in a single hit.
Averted in a Suikoden II side quest in which bandits decide not to attack, because they realize how outclassed they are.
Enemies in the Mario & Luigi series will always attack you regardless of your strength, attacks or anything else. Even the ones right at the start who can't stand up to a single hit from anything gotten after the first quarter of the game. The only exceptions are Gold Beanies, which like the Amazy Dayzees in Paper Mario, flee from battle as quickly as possible.
Enemies in the FreeSpace series will keep attacking down to the last man, regardless of odds. This is especially egregious with bombers, as a wing of AI bombers will continue on a constant course and speed even as their wingmen explode around them.
Both played straight and averted in Operation Flashpoint. On the one hand, AI squad leaders have a nasty habit of sending their men off on suicide missions to attack targets they have no hope of defeating, such as in one mission where the player's leader always orders the squad's anti-tank guy to attack four enemy tanks. It's suicide and utterly futile, because your squad has been ordered to retreat anyway. On the other hand, squads that take severe casualties will often abandon their mission and retreat, and you're specifically ordered to withdraw at several points in the campaign.
Subverted in Steel Battalion. All the enemy mechs do this, but this is exactly the strategy that will be liable to get the player killed, since the game is remarkably micromanagement intensive.
In the X series, scout ship pilots see no problems in engaging superheavy fighters that can blow them away by looking at them sternly, and they're foolhardy enough to try attacking capital ships. And it's not just limited to scout ship pilots: EVERY single being whether from an insane race of robots, a murderous horde of leeching bee people, or what have you is prone to attacking any ship even if they're biting at them a lot more than they can chew.
The later games of the series feature scripted attack by races at war with each other. While attacks on border sectors are plausible, occasionally the battle script picks a home sector as the target. Witness a bunch of ships sail headstrong across enemy space, heroically uncaring of the patrol forces picking them apart along the way, until the broken remains of a once-decent attack force smash themselves fruitlessly against the massed defenses protecting the home sector.
In Mech Warrior 4: Mercenaries, most enemies will throw themselves at you regardless of weight differences. A 20-ton Flea will charge into spitting distance to use its small lasers and machine guns, even if you're in an Atlas that weighs five times as much and could probably kill it with a single salvo at 600 meters. Only three missions in the entire game have enemies retreat when clearly outmatched, and this is usually only after a scripted tally is met. An early mission has the pilot of a small, 35-ton Owens challenge Specter and his entire lance of Battlemechs all by himself. Specter finds his chutzpah amusing. Briefly.
Guard: You have violated a Halloran Protectorate outpost! You are ordered to power down and surrender your 'Mechs! Specter: Spunky little fella, isn't he?
Third Person Shooter
The Silencers of the Crusader series of games are regarded as the most terror-inspiring, unstoppable killing machines ever born, bred, or built. Yet even the lowliest guards, all by their lonesome, will say things like "We've got him now!" before attacking and being duly slaughtered.
In Max Payne 1, in spite of the news going around that Max Payne is on the loose slaughtering mobsters and anybody in his way, the lowliest of thugs will try their hand at taking the player down. To be fair, plot-wise, there is a severe blizzard going on (disrupting communication equipment) and the game begins spawning Elite Mooks regularly by the end of the game, and if you're not well-practiced in the game, you can die as easily as a minor mook.
Nicole Hornelamp shades this over a loud speaker near the end of the game to her Elite Mooks, telling them they are better trained and equipped than Max is, in spite of an off-screen complaint that "He is unstoppable."
Turn Based Strategy
Advance Wars does this — the AI will always direct its units to attack whatever it can deal the most monetary damage to, regardless of actual strategic position. Thus, the AI will gleefully run its armies into your infantry squads to kill them, ignoring the fact that they're blanketed with artillery kill zones or has a megatank in its midst.
The various sequels actually change this from game to game. Advance Wars itself had a penchant for hunting down loaded APCs, with the apparent goal of trying to kill two units with one attack, and a loaded APC was wonderful bait, since you are risking only 6000 cash of units, which may not even die, to lure out an enemy unit that might otherwise do over 10,000 cash in damage to another, more vital unit. Later games skipped this, but still prioritized hunting down infantry attempting to capture cities or factories (which is generally quite smart, but still exploitable). Days of Ruin actually saw enemy units that simply refuse to attack your units if it would require running within range of two or more artillery units, or other units which could easily counter it (which would make it a suicidal attack). This depends somewhat on the AI package they are working with, however.
In the Disgaea series, some low level enemies are completely willing to bash your level 9999 character over the head, fully knowing they will more than happily counter immediately.
Played tragically straight in a stunning aversion of Story And Gameplay Segregation during Final Fantasy Tactics. During a mission roughly two-thirds of the way through the game, Ramza encounters a group of enemy deserters comprised entirely of low-level, underskilled opponents. Initially they plan to fight thinking they have no choice, whereupon Ramza points out that no, he's not leading a pursuit unit. They then recognize him as a dangerous man with a bounty on his head and decide that they can kill him where elite soldiers from both sides of the war have repeatedly failed. Cue Curb-Stomp Battle.
This is even more hilarious if you have Orlando on your party; he is a legendary and once highly-visible warrior famous (rightly) as a nearly-invincible killing machine capable of winning entire wars by himself. Starving, barely-competent NPCs will nonetheless attack him without a thought.
In Final Fantasy Tactics Advance, your average enemy will attack your units no matter what. Oftentimes, a white mage (capable of doing only 1 hit point of damage per melee strike) will try and hit your fighter (who blocks and counters all non-special melee attacks and can do 300 damage in one hit to a low-level white mage) if he/she's at good health. And promptly die later. Of course, oftentimes the same white mage, if he/she survives will then run, heal him/herself, and try it all over again. Until of course, white mage blood is scattered all over the ground.
Don't forget the archers who keep trying to attack the units with Block Arrows equipped. Or better yet, Return Fire.
This has more to do with A.I. Roulette, which makes the AI perform moves randomly, even if the ability will always fail. Could also be for balancing purposes since most reaction abilities would never be seen in action if the AI could always try to avoid it.
Very noticeable in the Fire Emblem series, where enemy units will almost invariably attack any of your units that come with their range. Even when they have absolutely no hope of survival, or even damaging them. It's actually quite annoying in places, such as where an enemy with a long range dark tome (which tend to have somewhat lengthy attack animations) will insist on attacking a unit that it has a 0% chance to hit.
The AI seems to favor attacking units who can not counter attack first. This seems solid until you unequip the weapons of a high defense unit, causing the AI to attack them even when they have no hope of damaging them. However, it is worth noting that the AI will also choose to attack really injured units even if they can counter attack in FE 9 or 10, even if there is a healthy unit that can't counter attack within the same range.
In fact, the AI is so enamoured by the idea of attacking units which cannot counterattack that in several games of the series, they will prioritise attacking units which are currently holding weapons with only one or two uses left in order to set up a unit which can't counterattack for other enemies. However they don't take into account any other weapons which the unit may have on them (and which they will automatically swap to using when their equipped one breaks).
The AI does show some relative brilliance though. If they are within range, they will target weaker Player Units. This is very exploitable though, as you can set up units you want to level up first in front of these units, and, unless the enemy can use long-range attacks, they will always die to your Wall (unless you get very unlucky with the RNG).
The only exception are enemy thieves, which generally don't attack you at all. Of course, their real point is to force you to rush to the treasure chests before they nab the loot and flee, and they're implied to not even be part of the enemy's army at all, but rather just unaligned looters trying to get their hands on the treasure of the palace you're fighting in.
Averted in FE 4, where enemies will not attack units if they have 0% hit rate, and in that game any successful attack will deal minimum 1 hit point.
The instruction manual for a computer game version of the board game Risk had a section in the back where members of the development team talked about their favorite strategies and tactics. The art director wrote, "Is there more than one army in a territory? If so, attack. Repeat until game is lost."
Trade Galleons carrying nothing but grain see nothing wrong with firing at you as you sail past them in Sid Meier's Pirates! if your infamy is high enough, even if your ship is the most powerful vessel in the Caribbean, you have defeated all the other famous pirates, are a baron in several different countries, and have a bounty of hundreds of thousands of doubloons on your head.
Despite the (likely visually obvious to the trade galleons) difference in ship quality, a large bounty may have actually encouraged them to attack the infamous pirate.
Ditto Super Robot Wars. The usual AI script has enemies making sure to attack the target that would take the most damage from a successful attack, but never bothering to check if it's even possible for the attack to hit.
Though this is getting a little worse in the newer games, where there seem to be a few more parameters than target HP.
Super Robot Wars Judgment tried the other way : enemies will attack mechs they have the biggest chance of hitting... which means they mostly target the Super Robots (that means serious damage at best, and BRUTAL RAPE at worst) and battleships (attacking the Archangel is a good idea. The Nadesico? Not so much.) The result was a terribly easy game, with your supers plowing through enemy lines like butter. So yeah, they're better off targeting reals.
Battle for Wesnoth has a similar problem to the Advance Wars example. The AI will engage the unit it can inflict the most damage on while taking the least in retaliation. This is a sound strategy that works with the Tactical Rock-Paper-Scissors nature of the game (sending archers against cavalry, mages against infantry, etc). It is also complete tactical suicide, as it leads the AI to frequently move into the worst possible terrain and positioning. For example an AI might move a bowman into a swamp hex next to a knight to shoot at him, completely ignoring the fact that the bowman has an absolutely awful evasion rating in the swamp and will be easily crushed by the knight's lance charge on his turn.
Wide Open Sandbox
Appears in the Escape Velocity series. Even if you're flying a heavy capital ship and have conquered dozens of worlds, pirates will still try to rob you while flying fighters or light freighters.
Actually averted in the third game, Nova, in which the AI takes the strength attribute of an opposing ship or fleet (including the player's) into account before initiating an attack. Still, they won't run away if the player attacks the AI ship, unless they're set to run away from every fight or run at 25% shields.
Taken to horrifyingly new heights in Borderlands. The fact that the player can cause low level enemies to explode simply by stabbing them doesn't stop level 4 bandits from attacking level 61 players in possession of all the shiniest equipment available.
In Spore, no matter the creature, your opponents will continue to attack until one of you dies or you stay out of their field of vision for about thirty seconds. Even if you are a huge monstrous beast and they are tiny and weak, they just attack. And attack. And attack.
Killing a baby or eating eggs will make the entire species act this way immediately upon sight.
This continues into the Space Age. You can be a level 5 superpower who whittled your enemy to an inhospitable ice world, and they will whole-heartily continue to futilely defy you.
The Panau soldiers in Just Cause 2 behave this way (they actually shout "Attack! Attack!"). Their radio communication remains very confident, and taking a bit of damage results in enthusiastic responses like "He's bleeding like a stuck pig!" This attitude will not change after killing two dozens of them, demonstrating the ability to fast-rope in circles around them, and hijacking their Gunship Rescue and emptying its miniguns on the troops armed with pistols.
They are smart enough to run away when you throw a grenade at them. But that's pretty much the extent of their self-preservation; they will not, for example, show any sign of fear while barreling towards the smoking pile of cop cars you blew up mere seconds ago with your military chopper's infinite-ammo rocket launchers.
Scarface: The World is Yours. No matter how many guys wielding chainsaws fall before your SUV/tank, the rest will come screaming at you. Until the last few decide to run.
Saints Row 2 is no stranger to this trope. Even better is the Ronin's attempt to do a full frontal assault on Aisha's funeral, taunting Johnny Gat, and then thinking they can take both Gat and The Boss in a straight up fight. It does not end well.
The sequel has random grunts thinking they can take on The Boss on the streets. This is after diving through a plane and performing a very public raid on the National Guard. It's justified early on since the Saints have no control of the city, but as the fight gradually turns against them you'd think more of them would run...
Matt Miller DID run away, but only after being nearly killed.
Prototype: Alex Mercer has more superpowers than he can count on both hands (when he has hands). He reacts to all threats to himself and his interests with increasingly violent murderous fury. He shrugs off melee attacks and is at best mildly inconvenienced by bullets, rockets, fire and explosions. If the attacker is unlucky, he/she/it will be eaten upon defeat, which will only make Alex stronger. Every living thing in Manhattan except the civilians will still attempt to shoot/claw/rip/pummel/explode him in a fight, instead of, say, running for the relative safety of another continent.
In Oblivion, non-enemy NPC's, and some creatures will only ever attack if the player attacks them first. A handful of creatures will actually run away if the player approaches. Sometimes, enemies will flee combat if their health gets low. However, there are very few NPC's or creatures that display this behaviour - most are ludicrously aggressive and will always fight to the death. Even if the player obviously very powerful and they do not stand a chance.
Yakuza has street punks walking up to you, challenging you to a fight if you're in their turf. This is normally somewhat justified in that they often have you outnumbered, but even so you have random street punks harassing a not-harmless-looking clearly-a-Yakuza, or even worse solo fighters challenging built-like-a-shit-brickhouse-on-steroids Saejima.
In Batman: Arkham Asylum there are two modes of combat: Freeflow and Predator. Freeflow involves fighting a large number of (mostly) unarmed baddies. Predator involves staying out of sight and picking off several armed baddies one by first. When you come across a group of unarmed thugs they will hesitate before attacking. When you encounter a group of armed thugs they start out confident, but as their numbers thin they become increasingly frightened (you can even check their heart rate) and desperate for mercy, while their Bad Boss Joker simply laughs at them for failing.
They will also try to use any kind of weapon they can find, so they do know that Batman's more than a little good at fighting. On Hard, though, large groups of baddies are actually pretty competent, and they will attack faster and more frequently. If you get hit, and it's later in the game, they will bounce you around mosh-pit-style and do a good deal of damage if you can't escape.
Batman: Arkham City ratchets up the aversion where armed thugs are involved. Successful Predator KOs (i.e. actual one-hit takedowns where the thug doesn't see it coming) intimidate thugs a lot more than getting spotted, getting a few punches in, and then retreating before being shot too much. Taking down most of a group with nothing but Predator KOs will often end with the last one horrified and in extreme cases unable to retaliate even if Batman walks right up to him.
This is especially apparent when a heavily armed thug will flinch if Batman appears from the front, giving him more than enough time to take the poor fool out.
Also, early in the game when Batman drops into a room with 40+ mooks, all but a few of them run away in a panic. Because he's the goddamn Batman.
Though they're the minority, some inmates will immediately run and cower in a corner. This is a permanent surrender, and Batman won't let the player attack them.
Played absolutely straight in the combat challenges, where even racking up a 507-hit combowithout taking a single hit in return for the entire duration of the fight will, for whatever insane reason, not make everyone else decide that perhaps hiding in a corner or immediately surrendering and pleading for mercy is a wiser plan of action than attacking a man who has just taken out dozens of their comrades, is showing no signs of tiring, and is stillsmiling. The mooks will continue to rush in, bragging about how easy this is going to be, and attack with complete confidence that they can take this guy. Perhaps it's because he'sincredibly pretty. No excuse for not fleeing from Batman, though.
One level in Max Payne 3 has an enemy run into the room you're in, as usual, but then gets on his knees, drops his gun, and surrenders.
Cubivore lets you break up large packs if you can take out a couple of their members quickly enough, and if they are not in large enough numbers, weaker foes will usually run or guard indefinitely on sight.
In the Halo series squads comprised of grunts or groups of grunts left over after the local Covenant heavies have been killed off will usually go into a blind panic and try to make a run for it when a power armored super soldier is bearing down on them, jackals will also tend to fall back to stronger positions rather than voluntarily remain at a range that allows a Spartan to beat them into meat paste with his augmented fists of death. Elites while generally confident usually try to duck somewhere safe and walk it off if their shields get dropped. On the other hand Brutes and Hunters tend to lose their cool and become even more aggressive if the situation is turning against them, sometimes to their benefit but usually not.
Enemies in the S.W.A.T. series of Tactical Shooters aren't just capable of retreating, they can also surrender (or fake surrender) and drop their weapons if you can pin them down, allowing you to restrain them.
Similarly, the otherwise unremarkable RTTChicago 1930 would sometimes have severely outgunned foes put their hands up.
Metroid Prime 2 has a Wolf Pack Boss that would be very difficult if not for the fact the others runaway once one dies. Also, Dark Pirate Commandos will flee if the fight takes to long. Ing will also avoid your charged light beacons if you just turn one on without trying to trap one. Hunters final boss becomes more annoying by not adhering to this trope, should you unlock its extra phase. Other enemies in the series only opt not to attack at certain plot points however, mostly playing this trope straight.
The AI for the Galactic Civilizations was designed with this in mind. A weaker race will not attack a stronger enemy without allies. Also, the AI remembers who started the war, and their subsequent groveling directly references that.
That said, the AI isn't a very good judge of who is a stronger opponent: it only counts existing deployed forces. It doesn't consider, for example, that you have 300,000 billion credits in your treasury and twice as many military technologies researched as it does, meaning it will gleefully attack only to see you instantly purchase an army that will flatten its forces in no time.
Escape Velocity: Nova features a mechanic whereby ships of a given government can determine that the odds of a battle are hopeless and withdraw. Each ship has an arbitrarily assigned "Strength" value, so the factions compare their preset maximum odds to the ratio of the sums of the Strength on both sides.
Also, ships with the "Wimpy Trader" AI are guaranteed to run for their lives rather than try to fight.
In  2, if a much larger stack of troops moves towards a much smaller stack, most of the time the AI will most often try to get away from their certain death, and will rarely attack your entrenched troops with nothing less than a much larger force.
Played straight in Dynasty Warriors, but averted in Samurai Warriors. In DW enemy privates will stay around so long as there's someone to fight. In SW, killing their officer will send the remaining four or so footmen fleeing.
Not completely played straight in DW. Subgenerals will flee as soon as their superior is killed. Everyone else stands around and lets you kill them, though.
Any enemy who sees you kick enough ass in Warriors Orochi will turn tail and flee. It's harder to invoke this if there's an enemy officer present as apparently, no one wants to be charged with desertion. The Warriors series is about taking on entire armies nearly by yourself, and this whole thing makes it even easier to remove large groups of enemies from the battle; kill a few in a spectacular fashion, and the rest will run away like cowards.
In later Sengoku Basara games, killing squad leaders will cause all the mooks in that squad to stop fighting and run away, unless there's another squad leader or boss around.
The Lord of the Rings Online averts this to a point. Any enemy that is 9 levels or below you will not attack you unless you either attack them first, or are in a group instance. This "feature" only affects initial aggro and not reactionary aggro. So if you attack one, his friends will join in.
In zOMG!, mobs too far below your level do not attack you unless you attack them. If you cap your level within the range when they would usually aggro you, they will. Certain mobs do not aggro at all unless attacked and it is unwise when players new to the area attack them, to say the least.
Kill somebody strong (or a group leader) with a critical hit in Incursion. Pass an intimidate roll. Watch everybody fleeing in terror. Also, enemies more often than not flee when badly injured.
No matter what they are facing, Goblins in Dwarf Fortress start out in Attack Attack Attack mode, but if enough of them get ground up by your elite troops/magma-filled death traps/giant guard-spiders the survivors turn and run for it.
Exaggerated by the elves, who will gleefully charge your adamantium-clad, artefact-wieldingtitan-slaying army whilst wearing cotton and brandishing wooden swords. They do still try and run away when they realize the sheer magnitude of their stupidity.
If you make an enemy of a civilization in Adventurer mode, the entire town will attack on sight, including civilians and infants.
In X3: Reunion, while most pirates will mindlessly try to kill you (sometimes entirely on their own accord) even if they are in a puny M5 light fighter and you are in a M7 light capital ship that just slaughtered an entire squadron of Khaak fighters on its own, pirate freighters carrying illegal goods will often choose to avoid a fight they can't possibly win and surrender their cargo if you order them to do so.
Occasionally averted in X3: Terran Conflict. Every once in a while somebody in a flight of fighters has a flash of brilliance and runs for his life.
Averted in FTL: Faster Than Light. If you have enough high level weapons you can intimidate enemies to not engage you. Other ships will try to run if they are simply transport ships or you have heavily damaged their ship. Still, you can run into ships that are physically incapable of hurting you (say a ship with only weak beam weapons if you have a shield or you have more layers of shields than they can fire lasers), allowing you to level grind to your hearts content.
Role Playing Game
In Final Fantasy, as your party leveled up ordinary monsters would begin fleeing battles of their own accord.
In the Suikoden series, the "Run" command in combat is replaced by "Let go" command if you sufficiently outlevel your opponents; the implication being that the enemy will flee as soon as you give them the chance, but can't escape if you don't let them. Since your reward for beating up on weak enemies is generally minimal to the point of irrelevance, it's a very handy feature.
Entirely avoided in Guardians Crusade. Enemies (represented on the overworld by white tadpole things) who are weaker than you are much smaller and actively run away from you, whereas the stronger ones are bigger and chase you down (as do the more evenly-matched ones).
In EarthBound, the enemies will actively run away from you if you're too powerful for them, although if you like you can catch up with them and instantly defeat them for free Experience points.
Done further where if you defeat the boss of a dungeon, even if the other inhabitants are around your level, they will flee from you because you kicked the butt of the strongest creature in the area.
In Persona 3, enemies weaker than you will attempt to scurry away instead of engage in combat. The game's Metal Slime - itself pathetically weak - will also run if it notices you at all, meaning you have to waste time sneaking up on them. And since the Reaper shows up if you spend too much time on one floor...
If you catch a weaker enemy, there's a very good chance that they'll start the fight with the Distressed status effect - they're freaking out.
Contact avoids this; if your stats are high enough or you've got a powerful weapon equipped, enemies will actually run away from you.
Baldur's Gate II: Throne of Bhaal features plenty of examples, but also exceptions. The first curious reversal is that all the unimportant thugs and soldiers you encounter become tough enough to make your above-20 characters break a sweat (though often still no more than that), and also start attacking in groups big enough to apparently justify their confidence, so that you end up fighting small armies of nameless Mooks more powerful than most heroes in the setting and laden with magical equipment. Another is that characters who are actually much more powerful numbers-wise than yours and whom you can only beat by utilizing your entire party to its best advantage and simply playing smarter than the computer start respecting your player character as a powerful "godchild" (literally) or demigod. Sometimes these are both combined, so that one random lich no-one's ever heard of is level 30 but still afraid of you. This would be Genre Savvy if they had realised you're The Hero, but that's not the reason.
In the Gold Box AD&D game Death Knights of Krynn, you'll get accosted by gangs in Kalaman, but after beating them, when they meet up with you again, they just say "Pass, friend" and rush away in a hurry. Same thing in Vingaard, when the gangs demand a road tax, a refusal leads to an easy fight, but after one or two they stop asking for the tax and say they were looking for someone else.
Both used and averted in the Deception series. Certain storyline encounters, as well as certain classes of invaders, will attempt to flee from the player, or even from the castle he inhabits, through the course of the game; if they escape, the storyline can change a little to reflect this. This can get very annoying if they start camping out inside of hallways where it's impossible to place traps.
In Fallout 1 and 2, if an enemy becomes heavily injured, they will try to flee. With the emphasis on try.
The Dragon Quest games play with this a bit. Nearly all enemies run on an A.I. Roulette, so those that can flee might not try before they're slaughtered. However, most of the games will allow the possibility of an enemy fleeing if the level of your character or party is much higher than theirs (with the exception of Metal enemies, which almost always run at the first opportunity). In particular, the early Slimes in the original Dragon Quest will start running away once your character reaches level 10. Some enemies still might not respond however, such as machines (implied to be hardwired to Attack! Attack! Attack!) and zombies (their rotten brains make them slow on the uptake).
In Xenoblade Chronicles the enemies will generally avoid engaging you in combat if they are weaker than you, although Unique Monsters and most plot-related nonboss enemies will still attack you on sight regardless of level difference.
In the first Gothic game, some human enemies (mostly civilian and thief types rather than professional fighters) will flee if the player provokes them into combat and has a higher level than them. This mechanic was removed in latter installments.
Enemies in The Elder Scrolls V: Skyrim may try to run away something like yelling "I yield!" if they take enough damage. When this happens in a dungeon, it's a fake surrender, but if it happens in the Overworld, they may just keep on running.
Enemies in Tales of Graces normally become aggressive when they see you, but defeat enough of any one enemy and it will drop a soul orb. Any monster you've harvested a soul orb from will instead run away if it sees you.
In Drakensang, at one point you may be assaulted by the power-hungry, vengeful militia leader of a small swampy village and his goons (who are all people from the village that you can talk to. If you manage to kill said boss first, all the other villagers will surrender to you and leave you alone. In the second game, during the big battle between Eiliff's men (that would include Eilif, your party and her three giant Marus bodyguards) and Soorman's goons, the "goons" will eventuallt opt for running away and surrender after witnessing you mowing them all down like barley.
Averted (or perhaps inverted) to a degree with Mario & Luigi: Bowser's Inside Story. The small enemies will run away from the huge Bowser without even bothering to fight (and get crushed in one hit when he walks into them)... but they've actually got better stats the giant monsters wandering around that are quite willing to charge into battle with pretty much everything that moves. It's to give Mario and Luigi a chance to level up when they return to the same areas later.
Both averted and played straight in Freelancer. If you're in a powerful enough ship and have similarly powerful weapons, ships of hostile factions while they know that you're an enemy will sometimes, instead of fighting you, know that they will stand no chance and flee and will even tell others not to engage you if they are part of a formation. Otherwise, this trope is done straight. Also, in part of the storyline, enemies play this trope straight even if you've cheated to get one of the end game ships and weapons at the start of the game.
Gloriously averted in IL-2 Sturmovik series. Chase a bomber close enough and they'll drop their payload and start evasive action, sometimes even before you start firing. Damaged fighters will disengage and try emergency landing. Every plane crew will bail out when enough damage is done, even when it's still flying.
In the Freespace mod Blue Planet, human capital ships will retreat when heavily damaged, provided their engines are still working, rather than fight a losing battle. This is in contrast to the original game, where a capital ship would fight back until the bitter end.
Stealth Based Game
In the Thief series, unless you're on easy the enemies really do have more hitpoints and better or almost as good weapons, and most of them will run away when badly injured.
Splinter Cell: Conviction starts out playing this trope straight whenever you meet a new batch of mooks. They know who you are and how dangerous you are, but they charge after you anyway. However, after you rack up a few kills the in-game dialogue shifts and the enemies start clumping together in ambushes, screaming for you to come to them and that they won't fall for the same tactics again. They do.
Avoided delightfully in Assassin's Creed I. Since you control an assassin single-handedly pursuing your target, the local guards always heavily outnumber you, which justifies their confidence that they can kill you in a second. However, after you use your superior dodging and counter-attack skills to ruthlessly dispatch most of your adversaries, the last one or two men standing often either turn tail or, if they're cornered, get on their knees and beg you to spare them.
Also, if you've just killed one of your opponents some of the others may cringe in horror, giving you a chance to strike.
If you engage them only with your assassin blade, they'll actually flee sooner, (up to three or four men will break) because as far as they can tell, you are killing them with your bare hands.
Played straight in that having killed two hundred guards in Venice and having max notoriety does not make random archer #201 conveniently ignore your presence in the interest of not suffering a tragic work-related 'accident', drop his bow and scream like a little girl upon spotting you, or perhaps prematurely start looking around for a stabler, safer line of work. He will start shooting, and then you will stab him dead and move on to random archer #202 who will be no less trigger-happy,
The Godfather. Earn enough respect and the shopkeepers who would just might give you a smackdown instead just hand over the cash.
Turn Based Strategy
In Heroes of Might and Magic, when encountering a relatively weak group of creatures, they will sometimes offer to join your army or run away instead of fighting. A few, however, had AI classified as "savage"; they were always hostile no matter if they were twenty goblins and you had a thousand dragons in your army. In addition, enemy heroes tend to flee from superior armies — if it's their turn, The AI always fires off their most powerful offensive spell before retreating, giving them the ability to decimate an army even if they can't win a single turn.
Similar to the Suikoden example above, in Napoleon: Total War, if an considerably weaker enemy, for instance, one regiment, attacks a larger army, instead of retreating, you can actually deny his attack and send him away. In addition, at harder difficulties, if the AI detects it is losing a battle incredibly decisively, it will typically try to withdraw more valuable units—if enough, the entire force—from the battle,as to not lose an army on the Campaign map.
In the Magic: The Gathering "Shandalar" computer game, winning a battle raises your character's notoriety with the various enemy factions. By the end of the game, enemies will beg for mercy and offer tribute if you spare them (with the tribute being roughly as good as winning the battle would have been).
Wide Open Sandbox
In Destroy All Humans!, ordinary people will, in fact, run away from Crypto whenever he shows up. Of course, they have no means of actually attacking Crypto. Anyone with a gun will usually charge head on into battle.
Possibly justified since, thanks to the mind reading feature, it's quite clear that all these people are idiots.
Averted in 2. Sometimes, cops and soldiers who are injured or intimidated enough will attempt to run away. A meteor falling from the Earth and wiping out their backup is a particularly effective way at forcing this reaction.
Way of the Samurai 2 averts this in a fashion quite similar to Assassin's Creed I (though years earlier). You are just some random wandering Ronin, so it's understandable that a band of Yakuza thugs think they can take you on, but after you've sliced a few of them in halves with well-placed counter-attacks, the rest become frazzled, hesitating in their attacks and losing their style, thus making them even easier to counter. Depending on how overwhelming your display of swordsmanship is, the last one or two may flee outright, and any seriously-injured mook is liable to try and make a run for it.
Sadly, the recent sequel Way of the Samurai 3 plays the trope completely straight - armies of enemy mooks will continue to charge you no matter how many of their colleagues you've killed with a single stroke, despite the changed 'Insta-Kill' system making it even EASIER to slaughter large groups in rapid succession.