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So, you've just finished laying the smackdown on your opponent with a devastating array of punches and kicks. The screen fades to black...
"Round Two, Fight!" What's this? You and your opponent are standing across from each other again, and you're both at full health. That's right, this is a Three Round Deathmatch. Even though it rarely makes much sense, this has been part of Fighting Games for so long that it's long since become an acceptable break from reality.
The usual way to avert this in Fighting Games is through a "team battle" system, where victory isn't achieved through knocking someone out twice in a row, but simply by taking out everyone on the opposing side. On defeating a member of the opposing team, the winning character sometimes gains health back, as though they got a chance to rest between rounds.
This term pops up in Pro Wrestling, where "deathmatch" typically just means no disqualifications.
Just about every Fighting Game ever made. Let's just leave it at that, and move on to the less-straight examples.
Not quite; we have to mention the egregious example of Mortal Kombat Deception and Armageddon; MK, being a fond believer of this trope already, took it to the ludicrous extreme when they added in death traps, which killed your opponent instantly if you threw them into it...but if you haven't won the Three Round Deathmatch, the next round starts with the opponent suddenly un-deadified and back to full health.
Although there is a slight aversion in the Mortal Kombat (and many others) series in that you can only perform signature Fatality and such moves at the end of the match-winning round.
Mild aversion in Mortal Kombat vs. DC Universe: Fighters do get their full health bar back between rounds, but the various bruises, cuts, and torn clothing they accumulate remain from round to round.
The same applies for Mortal Kombat 9, only moreso. In addition, when a round ends, the defeated character gets back to their feet (some even have special ways to do so - Noob Saibot, for example, drops himself through one of his portals and lands upright) to start the next round.
Killer Instinct uses a variant. Each character gets two life meters. When the first runs out, the character stands back up, the two face off, and the battle continues.
Dragon Ball Z Budokai is similar to Killer Instinct, but raised the ante with up to 10 life meters; there was no knock out until all life meters were depleted.
Vampire Savior also has a similar setup. In Darkstalkers 3, it's enhanced Sony Playstation port, one play mode allows your combatant to have up to four or five "lives" per battle.
Somewhat averted since things like the winner's health and the characters positions don't reset back after each "round." It's more like one long round with a slight pause in between.
Likewise with the first Touhou fighting game, Immaterial and Missing Power. Both players get a second to position themselves after a "knockdown" but there's no reset. This fits well with the single player story mode, where all of your opponents will have multiple stages anyway.
The Super Smash Bros. series doesn't divide the fight into rounds at all, though characters may (and often do) have multiple lives.
Then there are timed battles. Simply kill your enemy(ies) more times in two(give or take) minutes. Oh and grab the coins mode.
And then there's Melee's Bonus Mode, where your score is determined not just by how many KOs you score, but by the style of your fighting.
Examples of the "team battle" aversion include The King of Fighters (since the first game), Marvel vs. CapcomandCapcom vs. SNK. KoF and CvS end rounds whenever a fighter falls so a fight can be as short as one round (in Capcom vs. SNK 2 if your opponent only opted to use one ratio 4 character) or as many as seven (in KoF 2001 if neither you or your opponent opted to use Striker characters and battled to the final character on each team). The tag-team gameplay of the MvC games (and by extension Tatsunoko vs. Capcom) are isolated to single-round, "last team standing" format (KoF 2003 and XI also use this format).
Marvel vs. Capcom: Clash of Super Heroes played this straight in the Playstation version as it didn't have enough power to have 4 characters fighting 2-on-2 with assist characters, limiting it to one-on-one with assist. Once the opponent's life-bar is depleted, they immediately get up and look disappointed while the victor strike's a quick victory pose, before the fight resumes, though the positioning is the same.
It's unclear whether Namco is poking fun at this or not. Characters can suffer injuries that by all accounts would likely end lives, never mind the fight, including broken necks and backs (just try Heihachi's headlock throw. *CRUNCH* goes the neck) and after the round is over and it is transitioning to the next round, the character who was just defeated that round shakes it off, gets up, and assumes their fight stance again. Them crazy Namco guys.
Namco also differs in one team battle game, Tekken Tag Tournament. If ONE of your guys is knocked out, you lose; it's similar to Professional Wrestling's tag team rules, thus giving you a reason to get that injured guy out as quickly as possible. Street Fighter X Tekken also abides by the "first fall loses" rule.
In the same vein, Neo Geo Battle Coliseum that, well, didn't used the "one guy's failure is entire team's downfall" scheme, except, maybe one mode.
In Mike Tyson's Punch-Out!!, each boxing match is three rounds long, and it takes at most three knock downs to defeat an opponent- but the three knock downs have to occur all in the same round.
This is because real boxing works the same way. A boxer can be knocked down an infinite number of times during a fight, as long as they're not knocked down three times in the same round. If they are, the referee considers them to be completely outmatched, and call the fight with a Technical Knock-Out (TKO). In Punch-Out, however, Little Mac can only get knocked down three times in a fight, regardless of rounds; after the third time, no amount of button pushing will get him back to his feet.
The Wii version adjusts this. As before, three knock-downs in a round is a TKO. However, each opposing boxer has a hidden number of knock-downs they can take (generally five, sometimes lower); if this is exceeded, they won't get up before the ten-count (and usually give the special KO animation). Little Mac, meanwhile, generally lasts about three knock-downs, and will be knocked out by a fourth; mashing the buttons can give you one last chance.
Guilty Gear uses the round system (except in story mode, where fights are one round only). The original game, however, had "Instant Kill" attacks, which if connected finished the entire match. Subsequent games changed these to simply finishing the round.
BlazBlue solved this by only allowing Astral Heats in the final round. Story mode always shows you opponent as alive but injured afterwards, even if Ragna's Astral Heat erased them from existence.
This happens most illogically in the video game, Dragon: The Bruce Lee Story. If you've ever watched a kung fu movie, you know that Bruce is supposed to knock the opponent down, and he's supposed to stay down. Unfortunately, in the game, a sailor in a white uniform can not only kick your ass, but come back to fight you in the second and third round. And you're friggin' Bruce Lee!
Justified in Fatal Fury 2 and later games in the series - the first time a character loses a round, they get back to their knees and gasp for breath while the game tallies the round bonus. It's only when the match point is lost that they get knocked out. Notably, some of them even try to get back up only to fall over again (e.g. Krauser, Yamazaki, Jin Chonrei).
Subverted in Art of Fighting 3. The game has a traditional 2-out-of-3 setup, but if a fighter defeats a weak enough opponent with a Desperation Attack, they will be awarded with an "Ultimate KO" and the match will end.
In Gundam Vs series when "duels" are declared (The CPU is set to evade, preventing them from interfering), 3000 vs 3000 is best of 2 rounds while 2000s has 3 lives and 1000s have 5 lives. Time outs result in the defeat of both sides regardless of how much health/battle advantage your team has.
Skullgirls varies. If your opponent chooses to use more than one character, the game is played like Marvel vs. Capcom (one round, last team standing) but if both players are only using one character, it reverts to a Three Round Deathmatch (though both of these settings can be adjusted in the options so you can also set tag battles to also stretch to multiple rounds).
Primal Rage gives you a choice of one, three or five rounds.
Justified in The Last Blade, where the opponent sits up and recovers after the first loss, only going down (or dying) when the match point is scored.
Darkstalkers 3 had a subversion. Once a life-bar is depleted, the opponent immediately gets up with their life-bar completely replenishing while the victor's life-bar remains the same, essentially making the match divided between life-bars rather than rounds, though there was still a round counter. The positions of both fighters would be right where the match ended.
Injustice: Gods Among Us would use this system later as well, and outright said the match was divided between life-bars rather than rounds. A grey life-bar is seen on top of a red one, and once the grey one is depleted, the loser would be knocked really far back and roll a little bit and lie on the floor for a bit, enough time for the victor to deliver a taunt, before getting up and resuming the match in the same position. Again, the victor's life-bar remained the same, meaning it's not uncommon to see one character's life-bar depleted followed immediately by the one who did the depleting become the one that gets depleted. Being on your second life-bar also allowed access to clashes, a combo breaker that can be used to turn the match in your favor, but only once per match per character. Also notably, while the first life-bar depletion has the character lie on the floor motionless for a few seconds, the match point will have the user get back up to strike a defeated pose as if they're even less damaged from the first round end.
In Bob and George, Mega Man loses his fight against Pharaoh Man, and dies. Then there's a Round 2. Mega Man wins this round, then moves on to fight the next Robot Master. The volcano kidpoints out that there should be a tiebreaker round, and Mega Man shoots him.
Pro wrestling calls this the Best Two-of-Three Falls match. Back in the old days before the WWF took over, championship matches were almost always decided this way. It still pops up every so often as a gimmick match (usually with different match types standing in for the rounds; called "Three Stages of Hell" in WWE's nomenclature).
There's also the "most amount of KOs in a certain amount of time" variant, known as the Ironman match where both competitors try and score as many falls on each other in a set time period, usually 60 minutes. This will end with a one point difference, very rarely a Curb-Stomp Battle, or a tie, in which case no one will know what to do in the case of a tie, and eventually the heel will win due to some confusing rule.
Finally, the "Beat everyone on the other team" aversion also pops up in Elimination tag team matches, the most famous being the Survivor Series 5-on-5 match.
Actual kendo (and naginata, and kendo-versus-naginata) matches are fought as a sanbon shobu — a point is scored for a simulated kill on the opponent, but the match itself is the best two out of three, unless time expires.
The same is true of Western Fencing - a match is decided by an agreed number of points (hits of sufficient force to defined target areas), even if the first point would be a killing blow from a real sword.