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In League of Legends Summoner's Rift (5v5), there are 3 symmetric lanes.

If only the minions play, does it last forever? Are the lanes fully symmetric?

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No. Random variations in what targets the minions acquire will cause the game to eventually end. For example, if all 3 melee minions on the blue side target the same minion on the purple side, but each minion on the purple side targets a different blue minion, then the blue side will "win" that minion war by having one minion survive while the other side has no minions left. If this happens enough times, repeatedly, eventually minion waves alone will push towers, and ultimately, the nexus.

It can take a long time, but one team or the other will win. Which team wins, however, is random. Neither side has an inherent advantage if left to simulate itself.

This assumes that there are actually champions in the game but they are just idle at the fountain. If no one is in the game, it will simply end. It will not appear in the match history, and it'll be like the game never happened.

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Should mention the fact that if there are no players in a game, the game ends. forums.euw.leagueoflegends.com/board/showthread.php?t=584563 –  Waterseas May 15 at 18:31
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@Waterseas Added. Thanks for the link. –  StrixVaria May 15 at 18:32
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Someone should do an experiment on this and find out the percentages based on blue and purple sides. –  ChaseC May 15 at 18:40
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@Waterseas But when there are no players playing, and it's just minions, the camera doesn't matter. –  StrixVaria May 15 at 20:20
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@SysDragon Not really. If we assume that advantage is completely random, there is always a chance at every point of maintaining equilibrium. Then there is no logical upper bound to when the game ends. It should be noted though, that given infinite time the likelyhood of maintaining equilibrium indefinitely is infinitesimal; it is non-zero but for all intents and purposes negligible. –  evilcandybag May 19 at 13:23

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