There are many good reasons to have a jungler in your team:
The player that stay solo (topusually) while he's lane partnerjungle get more gold and experience.
The jungler can do or help doing some kills by ganking mid (2vs1) or bottom (3vs2) in any moment.
Some champions are more efficient in jungling than last-hitting in lane (e.g. Amumu, Rammus, Malphite)
Best junglers can also take the dragon (190 gold to all team members) early
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A good jungler will know precisely how to kill neutral monsters very quickly and effectively (HP + kill order).
Having jungler implies having two champions soloing a lane, so both solo champions gain more experience than either of the enemies in a two-champion lane.
If the jungler is experienced enough, he can keep up with the level of laning champions, but it's a job!
Don't expect to succeed on the first time.
Practice!
Usually (and unfortunately) some champs will have difficulties to do their jobs as jungler without runes.
(Since the bonus they provide can be quite significant at level 1)
You will have to request help to kill your first monster and make good use of healing potion.
(Take care, as they heal over time and not instantly!)
Then it will be up to you to know when to stop jungling (past a certain level it becomes useless) and also when to provide help to other lanes (since you are invisible most of time, the enemy will be always fearing you...
but you have to show up sometimes for that).
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Having a champion "jungle" allows your team to maximize the available gold and experience available to you.
See this link for experience and gold available per minion wave:
Experience and Gold per minion See this link for experience and gold available in the jungle: Jungle Experience and Gold Scenario 1 (no jungler) 2 champions top - shared experience and gold
1 champion mid - doesn't share experience or gold 2 champions bottom - shared experience and gold 0 champions jungle - "wasted" experience and gold Scenario 2
(jungler) 1 champion top (standard) -
doesn't share experience or gold
1 champion mid - doesn't share experience or gold 2 champions bot - shared experience and gold 1 champion jungle - jungle gold and experice (see the link above)
Now the speed and efficiency of the jungler will change the Experience and Gold they get but average junglers tend to keep up with the players who are in lanes with partners or better while allowing two champions to solo.
Other added benefits include less predictable ganking as the jungler can roam anywhere out of sight of the enemy team without the enemy laner calling them "mia" and better control of the dragon.
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Jungling allows for four things to happen:
It allows for an additional source of income for your team to be harvested.
While your top lane is farming gold, you're taking the gold in your jungle that would otherwise just be sitting there.
It allows you control over the red and blue buffs, which are important not just for you but also for your teammates.
It allows you to gank lanes, helping lanes that are faltering, punishing overaggresive opponents, or help cement an advantage.
Presence of a jungler puts a leash on how people behave in lane.
It gives you control over dragon and baron, which are important objectives.
Having smite allows you prevent stealing or steal these objectives.
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If you have a jungler, the overall xp and gold gain is going up for your team.
The solo laner gets to kill more minions (and perhaps champions) and the jungler earns his xp and money in the jungle.
win/win for both of you.
Do try to make sure not to put a squishy character in the solo lane.
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By having a Jungler, your team will have 2 solo lanes, giving you 2 characters that a re higher levels and hopefully more gold than your opponents.
In addition, some junglers get really high leveled quickly and can pick up more gold as well.
Junglers often gank the enemy for their team, allowing them to recover from unfortunate situations and scaring the enemy so they won't be too aggressive.
Also, in the jungle there are buffs that can help your team, such as Dragon that grants gold to your team and Red and Blue buff that can help the champion who kills the monsters that guard it; the jungler may take these alone or give them to allies to help them out as well.
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I'm fairly new to League of Legends (or DotA-likes in general).   What's the point of jungling versus just killing minions?  Do they give significantly more gold or experience than the peons from either side?
What's the point of jungling?
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The best junglers take the dragon early. They will know how to kill neutral monsters early and effectively. This will allow your team to maximise available gold. It also allows for less predictable ganking and an additional source of income.  Experience points, more gold and assistance with the enemies are some of the most prominent ways in which junglers can be of use.
Experience points, more gold and assistance with the enemies are some of the most prominent ways in which junglers can be of use.