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Riven is a champion that starts the game with no mana but uses lots of spells, that means you need to use runes, masteries, and items to provide her with the mana she lacks. Not only does this allow her to cast her spells more often but it can be turned into ability power once you finish Seraph's Embrace. Ability power is great on riven because a lot of her damage comes from her Broken Wings and Ki Burst abilities and ability power amplifies the amount of damage done by abilities (as the name suggests).

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You want to take mana Marks, Seals, Glyphs, and Quints to deal with your lack of mana early.

Alternatively, you can take 3 Quintessence of Ability Power to amplify your damage early if you are extremely confident in your riven play.

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Utility Tree

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The main reason you want a lot of points in the utility tree is so you can grab Meditation , Strength of Spirit , and Expanded Mind for the increased mana.

You also want Summoner's Insight so you can use clarity to regain mana more often as well as Alchemist and Culinary Master so that you not only get more use out of your mana pots, but when you use health pots you regain mana (which is overpowered).

Phasewalker allows you to recall faster while Scout gives you extra range on your Scrying Orb/ Farsight Orb allowing you to use it to get vision on even farther enemies.

Defensive tree

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You want to take 2 points in Tough Skin because it's overpowered.

Offensive tree

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You want to get ability power spells as you can, making sure to grab Expose Weakness , Mental Force , Arcane Mastery, and a single point in Archmage as they are crucial to Riven's kit (don't worry you don't have to be a wizard to be considered a mage, League of Legends just classifies mages as champions that use ability power).

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Starting Items

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You want to start Sapphire Crystal and two Mana Potion to deal with early mana problems. Scrying Orb allows you to get vision of ojectives like red buff and baron and lets you check bushes without having to face-check.

Midgame

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The second you get enough gold to buy a Tear of the Goddess you should recall and buy it because the longer you have it the more mana you get and this item is crucial to building Riven.

You want to do the same for Mejai's Soulstealer and Rod of Ages so you can stack them as soon as possible.

After buying the above items you can buy your Sorcerer's Shoes and start roaming to stack your Mejai's.

Endgame

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It's now time to finish off your build, start by turning your Tear of the Goddess into a Archangel's Staff (it will turn into a Seraph's Embrace on it's own), then get a Rabadon's Deathcap and a Void Staff to maximize your damage output.

Now that you have pretty much finished your build it is time to give your Sorcerer's Shoes the Enchantment: Captain. If your team had any doubts they will now recognize you as the leader which will make carrying them to victory significantly easier. You should also upgrade your Scrying Orb into a Farsight Orb for the increased range.

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Skill Priority

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You first want to max your W Ki Burst for the decreased cooldown time which allows you to stun more often and do more damage.

Next you want to max your Q Broken Wings for the increased damage as this is where a good amount of your damage comes from.

You max your E Valor last but take a point in it at level 2 just in case the opponent tries to hurt you.

Of course you want to grab your R Blade of the Exile whenever possible.

Skill use

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Riven is a complicated champion and as such there are many uses for her abilities.

You should use W Ki Burst on the opponent's wave as much as possible for the aoe damage as it helps farm.

When the opponent tries to hurt you you should E Valor towards them then mash Q Broken Wings, this catches them off guard and helps you win trades, the lower you are the better it works since it will be even more surprising.

Your R Blade of the Exile is best used for wave clear since Riven doesn't do a lot of damage to minions and the enlarged sword helps her farm faster.

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You want to take Clarity and Cleanse for summoner spells.

Use Clarity whenever you run out of mana to get free mana back allowing to use your abilities more.

You need Cleanse to remove any disabling abilities the enemy champions use on you to prevent you from damaging them further.

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As the leader you need to charge headfirst into battle, leading the way for your teammates. Fear will not help you here, people don't respect wimpy leaders and your team is much less likely to follow you if they don't respect you.

You should rush the first enemy to come into view, using your Q Broken Wings to close the gap before killing them to death with basic attacks.

As long as you follow code of a true leader nothing is your fault, and blame should only be directed towards your subordinates.

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As you can see Riven is a strong champion with lots of tools to carry her team to victory, and you should be able to get at least diamond as long as you follow this guide to the letter (unless you really suck).