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As it stands, in most cases I've found Bloodthirster as soon as possible to be the best possible setup for Riven unless I've been dominated in lane, since unlike other champions her pure offense does scale nicely into defense and most champions can't duel with her.
As for the importance of CDR, I understand it's still a very valuable stat for Riven, I've just found the brutalizer to be anti-snowbally, and don't typically build into it unless I've had a bad time farming in lane. That's why the brutalizer is eluded to in multiple chapters, but only suggested in one build that's designed around being countered at top.
Also, I completely agree with Flash's importance, I typically slot Flash/Exhaust whenever I lane as Riven, I only put Teleport there because experienced solo tops aren't likely to be reading this guide, and I find it to be a better suggestion to the general masses that are new to the role to start by using Teleport to help in team fights and securing Dragon.
I've never used Thornmail on Riven, but I'll keep it in mind. I feel it's completely inferior to Randuin's in every possible way, and while I typically never do build a Warmogs, I put it there for more general leeway for people starting out with Riven. Ideally in future updates I'll enthusiastically point out that most of the late game options for Riven are personal preference and not necessarily the optimal while giving very valuable counter picks to inferior options.
When I first played Riven, I put too much focus on building her Tankier, with her core being Frozen Mallet, Atma's, Randuins and Force of Nature, then I tried out the triple Doran's setup instead, and I should probably emphasize this is primarily a setup for making Riven snowball with viability for late game, and I might consider devoting the second team's Riven builds for an anti-snowball game where she doesn't fall off.
Your opinions seem valid and are greatly appreciated, I'm lucky enough to get groups that will typically give me solo top and am allowed the chance to play Riven at least 90% of the time, I'll test out some of your suggestions and of course update the guide accordingly.
If you're jungling, go Smite and Flash. If not, Exhaust and Flash. Flash is amazing on Riven and you should really always have it.
I agree with the three Doran's Blades. I actually had a rough 2v1 lane with failed ganks from our jungler, and ended up stacking Doran's Blades to try and catch up. I did, and carried the game. But you're going about the rest of the build all wrong.
Once mid game comes along, start building Phage and Brutalizer. You need that CDR. If you happen to do really well early game, instead of going for stacking Doran's, go for that early Bloodthirster. It's amazing the kind of damage Riven can put out with an early Bloodthirster.
Merc Treads are a better choice than Ninja Tabi. If they really have AD carries that are giving you problems, you may need a Thornmail. If the enemy team is very light on CC, go for Boots of Lucidity instead. CDR is REALLY good. Stack it.
After Phage and Brutalizer are finished, grab a Vampiric Scepter if you didn't grab one already. Then start building your Atma's Impaler for more defense. The attack boost will come later.
Finish Frozen Mallet and Youmuu's Ghostblade. Before going into a battle, hide in a bush and pop your Ghostblade and Ult. You'll be amazed at the damage output you gain. Finish Bloodthirster with all the delicious kills you just received.
Now no one can get away from you, and you still have a free spot. What do? Usually Guardian Angel. It just gives plenty of MR and Armor. The passive is just icing on the cake. If they're really AD heavy, get a Thornmail. If an AP got fed early game, you should have a Hexdrinker in this spot, and will probably sell it late game for GA or, if those casters are still a threat, Force of Nature.
With your CDR, Tenacity, escape plans, and raw power, you will definitely wreck face.
Edit: Also, with her recent changes, you should level her skills more evenly for the CDR to Ki Blast, boost in her Valor, and the now amazing damage output from Broken Wings.
The point of 3x Dorans is that it's still 300 HP, on the alternative to the Wriggles setup, which of course has little additional Magic Resistance to counter the mages anyways. Riven scales and becomes burstier with more attack damage, and I tend to snowball harder going with Bloodthirster unless I'm directly building to counter a mage in lane such as Sion, Kennen or Vladimir, which I'll always start building towards magic resistance after the second or at a stretch the third doran's blade.
For all intents and purposes, Riven is an escape champion, where it's harder in early game and much easier by later game to escape most situations without the ability to flash over a wall. The reason she seems a bit more glass cannon like with an earlier bloodthirster is because of the survivability added due to her high scaling on valor.
To address the second poster, I always max Valor last because Broken Wings is still very reliable damage. I put two points into Valor when I can't put points into Ki Burst because earlier on, that extra second off the cooldown is more imperative than 25 more damage at level 8, but beyond that it's damage per rank is more efficient than the shielding per usage of ranking up Valor in my opinion, since you gain more shield through AD by the time you would be leveling Valor than you would gain by shield per rank, and it has such a short duration that I typically only use it to poke at tower and absorb a single turret shot. I haven't done any hard math calculations, but without CDR I feel that Broken Wings promotes more damage output and threat while in lane than valor.
First off, getting 3 dorans blades and then
Secondly, why are you getting
I'd think that
I think you are building too offensively and leaving yourself very vulnerable, especially for a melee champion. You aren't even taking an escape for most of your builds...