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I'm not good with introductions.
During early game I prefer going duo-lane (right/left). Guan can't solo, at all, and he can definitely not solo mid.
Try and play defensively and only go for kills if the enemy gods have low health or no mana. Try not to overuse your abilities so that you can conserve mana unless you buy Meditation, which is great early game for heavy mana users such as Guan Yu.
Push lanes as much as possible while being cautious as it's easy for the enemy gods to gank you if you're by yourself. You should also try and help the other lanes if necessary.
Go to the jungle and get the blue (mana), green (health) and red (damage) buffs.
At this point the enemy gods have, more than likely, acquired a lot of items and Guan Yu isn't a tank who can take an amazing amount of damage. Play cautiously and only be aggressive when you have your Tactician's Advantage and friendly gods around you.
During said team fight you should play "neutrally". Support your team while being just as aggressive and staying back to try not to die.
I found a lot of success with Artemis. Her Calydonian Boar > Transgressors Fate combo allows her to lock the enemy god in place for 5 seconds and Guan Yu's can use Tactician's Advantage to slow, silence and stun. During this time they can do a lot of damage together. Even if you can't lane with Artemis, I suggest duo laneing with someone who has a stun.
Pretty much anyone can counter Guan Yu if you're not careful. You need tactics and maybe some help from your team.
Reinforced Boots. The (nerfed) sustain is nice, as well as the T3 passive. This is generally an all around good item.
Doom Orb. This item grants the most magical power in the game, and is the most cost effective item. Many will tell you that Doom Orb is bad on Guan Yu due to his lack of farming skills and his necessity to get up close and personal which can put him at risk. This is true, if you don't build survivability. The next two items go a long way in making Guan Yu extremely durable and as a result, make Doom Orb worthwhile.
Void Stone. This item is easily the best magical item in the game in my eyes. At the incredibly cheap price of 2280, this item provides a mediocre amount of magical power (50) with high magical resistance (60) and to boot, a 55 yard magical penetration aura of 30. This aura combined with the reduced resistances from your Taolu Assault give you all the magic penetration you'll need. Swap with item 4 if against heavy physical, or find yourself needing the mana.
Wall of Absolution. I used to buy Mystical Mark 3rd and Void Stone 4th, but after the much expected nerfs to Mystical Mark and the introduction of this item, I'd much rather pick this beast up. This provides the physical protection to help you tackle their physical god who has been conveniently fed from your other lanes, provides much needed mana and mana regen, which are even more valuable in light of the latest round of Guan Yu nerfs. The passive is nothing short of amazing, especially on a god like Guan Yu and will help you maintain magical penetration on targets when your Taolu Assault is on cooldown.
Rod of Tahuti. Second on magical power only to Doom Orb, possibly first when fully farmed. The sheer amount of power on this item typically makes it a no brainer, and by this point you should be a force to be reckoned with.
Pythagorem's Piece. Ranking third on the most magical power you can get on an item with 105, this item is even more accessible with it's reduced price. The magical lifesteal is not really great, but it helps. The main attraction is the magical power and the aura that will benefit your team.
You'll notice I've missed out popular items like Warlock's Sash and Gem of Isolation. I'm not the greatest fan of Warlock's Sash due to it's very high price and relatively low MP at 80 stacks (a mere 90) and considering how long it takes Guan Yu to get these stacks, I typically would not build this on him.
Gem of Isolation on the other hand can serve as a replacement for Doom Orb if you despise that item (in this case I would move Gem of Isolation to 4th, after the defensive items). I don't believe Guan Yu needs this item as much as other gods, nor does he get much benefit out of it. His Tactician's Advantage and Warrior's Will already provide slows. The only big addition this item will give you is a slow on your Taolu Assault, an ability which already provides knockback immunity. If you think that it's worth 2800~ for a slow on your Taolu Assault, then by all means pick this item up. Personally, I would rather the 160 magical power.