This guide will cover how to solo TANK/DPS Jax on Twisted Treeline (3v3)
With this complete build I can solo just about anyone, get dragon at level 6, and just plain wreak havoc. Very few can escape due to Leap Strike with only a few second cooldown.
With this build I have 3v1 Solo'd a Master Yi, Olaf, and Tryndamere. Although I do not encourage it, this build can back door mid-late game very well due to the damage output on Jax, and the health gained from the build.
Here are some of the average games that I get with Jax.
With masteries and runes, this build gives you the following at level 18:
+15 Armor Pen
-11.1% Cooldown Reduction
4% Damage Reduction
+15% Magic Pen
Blocked 1.5 Damage
Blocked 2 Damage from Minions
+10% Speed on Dodge
+10.8 Ability Power
+4% Ability Power
+2 Magic Resistance
3 HP per Attack Damage.
2 HP per Ability Power.
I have not verified runes, but some claim it still adds. Masteries do add to hp.
The recent buff to this removes the AOE, but adds some more damage, and a buff to damage increase from attack and ability power by double.
Now only deals damage to a single target rather than to an area of effect
Now resets Jax’s autoattack timer when cast
Damage increased to 75/110/145/180/215 from 40/60/80/100/120
Ability power and damage ratios increased to 0.4 from 0.2
Mana cost reduced to 20 from 35
Cooldown increased to 9/8/7/6/5 from 5/5/5/5/5
Tooltip corrected to accurately state it deals magic damage
Fixed bugs where Empower incorrectly did less damage when used at the same time as Leap Strike or each 3rd Relentless Assault strike.
This makes Jax a tough opponent incredibly fast. With Guinsoo's Rageblade and another attack speed item, you can have over 3 attacks per second.
The new active will protect you from ap characters while you face roll them.
New Active: Grants 20/35/50 + Jax's dodge percent in bonus magic resistance for 5/6.5/8 seconds upon activation. Costs 80 mana. Cooldown of 60/60/60 seconds.
Buff icon now dynamically shows the number of Relentless Assault stacks which Jax is benefitting from
Well, this section got deleted yet again, so I don't feel like fixing it.
Red: Armor Pen/Magic Pen
I prefer magic pen so that every third hit will hit extra hard because people tend to stack armor against you, but either are fine.
Blue: Cooldown Reduction/Mana Regen per 5
Cooldown for Leap Strike
Mana Regen to keep you in your lane longer.
Going down the Defense tree:
Take 3 points in Hardiness and one in Resistance. (Resistance used to work better, but Jax's ultimate covers this gap easily.)
Max out Evasion and unlock Nimbleness. (If you need an explanation...)
Max Defensive Mastery and take 2 points in Harden Skin. (I will cover this later, but reducing the minion damage is crucial.)
Max Veteran's Scars. (For an early game boost.)
Put the final point in Tenacity.
Going down the Offense tree:
Take Cripple and max Archmage's Savvy. (Improved Exhaust and AP per level.)
Max out Sorcery. (A nice CDR bonus putting up just over 11% CDR at level 18 with no items.)
Finish off with Archaic Knowledge. (15% Magic Pen will help with all of Jax's abilities.)
Putting one point in Counter Strike early game can save you from a gank early on.
Solo Jax can use this for harassment, but we will talk about this later.
Exhaust + the enhancement you took in your masteries.
This will not only help you early game, but also when you are outnumbered in fights, if you are escaping/chasing, or just if you are taking too many hits. This spell in incredibly useful.
This I like to keep mainly as an escape ability. Can put a wall between you and your death very easily. However you can also use this offensively if then enemy is one hit away, but Leap Strike is on cooldown. (Usually only early to mid game.) It can also be used to back door the Nexus if the main turret is down and at least one Inhibitor is down. Though I am not a fan of back dooring, this Jax can do so very well. (DPS + HP = Dead turret)
This is the core build. At this point you will still have a Doran's Shield but it is not included as you are not aiming to get one.
The Frozen Mallet can be situational, pass it up if you aren't taking much damage, even while targeted, but the other two items are essential for Jax.
At this point I pick up a Vampiric Scepter. It gives you much more survivability, as you can dish out damage, but you don't have a good way of getting any back.
I upgrade this to a [item=Emblem of Valour] if I don't plan on getting a The Bloodthirster and especially if no one has a [item_text=Stark's Fervor] and we have more than one physical DPS.
After this, I usually go with item pairs depending on the situation.
At this point, feel free to toss your Doran's Shield, but I try to keep it until I build that 6th item, as it adds 120 hp and 8 armor that could make a difference. Though, if I get a B. F. Sword I usually toss is, as 1850 gold is quite a bit to be holding because a Doran's Shield is in the 6th slot, plus due to [spell_text=Equipment Mastery] the B. F. Sword adds more hp.
I made this video to show you an example of how to use this build early game.
I strongly encourage you to watch the video. It is less than 3 minutes long and is a perfect example of what I am explaining/
Start with Doran's Shield and a heath potion. Go bottom to help cover your team from a gank, but do not go into the bush. While you are on the way to the bottom unlock Counter Strike. It will help you escape by giving you both dodge, avoiding damage, and allowing you to stun enemies and procing nimbleness to give you a 10% speed boost. Also, with runes and masteries you will be at a respectable 23% dodge at the start of the game.
On the way to the top take care to ensure that the enemy is not going to gank you, especially if you haven't seen any of them yet.
The following is situational:
Try to put yourself as close to their side as possible, ignoring champions even if they attack you. Take care to move back as new minion waves approach so that they target your minions and not you. Also take into consideration that if you move back toward your minions while you are taking physical damage from an enemy champion they will gain aggro from your minions, and the more minions that are in range, the more damage they will take.
Caution: Do not do this to every champion!
An example is Teemo, his poison will tear down your health beyond what hp regen and a health potion can recover from. This in addition to his blind can mess you up easily. With experience and knowledge of what abilities their solo has, you can play passive/aggressive against almost anyone.
Do not bother moving if they hit you with a spell as they gain no aggro from a spell. Keep in mind that allowing aggro on enemy champions can be a double edged sword. Although they are taking more damage, their minions aren't, allowing the minions free reign on yours. Although this shouldn't be too much of an issue if you are keeping their solo back.
If your stun is proc'd, quickly scan the situation. How many enemy minions are there? Is a new wave of minions on the way? Is the enemy champion in my range? If the answers are: less than 4, no, and yes, then feel free to put the hurt on them. If your stun is up and you are getting attacked, feel free to use it and back up a little while you let the minions do the damage.
Your combo at level 3 becomes W>Q>E. Use this to harass whenever all three abilities are available, but keep an eye on your mana and make sure that you don't drop too low, as early Jax is severely hampered without mana.
A quick note on Minions:
Minions are your tools. Use yours for damage, and use theirs to proc your stun. Know when and where to get aggro in order to get your stun and minimize damage at the same time. This is why Defensive Mastery and Harden Skin are in the build, it reduces Minion damage by 3.5, allowing you to use minions more often to proc Counter Strike and to win early fights in minion waves more easily. Minions are your friends.
Around Level 4 of so, you should have enough for Ninja Tabi. (850 gold) If not, pick up whatever you can to build it.
At level 6, if you have full HP/mana and the health potion, you can go solo dragon. Use the health potion and begin attacking. Use all three abilities whenever you can, and you will get the buff for your team.
At this point you are starting to go into mid game, be sure finish up the core build first, then move on to any other items.
I might add mid/late game, but it can vary greatly from game to game.