Hi, I'm FHZR and you are reading my first Mobafire guide. I write this Jax guide to just tell new Jax players how to play him, why you should (defenitly!) play him and why he's so damn strong right now.
I created several builds for this Jax guide, so you can find the one which you like.
Also, I want to tell you something about me. As I said, I'm FHZR (IGN is the same) and I play League since November 2013 or just end of Season 3. Started off with Fiddlesticks I made it to Level 30 and I don't really played Jax because no one did. Now, I'm in Silver V and Jax is one of my Main champs.

Jax is a Champion who's commonly played at top lane or jungle. He can either be a high damage AD/AP/Hybrid meelecarry, an AD/AP/Hybrid bruiser or just a tank. Therefore, there are many ways to play him. Mostly, the AD Carry or Bruiser role is played. Jax is a big late-game monster, he can easily compete with Vayne or Tryndamere in a 1v1 if played correctly. He beats most of the Champions who relei on AA because he can completly ignore their damage thanks to his Counter Strike.

Pros
+ High versatility in item building or playing
+ Good singletarget burst ( Empower, third hit of Master-At-Arms)
+ Mobile ( Leap Strike)
+ Best duelist ingame ( Counter Strike negates !ALL! the AA's)
+ Can make a use of the most items
+ Can be still be tanky if you build full damage ( Master-At-Arms)

Cons
- Weak early game (play wrong against Renekton or Garen and you know what I mean)
- AS reduction is a strong counter against him
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We start off with our masteries, you choose either 21/9 for the carry role or 9/21 for the bruiser role. I prefer 21/9 because Jax needs some several masteries to deal more damage, and as I said before he can still be tanky without tanky masteries.

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Offensive Tree

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Double-Edged Sword - Defentliy take this mastery when you are up against a meele Champion. The damage increase is just too good, and you shouldn't take too much damage when you use your Counter Strike correctly.
Fury - 1/3 of an Dagger. This is a great way to increase our damage early game and farm much better.
Brute Force - Free AD which scales into late game, why not?
Spell Weaving - This mastery is good for dueling. You build up to 2% extra damage for your Master-At-Arms proc. So, let's say free damage?
Martial Mastery - Another free AD increase for our early game.
Executioner - Extremly powerful mastery. IMO, one of the best. Free damage and also helps you to kill those pesky low-life guys faster.
Warlord - Another mastery for free AD. It scales somewhat into the late game, so when you have 200 AD you have a free Long Sword. Not that bad.
Dangerous Game - This is more useful than you would think. It helps Jax to fight several champions at once and is good for surviving Ignite after a tough 1v1.
Devastating Strikes - Another OP mastery on Jax. Since you deal mixed damage with your ablities and AA's, you can make full use of this mastery.
Havoc - Kewl, even more damage! Its an general damage increase, so a 3% (except true damage] damage increase.

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Defensive Tree

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Block - Helps us in early game trading. Block is also good with Doran's Shield, it gives up to 12 AA damage reduction.
Unyielding - Same as above.
Recovery - Some sustain for the first minutes of the game when you have less or no lifesteal.
Veteran's Scars - Let's say its 1/4 of an Ruby Crystal. Good for making us tanky early game!
Juggernaut - Jax has one of the highest base HP ingame. So, you can take this mastery because you will have like over 3000 HP when you have full build.

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Take flat AD marks, scaling Armor seals, scaling MR Glyphs and flat AD quints.

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Greater Mark of Attack Damage (9x) - We take the Greater Mark of Attack Damage because we need the early AD to win some trades and to last hit.

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Greater Seal of Scaling Armor (9x) - So, most people will argue with me. But, I would recommend the Greater Seal of Scaling Armor than the flat Greater Seal of Armor. Here are several reasons:

• Jax has a fairly high base amount of Armor (26) so, he doesn't really need flat Armor at the start. Use mixed (flat and scaling) if you take too much damage early. Cloth Armor is also an alternative.
• You won't going ham on your enemies pre-6 so, you will passivly farm and trade back with Counter Strike if needed.
• Greater Seal of Scaling Armor have at level 6 the same amount as the flat ones have so you have the amount of nine, that the flat ones will have at the start. Also, you will have 27 Armor with these at level 18. A much better late game scaling.

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Greater Glyph of Scaling Magic Resist (9x) - The amount of MR you will get per Level isnt very high. So, these runes help you to scale your MR much better into late game. You can also use mixed or flat ones if you have an AP Top.

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Greater Quintessence of Attack Damage (3x) - A no-brainer for every AD Top. Helps you to last hit better in early and to win trades.

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MUST HAVE

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D/F - Flash is a must have on almost every champion. You can close a long gap with Flash and Leap Strike, finishing off champions, juking... there are many ways too use it both offensivly and defensivly. Mostly you will use it to engage and disengage.

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Best Choices

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D/F - Teleport is a very good spell for Jax. You can get back quickly if you got an bad start or just for farming. Also, this makes you a split-push god. Teleport ganks are also open for you.

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P - Basic attacks increase Jax's attack speed by 4% / 6% / 8% / 10% / 12% / 14%. Relentless Assault lasts for 2.5 seconds and stacks up to 6 times for a maximum of 24% / 36% / 48% / 60% / 72% / 84%.

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Q - Jax leaps to target unit, dealing physical damage if the target is an enemy. Physical Damage: 70 / 110 / 150 / 190 / 230[/color] (+ 60% AP) (+ 100% bonus AD)

Facts and Tricks

• This ability should be maxed 2nd. The cooldown goes down, to a maximum of 6 seconds.
• Don't spam this ability in early game. The mana costs are somehwhat high and you shouldn't spam it because the damage is high. We use it either to engage or to disengage.
• Jax can jump either to friend or enemy. This includes champions, minions, friendly and (visible) enemy wards and any champion pets. Such as Shaco's Jack In The Box.

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W - Jax's next basic attack or Leap Strike within the next 10 seconds deals additional magic damage. Empower resets the autoattack timer. Magic Damage: 40 / 75 / 110 / 145 / 180 (+60% AP)[/color]

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E - For up to 2 seconds, Jax dodges all basic attacks and takes 25% less damage from area of effect abilities. At the end of the duration or if Counter Strike is activated again, Jax deals physical damage and stuns nearby enemies for 1 second. This spell deals 20% additional physical damage for each attack dodged to a maximum of 100% increased physical damage.
Physical Damage: 50 / 75 / 100 / 125 / 150 (+ 50% bonus AD)
Maximum Damage: 100 / 150 / 200 / 250 / 300 (+ 100% bonus AD)[/color]

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R - Passive: Every third consecutive strike Jax deals additional magic damage. Magic Damage: 100 / 160 / 220 (+70% AP)
Active: Jax strengthens his resolve, granting him greatly increased resistances for 8 seconds. Armor: 25 / 35 / 45 (+ 30% bonus AD) | Magic Resist: 25 / 35 / 45 (+ 20% AP)

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Before you get to the mass varity of items, you need to look what Jax needs for stats. Take a look on Jax's base stats, then you might have an idea what are important stats.

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As you can see, the base Attack Damage is fairly high. With the our AD runes and a Doran's Blade or a Long Sword start, the AD goes up to 90. A very good starting value. Ability Power is not needed for the beginning, as you will max Empower first. The attack speed is not that high. But it's definitly improveable, the 5% from Fury can help out there. Movementspeed is high, a start with Boots is not needed. Armor is also high, flat Armor runes are not really needed for the start. Magic Resist scales with level because Jax is an meele Champion, the Greater Glyph of Scaling Magic Resist runes help out that the magic resist value isn't that low when it comes into teamfights, where magic damage more present. Health will be 561, while Mana being 265.

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Your itemensation should have:

• Attack Damage - Of course, attack damage is important to be an scary DPS champion.
• Ability Power - Empower and the passive proc of Master-At-Arms scale with AP. You often combine Empower + passive proc of Master-At-Arms, therefore AP is for burst.
• Attack Speed - An very important stat on Jax! It helps us to proc the passive of Master-At-Arms faster and to deal more physical DPS. Despite having a big attack speed buff with Relentless Assault, it scales with level and is more scary later. Also, its very annoying to stack Relentless Assault with slow attack speed...
• Lifesteal / Spellvamp - Jax has no innate sustain. He needs sustain against poke damage and in duels. When using Lifesteal, you have to build more attack speed and attack damage. When building Spellvamp, focus on cooldown reduction, Ability power and less (but not to less!) attack speed.
• Armor, Magic Resist, Health - I want to combine these three. Its for our general survivibillity. Jax has an very high endgame base health value, so you only need one or two health items. Same for Armor and Magic Resist, you don't have to build three or four items. One or two are enough. Don't forget that you have scaling Armor and Magic Resist runes, these scale into the late game pretty well and you can activate Master-At-Arms for more armor and magic resist. The active scales with damage, both AD and AP, so offense is the best form of defense.

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Starting Items
You will have some gold left, buy Health Potions, Mana Potions or Stealth Wards to suit your preferences. I recommend for every starting item Health Potions!

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• Doran's Blade - 7 Attack Damage, 70 Health, 3% Lifesteal | 440 Gold
• Doran's Shield - 80 Health, 6 HP5 Unique: Blocks 8 damage from champion basic attacks. | 440 Gold
• Cloth Armor - 15 armor | 300 Gold
  

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Early Items
Note: If you have some little Gold left, buy Health Potions and stealh wards! Both are very important, especially the Stealth Wards which can help you escape with Leap Strike

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• Bilgewater Cutlass - 25 Attack damage, 8% Lifesteal | 1440 Gold
• Boots - 25 Movement Speed

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Mid-Game Core Items
At this stage of the game, Health Potions and Mana Potions are not needed, focus more on Stealth Wards and Vision Wards! Tip: Place only two Stealth Wards to have one for escaping!

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• Blade of the Ruined King
• Trinity Force
• Mercury's Treads, Ninja Tabi, Boots of Swiftness, Berserker's Greaves