EDIT: CURRENTLY UNDER CONSTRUCTION TO BRING UP TO DATE WITH S3.

Hello, I'm H4xDefender, a 1700-1800 player who watches a lot of online/offline league of legends tournaments as well as pro streams. I was a competitive player of some renown in some other games, but thats not important. I made this guide because I felt that I didn't really see many good (if there are any good ones at all) Jax builds on this site.

If you can't stand the layout of the build, then don't read it. Its your loss, not mine.

Jax is currently in a great spot after all the changes to him in the past few months. I don't like how they changed his ult into more like an Olaf ult but it was neccessary. I feel jax is much better top then he is jungle as he needs farm badly, but if top isn't available, he is alright as a jungler as well.

EDIT:
Recent empower nerf doesn't hurt him at all really. He slows down a bit in the jungle and does a little less damage in lane but its hardly noticeable. Expect further nerfs.

Straightforward stuff.

Greater Mark of Attack Damage: The AD is good for lasthitting and making you burst a lot more early on with Leap Strike and Counter-Strike.

Greater Seal of Armor: The armor allows you to trade early on vs other AD bruisers without getting destroyed, and helps to negate a lot of creep damage early on.

Greater Glyph of Magic Resist: Early MR helps if you are laning an AP top such as Vladimir or Kennen it mitigates a good amount of their early harass.

Greater Quintessence of Attack Damage: Helps with last hitting and gives a good amount of damage to Leap Strike and Counter-Strike.

Possible Alternatives

Greater Glyph of Scaling Magic Resist: Take this if the other team has no AP jungler and you are not laning against an AP top.

Greater Glyph of Attack Damage: I bring these if I'm playing aggressive early on and i'm not vs an AP top. Gives you a page of 18 AD and 13 armor which is sick against ad bruisers ie: Riven.

If you don't have AD marks/quints armor pen is fine, it doesn't make too much of a difference, it just isn't better then ad.

Movespeed quints are good too if you are more passive early on. I personally am not.

Well this is the third time i've changed masteries on Jax and i'm pretty sure i've finally got the optimal ones down. Yes it looks weird but it is the best, trust me. (Yes i've tried 9-21-0 and 21-9-0.)

Breakdown:
1 Points in each Resistance and Hardiness , two in Tough Skin , two in Indomitable . This makes it so creeps don't really do any damage to you, which lets you walk up and **** up the enemy laner starting at level 1.

For offensive tree, taking both penetrations really amps up your damage, a bit of bonus ad for that little extra damage, and the armor pen to top it all off.

The AD is preference over the lifesteal, neither make much of a difference.

I run Flash Ignite every game but i'll run down the list of all the summoners anyway.

Exhaust Its total preference whether you want this or Ignite, I always take ignite as I am just accustomed to its bonus damage.

Ghost Preference really if you want this or flash, its a decent pick vs some champs like Olaf or Vladimir who usually take ghost as well to counteract it.

Smite For jungling.

Teleport Take this in difficult lanes, farmfest lanes, or if you want to be there for dragon fights in organized games.

Cleanse This is good vs heavy heavy CC teams, keep in mind it doesn't remove suppression, its ok overall. If you like cleanse a lot, take it. Cleanse Leap Strike can be very clutch.

Surge Good in theory, but no.

Revive For dunkmaster team comps.

Promote Bad choice overall.

Clairvoyance Save it for supports generally.

Heal If this is your cup of tea go for it, its been heavily nerfed and I personally hate it.

Empower is maxed first always because it becomes your highest uptime skill and provides you a lot of extra magic damage, making Jax impossible to itemize against in lane. Take a point in this at level 2 or 3, depending on the jungler and lane opponent.

Counter Strike is maxed second to lower the cooldown on it significantly, Jax doesn't have the luxury to build items for CDR. It is your only built in CC, and does almost the same damage as Leap Strike when maxed second, and it is AoE. Take a point first in level one always though.

Leap Strike is maxed third since it is mainly just used for the utility of gank escaping to minions, allies, or wards, and to gapclose to enemies to kill them. It provides more raw burst damage then Counter-strike, but isn't all that noticeable, doesn't cc, and isn't AoE. Take this at level 2 or 3, depending on the lane and the enemy jungler.

Master-At-Arms is skilled whenever possible at levels 6, 11, and 16 for bonus damage and tankiness. Very straightforward.

Relentless Assault a decent passive, gives you some nice attackspeed for lasthitting, dueling, and jungling. Stacks 6 times.

Cloth Armor Start this when planning to do golems or wolves level 1 or against an ad based laner.

Boots Start this vs weaker laners, or if you suspect the enemy laner is going to start this and having mobility is important against whoever you are laning against. (Make sure to get 4 pots if at all possible.)

Vampiric Scepter I don't ever start with this item, but if you are running Teleport you could potentially rush a Bilgewater Cutlass out of it. Not recommended.

Doran's Blade Don't ever start this.

Use your Master-At-Arms early if you suspect a fight, it has a long active.

Try to keep Leap Strike harassment low, it is very mana intensive in laning phase without blue buff, especially before you get Sheen.

Try to tag enemies with a quick Empower when they go to last hit, (Preferably with your ultimate's passive up) as it does heavy damage as you are maxing it first, and has a low mana cost.

If the enemy laner is pushed, punish them. After landing a full Leap Strike, Empower, Counter Strike combo, activate your Bilgewater Cutlass/ Hextech Gunblade active to stay in range until your Leap Strike comes back off cooldown to secure a kill.

Using Flash followed by a Leap Strike, Empower, Counter Strike combo, can dish out heavy damage very quickly to unsuspecting champions hugging towers from long distances.

Jax does a lot of damage. A lot. You can go 0-2 and come back to win lane once you finish a few items, namely Bilgewater Cutlass and Phage/ Sheen. Once he has his Empower maxed and a level 2 ultimate, there is pretty much nobody who can fight him 1v1, so abuse this. Jump on the enemy laner constantly and harass them out of lane/kill them. Jax is one of the best tower divers in the game as well, so don't be afraid to dive if they are sub-50% hp or somewhere around there. Just make sure you pop your ult early and have your ult's passive up.

I'll list matchups against some of the more FOTM and common top laners here and details about how the lane generally goes.


Starting Item: Cloth Armor
Difficulty: Medium

Warwick is actually not that much of a problem, especially if you can time your Counter Strike to cancel his Infinite Duress. Make sure you ignite him as soon as you land Leap Strike when going for kills, his ult usually doesn't save him if you have your ult on when diving. Make SURE you ward everything, Infinite Duress into a jungle gank is almost always a guaranteed kill, this is no exception on Jax.


Starting Item: Boots/Cloth
Difficulty: Medium

Yorick is a problem, but not as much as he is made out to be. You won't beat him in lane if hes of equal skill to you, but you can do fine if played correctly. Try to get ahead early on in lane against him by auto attacking creeps to hit level 2 before him. If he tries to auto attack you at level 1, immediately Counter Strike and walk up to him and keep auto attacking him and then stun him. You do sick damage at level 1 this way. Once you hit 2, take a point in Leap Strike and immediately jump on him with Counter Strike. This will generally scare them into flashing or refrain from harassing you too much in lane. If he goes balls deep on you with his ult and all three ghouls, queue up Counter Strike and DON'T PROC THE STUN YOURSELF. LET THE DURATION RUN OUT. I cannot stress how important this is, you will take no damage for three seconds which is huge. Eventually he will have too much mana and tankiness for you to push out, hopefully you have gotten some kills or a good amount of CS by then. Call for ganks as well as Jax synergizes well with junglers because of his gapcloser, stun, and big damages. Yorick has no escapes as well.


Starting Item: Cloth Armor
Difficulty: Hard

With the nerfs to Lee Sin's sustain, he is very possible to beat in lane, make SURE you avoid him from levels 1-5, go for Leap Strike Empower combos on him at level 6 with the third hit from Master-At-Armss passive for big damages, try to save counter-strike because he will most likely Flash or Safeguard/Iron Will away if you do too much damage to him, which is your que to activate Counter-Strike and flash to him to get a stun off and kill him, do your best to make him waste his Dragon's Rage before going for a kill on him, be wary of the low cooldown on it.
Tip: You MUST adapt to the skill Lee Sin is maxing first. If he maxes Safeguard/Iron Will first, you can abuse him. If he maxes Tempest/Cripple first, let him blow it on creeps before going in on him. If he maxes Sonic Wave/Resonating Strike first, either wait for it to blow it on creeps, or just bait it out and juke it. Avoid him from levels 1-5 ESPECIALLY if he maxes this first.


Starting Item: Boots
Difficulty: Hard

Malphite is solid as a rock, and is one of the few champions Jax doesn't do favorably against. Try to keep his Granite Barrier down by breaking it once with Empower and then auto attacking him every 7-9 seconds to make sure it doesn't come back up. Most Malphite players will not realize what you are doing, you hurt Malphite's trading power and sustain by quite a bit if done correctly. If he blows Ground Slam on creeps, you can jump on him immediately and he will be forced to back off unless he has already amassed a lot of armor and magic resist. If you are going to kill him it is going to be at levels 1-5 unlike most other champions, simply because Unstoppable Force is an amazing escape. Beware of jungle ganks, much like Warwick's Infinite Duress, Unstoppable Force has great synergies with junglers, and he has a slow from Seismic Shard to boot. Try to just passive farm if he is just too tanky for you to kill.


Starting Item: Cloth Armor
Difficulty: Hard

I've never found riven to be too much of a problem, but good ones are a pain. Tts mainly common sense of you to not take free harass in lane from all her dashes and her stun, and its easier said then done. As Jax you can break the rules and out trade her if you play it right. When you comes at you, pop Counter Strike and hit her with Empower. After the stun, she will generally try to run which is when you jump on her and activate Bilgewater Cutlass's active. When she is too scared to initiate trades, start abusing Master-At-Arms's passive coupled with Leap Strike and Empower to harass her, SAVE Counter Strike as Broken Wings and Valor will get her away from the radius of your stun. Use Bilgewater Cutlass's active to get a stun off and make sure she will die quickly before going for a kill on her. Blade of the Exile is a strong execute that can punish you if you go for dives too hastily. All in all not that difficult a lane.


Starting Item: Boots
Difficulty: Medium/Hard

Udyr is very very annoying. Avoid him until levels 6-9 because Wilding Claw hurts a lot. I generally do not try to harass him at all until I max Empower and have Bilgewater Cutlass and Phage or Sheen. Note that Wilding Claw's bonus damage and Blazing Stampede's stun will go through Counter Strike although you will not take damage from the actual auto attack. Beware of diving him because of his low cooldown stun and and shield from Iron Mantle.


Starting Item: Boots
Difficulty: Easy

Tryndamere is a champion you have traditionally countered because of your dodge, and you still do. Just be wary early on and when he has rage built up. When he has rage built up, jump on him but save Counter Strike until you land and he either tries to run or fight back. If he runs with Spinning Slash? Save it. If he runs normally? Stun him. If he fights back? Activate it and **** all over his face. Even with his ultimate you can generally dive him easily. He can't kite you effectively and you can mitigate a lot of his auto attack damage. Turrets wont hurt you much with the active from Master-At-Arms.


Starting Item: Boots/Cloth
Difficulty: Medium

Olaf is annoying early, but if he chooses to max Reckless Swing he is going to lose lane. At level 6, you out DPS him in fights hardcore. If you walks up to you to hit you with Reckless Swing, tank it like a boss and hit him back. Reckless Swing has a heavy hp cost to himself, and this coupled with your sick damage will ALMOST ALWAYS force him to burn a summoner spell, or Ragnarok in fear. If you can force out Ragnarok you can generally kill him pretty easily under his tower, even if he has Ghost. If he has Flash make sure that is down before diving him. Avoid him early, and at level 1, he has a stronger level 1 then most champions if he takes Undertow first. If he doesn't, once again tank Reckless Swing and punish him with auto attacks plus Counter Strike. Not that tough a lane.


Starting Item: Boots/Cloth
Difficulty: Medium/Hard

Shen is an unkillable monster in lane that harasses you constantly with Vorpal Blades. If he goes Trinity Force its possible to kill him early, but not recommended. His Shadow Dash has ridiculous synergy with junglers and he scales amazingly with just HP and tank items. If he ults though, ALWAYS CANCEL IT IF HE IS IN SIGHT OF YOU. If he runs back to tower with high hp, go look if he is ulting and jump and stun him if you isn't going to kill you instantly. He is immobile while ulting, and immobile after you stun him which makes it generally pretty easy to get away from him and turret range after cancelling his ult. You need jungle ganks to get momentum to beat him in lane, unless you abuse his weak early levels. You can abuse him generally up to level 8-9 where he maxes Vorpal Blades and just starts to wreck you. Get early MR to deal with his kit of all AP damaging abilities.


Starting Item: Cloth Armor
Difficulty: Medium

This might seem unneccessary to detail on how to lane vs a Nasus and it might seem this lane is free win Jax, and its definitely a pretty easy lane, but it by no means is free win. If you are going to kill Nasus it has to be REALLY early, im talking level 1-2 early before he skills Wither because wither absolutely shuts down your damage output, and later he is way too tanky for you to mess with. Wither also has a great synergy with jungle ganks. If you see him activate Siphoning Strike and not immediately use it, go aggressive on him right away and force him away from the creeps, or force him to blow it on you or Wither you. This is one of few lanes I may consider taking Cleanse or getting an early Quicksilver Sash in.


Starting Item: Boots
Difficulty: Hard

Singed actually does quite well against Jax if he goes on the aggressive and takes early AP. Do your best to not get flung and just try to farm. If he goes full AP he will be squishy but be careful not to overchase, as his poison will hurt. Try to force him to blow mana on his poop and do your best to farm safely. If he farms inbetween turrets, ping your jungler to come kill him with you. If he is ahead of you or is already tanky when he does this though, ignore him. If you are ahead of him and your jungler isn't in the area, go straight towards him and force him to blow Insanity Potion and or Ghost/ Flash. Once he has blown these and he comes back in front of your turret, kill him.


Starting Item: Cloth Armor
Difficulty: Medium

This is a skill lane up until level 10-11 where you start to outdamage him. Active Counter Strike whenever you see him pop Decisive Strike, and tank the Decisive Strike and the Judgment combo unless you are low hp. You outdamage him with the active effects from Counter Strike and you can chase him down with Bilgewater Cutlass and Leap Strike. Don't overstay in lane, as Flash, Decisive Strike, Judgment, Ignite/Exhaust, followed by Demacian Justice is a ton of damage, and he can take turrets easily with his innate and active tankiness from Courage. Make sure to not trade with him when he has Courage active, just wait it out as it has a long cooldown and doesn't last very long. You SHOULD win this lane but you need to understand how to play Jax and how Garen works if you are of close skill to your lane opponent.


Starting Item: Cloth Armor
Difficulty: Medium

Needs further testing, but from lanes i've played so far, this is a skill lane, or something close to it. As long as you farm carefully, watch out for jungle ganks, and don't get baited by Dominus this lane should be yours. You outscale Renekton hard.


Starting Item: Cloth Armor
Difficulty: Easy/Medium

You have an advantage in lane, but if you take free hits from Martial Cadence you will lose. Avoid him early on and punish him when you have damage when he goes to hit you with his passive. Generally try to save Leap Strike as Jarvan can hit you with Cataclysm and Flash or Dragon Strike Demacian Standard out, or just Dragon Strike Demacian Standard away or into a bush. He does big damage early on, if he stacks multiple Doran's Blades or builds an early The Brutalizer avoid him. If he goes for Philosopher's Stone and or Heart of Gold harass him constantly at level 6. This is a lane that is easily losable but one that you should win.


Starting Item: Cloth Armor
Difficulty: Medium/Hard

Pantheon is a very big problem, and he is a laner you will generally lose to. His Spear Shot harass is very strong, and his follow up to jungle ganks/initation of them with Aegis of Zeonia is ridiculously strong. Heartseeker Strike is very good for finishing off people, because of both the passive and active effects it has. If he goes glass cannon, you can kill him at level 6 on a balls deep engage. Do not attempt this pre 6. His ult is more of a ganking ultimate then a 1v1 ultimate, you can wreck him in a straight up fight. You outscale him hard, so just farm up and don't feed him.


Starting Item: Boots
Difficulty: Medium/Hard

Rumble is tricky early on, as Flamespitter + Electro-Harpoon do lots of damage when hes in the danger zone. (Yellow heat bar) The trade off is that if he does this, he will be pushing the lane hard. Call for jungle ganks, as Rumble has a weak escape. Try to bait out his shield before trading with him. You will win this lane hard, as you scale better then him, and Counter Strike mitigates a lot of his damage from Flamespitter and The Equalizer.


Starting Item: Boots/Cloth
Difficulty: Medium/Hard

Darius is a lane you should win if you play smart, as long as you don't let yourself be continually harassed for free by Decimate. If he has his passive ticking on you, get out, the amplified damage it gives to his ultimate is ridiculous. If he grabs you at level 6, pop Counter Strike and start pummeling him. If not, tag him with Empower and pop Counter Strike if neccessary, but do NOT fight him in a hard engage. Beware of a Flash Apprehend combo, it is deadly with jungle ganks because of the immense damage Darius puts out. He has no escapes, so if he is losing a fight or gets ganked when pushed he will most likely die.


Starting Item: Boots/Cloth
Difficulty: Easy

Fiora is pretty much a free win as Jax. Avoid her early on, you start to beat her around levels 4-5. Her Riposte will block your auto attack damage, but not the bonus magic damage from Empower. When she ults, pop Counter Strike and laugh as she misses every single tick of damage and gets stunned as soon as she is targetable again. She cannot trade with you past levels 4-5 so just continually harass her or bait her into a hard engage and destroy her. Most of her damage comes from auto attacks and her ult, both of which you negate with Counter Strike.


Starting Item: Cloth Armor
Difficulty: Easy/Medium

Gangplank is annoying, but hes been nerfed too much and should be an easy lane for you. Counter Strike dodges Parrrley and his only other damaging spell is his Cannon Barrage which is random damage and scales off AP. (Gangplank is standardly built AD) You can punish him the whole lane phase because he has weak drawn out fights and weak trading against Jax. If going for a kill, try to bait out Remove Scurvy on either the Bilgewater Cutlass slow or the Counter Strike stun. Do not stack them as he will just remove both at the same time and run away with his bonus movement speed from Raise Morale.


Starting Item: Boots
Difficulty: Easy/Medium

Really easy lane most of the time, most Cho players want to farm as much as possible, force him to use his spells on creeps and jump on him and pummel him. If he has to continually use his spells defensively, he cannot farm and you can zone him hard. If you get hit by Rupture with the jungler last spotted in the area, start running immediately, the followup with his silence and jungle ganks is absolutely nasty.


Starting Item: Boots
Difficulty: Easy

Nautilus is easy, once you break his shield he has almost nonexistent damage to you in lane. Watch out for his level 6 burst, its lethal if you aren't full hp, especially with jungle followup. Hes a lot like Gangplank in the sense that if you are losing a fight you are going to have a tough time escaping, but unlike Gangplank he doesn't really score many random crits, so you should never lose an engage to him. His Staggering Blow is similar to Jarvan IV's Martial Cadence in the sense that the damage will add up if you take repeated auto attacks for free. Also take note he does mainly magic damage.


Starting Item: Cloth Armor
Difficulty: Hard

Kayle is a difficult lane, when you combo her make sure you save Counter Strike until after she starts harassing you back, as most Kayles fight back. Her pre 6 damage is insane, especially level 2, so avoid her as much as you can until you build some tankiness and damage. She is primarily physical damage if she is building optimally. If she ults herself under tower on a dive and she is low walk around and kite her while staying in Leap Strike range to kill her when her ult wears off. Try not to be to obvious when you jump in to engage, as her ultimate can absorb one full jump of your burst which will usually lose you engages.


Starting Item: Cloth if AD, boots if AP
Difficulty: Easy/Medium

Sion is a really easy lane if hes ad. If he is just harass him as much as you can, his passive won't be enough to deal with you. Make sure you make use of the whole duration of Counter Strike to prevent him from lifestealing ridiculous amounts in hard engages.

If he is ap, just try to make him waste his mana early on pushing the wave and cs under tower. He can wreck you early if you are not careful. Once you are level 6 and get some damage, pop his shield when he activates it and punish him as much as possible. Since he is top lane he probably won't get blue buffs which means when he is out of mana he is a sitting duck.


Starting Item: Boots of Speed
Difficulty: Varies

This matchup is almost entirely player skill dependent and or jungler dependent. Neither of you should die to eachother until you finish Bilgewater Cutlass and can kill him pretty handily. If you fall behind in this lane, get an early Hexdrinker but hold off on upgrading it as Maw of Malmortius is expensive and isn't a great item.


Starting Item: Boots of Speed
Difficulty: Medium

Irelia is really really annoying. She punishes mistakes almost as much as Riven, which makes this lane a real pain. I don't agree at all with people who say this lane is free win Jax simply because of Counter Strike. Hiten Style which is 80% of her damage has a decently long active and hurts like hell. Do not pop Counter Strike on her until she has blown Hiten Style and you will win straight up 1v1s. Do not EVER fight her with Counter Strike down. Ever. Jax is a great duelist, but he isn't jesus. Her only CC, Equilibrium Strike is very very annoying as well, it basically forces you to build Merc Treads if you ever want to kill her. Irelia also does a mix of magic and physical damage (as well as true damage from Hiten Style) so don't think you are safe just because you have a lot of either MR or armor.

Leave a comment or PM me for any matchup you have problems with, I will be adding more matchups periodically.

The best items for Jax in normal games are in the cheat sheet, but i'll go over some others and when to buy them, when not to buy them, and why you should never buy them.

Niche/Unneeded Items
Wit's End: Decent if you need MR, but you have a defensive ultimate once again, and passive attack speed. The magic damage on auto attacks is nice but this isn't really needed overall.

Void Staff: Don't buy this, you do mainly physical damage. They can stack all the mr they want and you will still hurt like hell.

Guinsoo's Rageblade: No longer cost efficient as it doesn't give HP anymore, and there is just no room for it as it is a rather expensive, midgame only item. Bilgewater Cutlass is better for Jax now in almost every single way.

Warmog's Armor: You get enough hp from this build and Jax's hp stat, unneeded with his new defensive ultimate, mallet and rylai's are better in every way.

Rabadon's Deathcap: Honestly, Hextech Gunblade gives so much more for the same price to Jax. Don't buy it unless your team needs a LOT of ap for some god forsaken reason.

Lich Bane: If you really want to split push, you can grab this, I don't like it for teamfighting though, it isn't better then any of the core items listed.

Infinity Edge: Expensive and unneeded.

Shurelya's Battlesong: This would not even get considered if it did not build out of philo stone, the stats it provides are not very good on Jax.

Banshee's Veil: I don't know why you would ever buy this, Quicksilver Sash outclasses this bigtime. You don't need the hp and the passive is super unreliable.

Phantom Dancer: Jax needs AD and AP, not attack speed and crit chance.

Atma's Impaler: I used to build this even after the nerfs, but it really is not that great on him anymore, I've found Maw of Malmortius is better in almost every way.

IF you have any other items you want to know about on Jax leave it in a comment below.

CORE:
Bilgewater Cutlass: Need that slow, good ad, good sustain.

Mercury's Treads: Well needed MR, great tenacity, Jax is hampered by CC

Doran's Blade: Really compliments your other stats nicely, gives you a much stronger lane presence overall.

Trinity Force: Gives you a lot, more burst, survivability, a slow, and movement speed and crit are just icing on the cake.

Situational Items

Frozen Mallet: A matter of preference whether you want this or Rylai's Crystal Scepter honestly, if you really can't live without that extra 200 hp and you need more armor from your ult then go for it. Bilgewater Cutlass/ Hextech Gunblade/ Trinity Force already provide sufficient slows, so don't buy it for the slowing effect, only for the HP.

Wriggle's Lantern: Decent item, but I like the sustain from Bilgewater Cutlass and it's active is way better for Jax as well. I personally almost never buy this, but you should vs strong AD laners like Lee Sin.

Last Whisper: Buy this if the other team all buys thornmails, or just have a ton of armor to the point where you just can't hurt them.

Maw of Malmortius: You see this in the cookie cutter build at the top as the last item, but if you are against an AP laner giving you trouble, build an early Hexdrinker before Sheen and leave it there until after you finish Rylai's Crystal Scepter or Frozen Mallet. There isn't much alternative for this as your last item.

Rylai's Crystal Scepter: The reason I get this is over mallet every game is because when you Leap Strike combo somebody they will tend to flash if they take too much damage and the slow it applies can keep you in range to get a stun from Counter Strike off even if they flash sometimes. I also feel you need the MR it provides to your ult over Frozen Mallet's armor buff and the extra 200 HP.

Randuin's Omen: If the other team has a double ad comp ie: Vayne top and another ad carry bot, you can build a HoG in lane and upgrade to this somewhere in your build, depending on how they are doing. I personally do not build this.

Quicksilver Sash: If the other team has some gay cheese aoe cc comp then build this over Maw of Malmortius.

Ninja Tabi: Build this vs Lee Sin, Pantheon, Gangplank if he gets ahead of you, and Riven. Always sell it for Mercs unless the other team has 0 AP though.

Important Note:
Yes, I usually sell the Cloth Armor I start with. Sometimes I'll upgrade it to Ninja Tabi or Wriggle's Lantern, but if I do upgrade it to tabi, mercs are always better lategame so you will sell them anyway.

Jax is an anticarry. He makes those hard hitting AP and AD carries cry, because he gives no ****s and jumps right through a team to blow up the carries in the back, while being tanky as hell from his items and his ult. Always hang around and try to jump on carries from the back, they are squishy and melt quickly.
Keep in mind Jax can fight most if not all fed ad carries alone because of his Counter Strike, (Make sure you don't pop it early for the stun though if its a straight 1v1, keep it on for max duration to avoid the heavy auto attack damage.)

Also keep in mind you can jump to champions close to the carry you are trying to kill, or drop a ward to jump to to tag them with your AoE stun, and follow up with your Bilgewater Cutlass/ Hextech Gunblade's active slow to drop them quickly.

Golden Rule:
NEVER BE THE FIRST ONE IN A FIGHT. EVER. EVEN IF YOU ARE THE TANKIEST MOFO ON YOUR TEAM. NEVER.

Jax is a fun and strong champion with the versatility to go mid lane vs melee mids, crush weak solo tops, go in kill lanes at bottom, and jungle pretty well as well. He has a ridiculous lategame, even with the loss of his old passive. If you dropped Jax after dodge was removed, you should seriously consider picking him back up.

I'll add some videos on how to play Flash Ignite Jax later when I have time.
-H4xDefender