Ull see my items and think like wtf is doing this dude? Not buying guisons?!
Believe me its one of the hardest build, but if played right carefully and get feed/farm your will be so overfreaking op lategame.

My max hp is about 4760. Ur ulti procs with + ~850 ap, also leapstreaks gets every public played carry halfdown.

AC, FH and NT are changeable compared to the enemy team.
AC for tanky nukers / WWs etc
FH against tryn nubs
NT for overfreaking high cdr nad little ap

Pros
U dont need hp items, ur get through ur high ap that much hp its rly the best oftank ever.
With cdr runes and nashor u get rly low cdr, rly needed for stun! CC is one of of the biggest aspects of and against jax!
Bad jungler (compared to the real jugler)

Cons
Really mid/late game hero, public even more early if u get fed.
If u bought ur Mejais and ur elixir ur not godlike, use it in the right moment like teamfight at dragon. If uve some stacks ur even get more piled then before! Dont loose them (should have always a minimum of 7, otherwise the item was a waste).
Dont iniate teamfight, rly they throw ccs against u = dead, ur offtank but not unkillable.
Hard to solo/duo lane against rly long range nukers like oriana or fiddle (early game - dont feed them ull be soon op :D)


Douh so many cons? - well try out

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Every public ull shoud be dominating if ur teams plays as team and dont feed, rembember ur one of the biggest carrys