Gragas vs Jax

Let Barrel Roll (Q) charge before detonating it: damage and slow grow the longer it sits on the ground, and if you don't recast it, it explodes on its own.

Drink Drunken Rage (W) before engaging: drinking takes 1 second, then you take less damage and your next auto hits every nearby enemy.

Engage with Body Slam (E) through a path without minions: you stop on the first enemy you meet, and hitting reduces its cooldown.

After Body Slam (E), cast Explosive Cask (R) behind your target: the blast knocks enemies away from the impact, sending them toward your team.

Take a short trade, then back off: Relentless Assault (passive) increases his attack speed with each consecutive auto.

During Counter Strike (E), back off instead of attacking: he dodges your autos, then stuns nearby enemies, dealing more damage per dodged auto.

Trade right after Counter Strike (E): it's both his defense and his only stun, and it has a 17 to 9 second cooldown.

In the late game, don't leave his split push unanswered: send someone to hold his lane, or force an objective on the other side of the map.