Gragas E Range: 600 Units, which is the same as your E range.
Gragas' Skill Max Order: Q → E → W
Level 1: Gragas usually starts Q, so you are free to do the Quinn Cheese from the bush level 1. He will Q you, but you still win the trade. The other alternative is to auto him from bush, and then dodge his Q with your E.
Level 2: Gragas has E now, and his E cancels your E. His E range is identical to yours, and he can't pass through minions. If you want to be aggressive with your E, use your E behind the minions. If Gragas retaliates with E, your E will push you behind the minions and you will be safe.
Level 3: Gragas W makes him tanky, so just be cautious of him using it if you are trying to dive. Usually in lane, I like to stand behind minions, and when Gragas Qs me to poke, I E him to dodge his Q, and my E will push me back so he can't E back. This gives you free trades in lane.
Level 6: Gragas R pushes you back, but if you vault Gragas during his R, you can end up in a different landing than he anticipates since your E animation travels so quickly. If he tries to R you away when you're chasing him, save E to use to react during his R. If you time it correctly, his R will shoot you closer to him.
Gragas poke is annoying early game, and his range is slightly longer than yours.
Stay in E range of Gragas because his Q range is longer than yours, and his Q hurts you a lot.
Stand behind minions in this matchup so he can't E you as easily.
What I like to do is E Gragas when I'm behind minions, and then Gragas will E me back right after, but since vault is so fast and pushes you back to your original position, you will actually force him to E the minions in front of you.
This is really helpful to beat Gragas becasue if he misses his E, he is vulnerable.
His E is 4 secondsl onger than your E CD, so it is huge to bait it. However, if he lands E, the CD does refresh back quicker, so keep that in mind.
Post 6, use Galeforce + E to dodge his abilities and to also make his R put you in a place he doesnt want.
If you anticipate Gragas R, E him first because your E animation is so fast.
This will shoot you in a place Gragas doesn't want to hit you since he Rs in a certain angle to launch you to a certain place.
If you E first, his R can actually push you to safety, depending on the circumstance of course.