Lots of crit + lots of CDR = spam Q to win.

• red - ArPen is essential to maximize crit damage.
• yellow - Health or armor, depending on who you think you'll be up against.
• blue - If for some reason you feel that you don't need the MR, mana regen glyphs are decent for spamming Q in the early game.
• quints - Boost your crit damage.

Focused on ArPen and Crits, with a few points for defense. Self-explanatory.

Ionian Boots of Lucidity -
Always buy this. CDR to spam Q.


Youmuu's Ghostblade -
Always buy this. It gives you everything GP needs: AD, ArPen, Crit, CDR. Plus it has an active that synergizes with E.


Infinity Edge -
Always buy this. You are not Critplank without the Infinity Edge.


Shurelya's Reverie -
Makes use of the early game regen items, gives additional CDR, and has an active that synergizes with E. An all-around good defense/utility item.
Alternatives (in order of recommendation)
More aggressive, and helpful with farm.
Not a bad option if you want to provide some additional support.
A little underwhelming, but solid if you just want something cheap. The passive slightly buffs your W and the Bloodthrister (if you so choose to get one).
Against heavy AD.
Against heavy AP. Not recommended otherwise.
Not my playstyle, but it's doable.


, Phantom Dancer, Atma's Impaler -
You will want at least one of these two. The final slot can be switched out with something else.
Alternatives (in order of recommendation)
ArPen - Make the crits hurt as much as possible.
AD / lifesteal.
AS / lifesteal / support.
You have too much gold.

Final Builds

I haven't tested the non-standards very well; use at your own risk.

Standard
100% Crit (Build Avarice at start; sell Boots and build 2nd Phantom after Whisper)
Support-ish (Build Emblem at start)
Tanky (Get Pendant or Ruby at start)
Anti-Mage (Build Catalyst at start)
Anti-AD (Get Cloth or Sapphire at start; build Shroud after Infinity)

• Max Q first. Duh.
• Max E second for maximum farmage and team support.
• Max W third. Nice anti-CC but not much else to say.
• Ult: Have map awareness. Regularly check the other lanes for champs limping away with low health. Can also be used to defend an unprotected tower until the laner returns.

Early Game -
Gangplank's early game is all about farming. His Q is excellent for this purpose. It is also very good for harassing, but farming takes precedence - building the Infinity Edge is expensive and quite important for Gangplank.

Why don't I rush IE, then? Well, because GP starts off rather passive, and then becomes a lot more aggressive in the later part of the game. Consequently, you don't need all that damage right off the bat. The Brutalizer gives you good enough harassing / farming capabilities in the early game.

My first built item thus focuses on farming. Philosopher's is the obvious choice - it provides health/mana regen for sustained farming, as well as some extra gold.

Youmuu's ups the three most essential stats for Critplank - crit, arpen, and cdr. It remains useful throughout the whole game.

During the early game there really isn't much reason to ever leave your lane. You should, however, have good map awareness. Whenever your ult is up, you must check the other lanes frequently for the opportune moment in which to use it.


Mid Game -
By now you should have your B.F. Sword. You'll still remain in your lane, but now you can be much more aggressive. Your enemies should be constantly getting Q'd. Remember that your W removes any CC and your E provides a small speed boost, should you need to escape from an overwhelming situation. With these things in mind, I personally like to play a little on the risky side.


End Game-
The mid game was your opportunity to get fed. While you're still able to do massive damage, you'll now find yourself getting a lot of assists, and helping to support your team with your ult and your buffs.

Shurelya's Reverie provides decent sustain, so you shouldn't have to go back for health/mana too often. Shurelya's active is a perfect compliment to your E, and can be used for pushing, chasing, or escaping.

Your ult is better than you may think. It can be used on a tower dive to force your enemies away. It provides a slow, should your team need to retreat. It can also break up the positioning of your enemies in a teamfight.

Otherwise, you should be using your Q and E liberally, staying with your team and helping with towers or baron. Throw crits on focused enemies, squishies, and champs with low health. You can chase them down, destroy their health with autoattacks, and finish them off with Q.

GP's Q OP! K.