Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
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Gangplank may be seen as more useful in 5v5 than 3v3, however seem to be able to rack up amazing scores and some of the longest win streaks I've ever had using him in 3v3.
This build is slightly based off of another guide on Mobafire which is however more for 5v5, I followed this build and realized that the items are very costly and in a 3v3 you do not have much time to build expensive items.
The changes I have made are to make Gangplank more viable in a 3v3 situation. Starting off with putting the first point in Parrrley rather than Raise Morale. You may wonder why, seeing as with putting the first point in Raise Morale will enable you to kill 2 minions of the first wave, denying the opposing team to level to 2. The issue with having Raise Morale first is that 3v3 is gank heavy and it is important to have a very early firstblood, so working with your team, your Parrley will ensure, along with your passive DoT and Ignite that you will get firstblood. Denying the other teams exp. through killing your own minions in your lane is also not as effective as in 3v3 Jungling is an even bigger aspect of the game. Gangplank is not one of the best junglers, unless of course you go for some lifesteal early on or a little bit of armor/hp regen but as Gangplank you want to focus on teamfights and how you can help your team win them.
Raise Morale will give your team a few stat increases, the extra run speed being a good one, especially if your teammates lack slows. You also have great survivability with your Citrus Fruit ability, soaking up any CC. I still wouldn't say that Gangplank is a good initiator, however he's good at getting away so he's a great harasser. It is easy to run towards them and load off a Parrrley. Although Gangplank does have some mana issues in the lower levels, so be sure you don't spam your abilites too much. You want to be able to kill as many of your own minions as you can.
Your ultimate is in my opinion one of the best ulti's in the game. Cannon Barrage can not only deal a lot of damage and slow enemies for an easy gank or even so an easy escape, but it can also be used to save teammates or jungle... WITHOUT having to even enter the jungle or go near your teammate. Be sure to place your Cannon Barrage well, look at the direction the enemy champions are running in and place in in their path. Even if they have quick reactions to walk in the opposite direction it's going to force them away, in the direction they don't want to go. So either saving a teammate or helping him with a gank.
If it is to preferance, it is also possible to take the Black Cleaver instead of Atma's Impaler but that is of course just your last item and if you just want a quick upgrade it's going to cost you more. You can also use Frozen Mallet, however it works out to give you about the same survivability ratio as the Atma's Impaler armor bonus. The best thing about Frozen Mallet is the passive slow chance, which is good to stop those damn Olympic running champions from escaping your reach!
Do not forget that you have to contribute some of your gold earnings towards sights, map control IS one of the game winning aspects in 3v3. If you can constantly see your enemies movements, I say that you have already won. Knowing where the enemy champions are is a HUGE advantage. You can see when they are alone or when they are in a difficult situation, such as soloing the Dragon. You can go in for the easy kill or prevent them from killing it with a Cannon Barrage. The best one is when a low level champion is going for the Lizard and you can team gank him without him even knowing what hit him. Knowing when enemies are switching sides is also a great advantage as you know when someone will be in your back, giving you the opportunity to retreat before they get there.