2 stuns go much further when there are only 3 opponents!
In 3v3, every champ needs to go further, do more, be all that they can be, etc. etc.
This Amumu is:
- Tanky and hard to kill mid to late game (very important)
- Extremely heavy CC
- Devastating in team fights
- Rips tanky characters to shreds with Despair
- Powerful Ganker who can stun from a bush or stun a chasing opponent
- Able to resist/escape ganks
Because of this, he's one of the best suited champions to Twisted Treeline.
Boots of Swiftness are a must for Amumu! You need to be up close to them all the time, and when they focus on you, you need to get out of there fast. There is lots of CC in 3v3, but not enough to make Mercury's Treads better than boots of swiftness. Also, mobility is one of the keys to 3v3 since the map is so small. You can get anywhere fast using Boots of Swiftness, which makes them valuable for every situation in the game, where the other 2 common Amumu boots are only valuable in combat.
Maki Pendant is optional, but I usually find I need it early game to spam Tantrum. You can later upgrade it to Fiendish Codex if you want, especially if you are against a tanky team and want to have Despair on all the time, and later upgrade to Deathfire Grasp. Because of Greater Seal of Scaling Mana Regeneration, the Codex is optional.
Sunfire Cape is designed for Amumu, since he always needs to be up close. It deals magic damage, which means is has a great synergy with Amumu's passive.
At this point, you are still squishy, and can be quickly focused down and CC'd. Because you don't have Mercury's Treads, Banshee's Vail is extremely important for mid to late game survivability. If you find you have no trouble staying alive you can skip it.
Rylai's Crystal Scepter rounds out the build, and makes late game unwinnable for the opposing team. Get Blasting Wand first, since you are already hard enough to kill. If you finish crystal scepter, you will be slowing opponents with all of your abilities, and since you have Boots of Swiftness there is no hope of them escaping! If the game gets to that point [almost never does] you will know it's over for them.
If the game is still going and you are feeling squishy, go for Guardian Angel, or if you want to deal more damage you could go for Deathfire Grasp. Remember to use it's active ability at the beginning of the fight! It's especially good against off tank teams, which are common in 3v3.
How to Play
The most important part of 3v3, especially with a slow character, is map awareness. You need to know when ganks are coming your way, and when an opportunity to gank shows up.
Bandage Toss can win you the game if you hit them, and lose you the game if you hit a creep by mistake. Practice practice practice, because when it counts you will be glad you did.
Play style for Amumu is similar to 5v5: Q, W, hit, E, hit, hit... if their team showed up, R. If they're still alive, Ghost or Bandage Toss again. If they chase you or stun you, hopefully you have flash, cleanse, or exhaust.
When played well, Amumu is the ultimate champ for turning team fights. Dirty tricks like bandage toss from behind a wall into their team, followed by Curse of the Sad Mummy while your team focuses them down, create many opportunities for Aces.