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I like it because in a 3v3, I feel like I have more of an impact on the direction of the game. Instead of just being 1 in 5 players, you are 1 in 3, every action you make has a lot more weight to it.
The feeling of the map is just great, I've always liked 3v3. The only reasons why I don't play it more is because if you don't have certain champs and the enemy team does, you are at a massive disadvantage and there is no Normal Draft.
That and it's obnoxiously difficult to actually finish the game, breaking a turtling team is painfully difficult even if you are leaps and bounds ahead.