I see lack of 3x3 strategies. And I would like to share my experience, as we mostly play 3x3 on ICCUP Hunters.
The most dominant setup is PZZ (except RRR=>ZZZ which of course is cheat setup).
The strategy is simple and we won games easily.
P - 5pylon 5gate
Z1 - 9pool, 3h mass lings
Z2 - 9pool, 1h fast muta rush
The main success of this setup is Protoss aggressive playstyle. With 3 zealots and 2 probes and with support of 12 (6x2) lings, Protoss can photon mid map entrance and prevent the move of the most dangerous opponent in mid game (for example 2 rax mm - Terran or 3gates zealots - Protoss). Then Z1 hold at entrance of opponent Zerg, Z2 after 6 lings can strictly go to 1h muta rush without defense. P hold entrance of last opponent.
The main goal is strategic dominance in the mid with initial 3 zealots 2 probes and 12 lings. And of course the reason of fast muta (huge harass) you can choose whether attack 3 vs 1 or expand mid and go to late game.