If we consider these compositions to be the strongest, that might be slightly misleading as each composition has its own specific counters. However, in Teamfight Tactics Season 3, players may end up in one of the five special galaxies, and each galaxy often inadvertently “favors” a particular composition by boosting its power. To increase your chances of winning, you can refer to and use the compositions favored by that galaxy.
Here is the list of the best compositions to play in each galaxy:
Neeko Galaxy (offers 2 Neekos)
Since you start with 2 Neekos, in this galaxy, compositions with cheap carries (1, 2, or 3 gold) will be the strongest early on. The simple reason is that you can easily upgrade to 3 stars early on, gain a winning streak, and snowball the entire match. The compositions that fit this condition are:

This composition allows you to roll early from level 7 to acquire the main carries of the team, which are Shen, Master Yi, and Yasuo. This composition is nearly balanced in both offense and defense because Shen blocks basic attacks (physical damage) and has 2 Mystics to increase magic resistance. The damage is provided by Master Yi who “slices through armor like butter,” regardless of whether the enemy has high or low armor, along with Yasuo who specializes in hunting down enemy carries.

The composition includes main carries of 2 and 3 gold, namely Darius, Rakan, Jayce, and Xin Zhao. Darius will be the primary damage dealer with his continuous “axe chops.” You should maintain experience at level 5 to roll for Darius 3 stars early; rolling at this level can also conveniently yield Rakan and Xin Zhao as well as Jayce and Kassadin.

This composition also features many 2 gold and 3 gold carries like Neeko, Ahri, and Syndra. With 2 Neeko items, you can completely have the chance to obtain Syndra 3 stars very early and one-shot opponents continuously. However, it’s still advisable to check the opponents’ boards before rolling to avoid wasting roll money without getting results.

Being one of the compositions that appeared in many previous updates, the duo of Xin Zhao and Rakan is still highly trusted in this galaxy due to their strong carry potential when reaching 3 stars and having 3 defensive items.
Trade Galaxy (free 1 roll each round)
Basically, all the compositions you should use in Neeko Galaxy should also be used in this galaxy. The reason is that being free to roll once each round allows you to acquire “cheap” 3 star carries very early, clean out your money to gain a winning streak, and snowball the entire match.
Purple Nebula Galaxy (4 gold units available in the first shop)
In this galaxy, almost anyone who gets hold of powerful carries like Irelia or Kayle will have a very high win rate. Therefore, compositions combining these two champions will “gank the team extremely strong” for you, and that composition is:

With many high-damage champions along with the main carry appearing from the first shop visit, the 6 Bladesmen composition is extremely powerful in the Purple Nebula galaxy when you catch Irelia or Kayle.

Similar to the 6 Bladesmen composition, this Hypertech composition also gives you tremendous power if you obtain Irelia or Kayle early. At this point, Irelia will have a lot of health and damage, while Kayle can unleash damage freely against the tanky units of Hypertech.
Island Galaxy (free 1 Natural Armor at level 5)

The composition that benefits the most in this galaxy continues to be Hypertech – the top meta composition. This is because it provides a free item that makes one Hypertech champion stronger, saving an item for the main carry of the team. Additionally, with one more slot at level 8, you can add Thresh to activate the Cursed and pull down crowd control champions, creating more space for the carries to operate.
Medium Legends Galaxy (increases health cap to 125)
This galaxy gives players more time to “burn health” to find the most crucial pieces, so the most suitable composition will be:

Rebels is one of the more luck-based compositions of Season 3 because this composition is very strong in the early game but significantly weaker in the mid-game compared to other compositions. Until you have the last piece, Aurelion Sol, this composition may struggle to escape a losing streak. However, with up to 125 health, you can take a losing streak to earn money to level up to 8 or 9 and roll for Aurelion Sol to complete your composition. If you’re lucky, you might also find 2 Rebel Emblems to activate 9 Rebels, maximizing the power of Rebels and Aurelion Sol.