Clearly, thri-kreen are meant to resemble some kind of eusocial insects, most likely ants or termites; I’m not entirely sure which one. (ETA: On Reddit, ghost_warlock kindly refers me to Wikipedia, where “the very first line . . . explains that they’re ‘mantis warriors.’ I am suitably shamed over not having thought to check Wikipedia for the answer.) However, these four-armed humanoids don’t possess the kind of hive mind or hive mentality you might attribute to them, based on their appearance. They’re not telepathic, nor are they even lawfully aligned. They don’t sleep, though, and they have the ultimate poker faces, betraying nary a hint of emotion.
Being chaotic neutral rather than chaotic evil, thri-kreen largely want to be left to their own business. The Monster Manual flavor text does say they “consider all other living creatures as potential nourishment,” and in the inevitable silly twist, “they love the taste of elf flesh in particular.” (Between thri-kreen and perytons, I’m getting the impression that elves must be delicious, like truffles or something.) But this seems to me to verge on evil, so I’d say that thri-kreen don’t attack other humanoids just to eat them unless they’re experiencing some kind of shortage of other foods. That being said, having already killed a humanoid for some other reason, they probably wouldn’t have any scruples about consuming the corpse.
Thri-kreen have high Dexterity and above-average Strength and Constitution. This gives them a bit of flexibility between brute melee combat and skirmishing, perhaps with a slight bias toward the latter, since they’re fast-moving (speed 40 feet per round). They also have proficiency in Perception and Stealth, plus Chameleon Carapace, which gives them advantage when trying to Hide. All these factors point toward ambush as a favored strategy.
Their Standing Leap feature is useful for surmounting obstacles, moving vertically between ledges and the ground, and crossing rivers or crevasses, but it doesn’t do anything to enhance their speed over level ground—unless the terrain is difficult. Then it gives the thri-kreen a pronounced advantage over opponents with move speeds of 30 feet or less, whose movement will usually be cut in half. And the thick, tall grass of the savanna, and the sharp rocks or shifting sands of the desert—the favored habitats of the thri-kreen—will generally constitute difficult terrain. In this respect, therefore, they’ve got the home field advantage.
Thri-kreen have an armor class of 15, which isn’t quite high enough to make opportunity attacks something they don’t need to worry about. But skirmishers need to be able to engage and disengage somewhat freely. How do they get around this?
Well, they do have one thing going for them: the poison in their bite. A poisoned opponent attacks with disadvantage, which gives the thri-kreen a better chance to elude an opportunity attack. However, the difficulty class of the thri-kreen’s poisonous bite is pretty easy to beat, especially for an opponent with a high Con. Thri-kreen are simple-minded, but they’re good at choosing targets, so rank-and-file thri-kreen will steer clear of tougher-looking opponents at first. They’ll leave those foes to their armed allies.
From a place of hiding, thri-kreen will initiate combat when foes come within 30 feet of them, springing out and attacking with the element of surprise, distributing their attacks across all opponents who don’t appear to have above-average Constitution and continuing to fight hand-to-hand until either the opponent is down for the count or they themselves are moderately wounded (reduced to 23 hp or fewer). At that point, they’ll chitter for help, and other thri-kreen who’ve managed to poison their opponents will leap over to assist, while they themselves leap away when their own opponent is poisoned to go fight someone easier.
Thri-kreen communicate constantly during combat, in their impenetrable language, but mostly they just tell each other things like, “I’m hurt,” “This one is tough,” “This one is fragile but dangerous,” “This one is poisoned.” They exchange information, but they don’t really coordinate. If one accidentally engages an opponent that’s tougher than it thought, one or two other thri-kreen may come to help, attacking from behind for the flanking bonus (“Optional Rule: Flanking,” Dungeon Master’s Guide, page 251—I don’t consider it optional!). When half of a group of thri-kreen are seriously wounded (reduced to 13 hp or fewer), or when all of them are at least moderately wounded, they’ll call a retreat, favoring the Dash action if they’re outnumbered and the Dodge action otherwise (they’re not quite smart enough to know how to Disengage).
Variant thri-kreen may be considered to be better trained than ordinary thri-kreen, and with this training comes a discipline that does allow them to Disengage. However, these thri-kreen will stay in the fight long enough to cover their allies’ escape before Disengaging. They’re also the ones that will engage the toughest opponents, if they’re present. First, they’ll close to a distance of 30 feet and throw their two “chatkchas” in a single Multiattack action. After that, they’ll close and fight with their double-bladed polearms, called “gythkas,” also combining two attacks in one Multiattack action. When one of these “soldier thri-kreen” is engaged with a melee opponent, a regular thri-kreen will often come up behind it for a flank attack, in the hope of poisoning the foe with its bite. (In any thri-kreen encounter, it’s good to have the thri-kreen slightly outnumber their opponents in order to allow a few to dart from opponent to opponent.)
Because magic weapon is no good unless you’re a carrying a weapon already, psionic thri-kreen will usually also be soldier thri-kreen—either that, or they’ll never use their ability to cast magic weapon, which seems like a waste. Psionic thri-kreen engaged with the toughest of their opponents will use invisibility to vanish and relocate when they take a particularly serious hit (one doing 10 points of damage or more). Once they’ve used this once-per-day ability, they’ll cast blur upon re-manifesting, giving their opponents the same penalty against them as if they were invisible, although they themselves won’t get advantage on their attacks, as an unseen attacker would. Soldier thri-kreen will cast magic weapon on their polearms, not on their chatkchas.