They fire bows.

I always imagined them doing the Naruto run majestically across the plains.

they clack together two halves of split open coconuts to confuse the enemy

I think it depends partially on where it sits on the centaur scale.

They shoot you with their bow.

Maybe they Naruto run while galloping

They hold a polearm. Always.

They shoot arrows with a bow?!

With the whole upper half bobbing up/down like a horse nodding it's head while it runs.

Hmm, humans swing their arms while running to counteract angular movement. Presumably, the horse undercarriage wouldn't have this problem, because there's more legs in an offset motion and just some distance between the pairs of legs to hold the body straight.

But horses nod their heads during gallop, so maybe the centaurs would do a little chug-chug motion with their arms instead.

This is just another reminder how weird a centaur is as a concept. Vertebrates don't have more than 4 limbs. Land vertebrates mostly have 4 legs, but the structure of their forelegs is very similar to human arms and wrists. Bats have wings, but their wings are basically arms with a membrane of skin between the bones. Even a Naga (human / snake hybrid) makes more sense than a centaur.

Also, think how unbalanced a centaur would be. Instead of a trunk that merely has to support a neck and a head, a centaur has to support a full half-human right at the front of its body. That would shift the centre of mass way forward, so most of the weight would be on the middle limbs. That would affect its ability to gallop, because in a gallop most of the running power of a horse comes from the back legs. If the back legs are almost completely unloaded because all the weight is at the front, the back legs wouldn't be able to push with much force.

A more realistic centaur would have the trunk weight shifted backwards, so instead of having a human torso replacing its neck and head, it would be like a rider on a horse but without the rider's legs or the horse's head.

I have visual references

Hold a shield and spear or somethin like that maybe?

Spank the butt

They cross their arms since they also don't know what to do with them.

Steam Deck.

One hand scrolls through tiktok and the other holds an iced coffee, just like humans do while driving a car.

Naruto run.

I would be holding on to my dick and balls so they don't smack me in the asshole every gallop.

Does no one watch Xena anymore?

Noodle arms

they actually just bend down and use the human arms to help walk (more legs = faster, since less time without touching ground, more time propelling themselves forward)

They place them majestically on their hips, as if they're the captain of a boat.

they hold them out in front of themselves like they’re holding motorcycle handlebars and they make the sounds with their mouth

Just windmilling their fists like wrecking balls.

Centaurs (and other *taur types. Looking at you, furries) are overall an incredibly dumb design.

The more you think about them, the more they just don't work. I went from meh, to dislike, to hate for centaurs over the years.

They hold crossbows.

This is the real reason centaurs are almost always drawn with bows and arrows. Not for horse archer vibes, so the artist had something to do with their hands.