This is fresh off the top of my head, so it may not be very well balanced. It looks a tad under-powered to me, compared to standard races like dwarf and elf; except the "monstrousity" type may be very powerful, it's hard to tell (in my experience, PCs don't get hit by
hold person or
charm person or
crown of madness all that often; but immunity to
dominate person is pretty cool). But I would contend that it is entirely playable -- meaning, I think it's pretty clear how playing this race would work, and their drawbacks aren't severe enough to cripple them as adventurers.
I'm releasing this Pay-What-You-Want, although at present the only currency I accept is ENWorld XP.
Centaur
Ability Score Increase. Strength +2, Constitution +1.
Speed. 50 ft.
Size. Large. Your carrying capacity is doubled, but armor and clothing for you weighs twice as much as for a humanoid, and costs four times as much. You require four times as much food and water as a normal humanoid. Moving through a passage big enough for a medium-sized creature requires you to squeeze.
Monstrosity. Your creature type is "monstrosity," rendering you immune to effects that only affect humanoids, such as the spells charm person and hold person.
Equine Shape. You have disadvantage on ability checks made to climb, tumble, or balance on a narrow surface.
Equine Toughness. Your hit point maximum increases by 1, and it increases by 1 every time you gain a level.
Hooves. Your unarmed strike deals 1d6 bludgeoning damage.
Centaur Weapon Training. You are proficient in the spear, pike, shortbow, and longbow.
Languages. Common, Elven, and Sylvan.
My theory is that the stat block in the
Monster Manual represents a centaur warrior, a protector of the tribe, who's got some skills, ability scores, hit dice, and special abilities above and beyond your typical "I am a 1st-level PC" centaur. (By way of analogy, the lowest-level drow and lowest level svirfneblin in the
MM are both 3-HD creatures.) I know some people don't like to see a discrepancy between player race stats and monster stats, but I think it works well in this case, because if you create a 6th-level centaur fighter with the Charger feat, the result looks remarkably like the
MM stat block. (The numbers aren't exactly the same -- your hoof damage and charge damage will be less -- but you'll have more hit points and skills, plus all those great fighter special abilities.)