how thick should bjj mats be to avoid injury?

i would say minimum of 1.25". depending on the mat itself, there is always a maximum. you obviously dont want mats that sink in when you walk on them. i would ideally go somewhere between 1.5 and 2", depending on the give of the mat. if you do a lot of throws, then go bigger. if primarily jiu jitsu, then you dont have to exceed 2 inches. hope this helps.