Hand to hand
The time window of precognition is going to have a huge effect on how hand-to-hand works. With precognition times of more than a couple of seconds, one of the fighters will seek to run away, knowing that they can't win. The vast majority of real-world fights are over in a couple of strikes.
With a window of a tenth of a second, the two fighters would circle each other, with every feint and shuffle being broadcast through time. They wouldn't bother doing them unless they could connect. It would be a fight of attention span, waiting for the opponent to get distracted so you could come in with an effective attack.
If you ever watch MMA, you know how difficult it is to keep a fight from devolving into mat work (wrestling, or Brazilian Jiu jitsu). It's the inevitable state for well matched fighters. Precognition would make this inevitability more obvious.
What you would see is a significant increase in the value of strength, endurance, and speed. Being able to predict your opponent's moves and fighting styles, knowing how their reactions will get them to tangle their feet, knowing that your opponent will put up their guard when you do this, leaving that unprotected, is what almost all skill in martial arts revolves around. As such, the focus would shift to improving the raw physicality.
To an outside observer, equally matched combatants would approach each other with their hands poised to shoot out and grab. They'd slowly circle each other, then one would rush in, and it would be a wrestling match.
Blades
Bladed combat wouldn't be much different than hand-to-hand. Both opponents would see a probability cloud of where their opponent could get their blade to go, based on the blade's mass and the wielder's strength and speed. Again, if you have more than a couple of seconds, an inferior swordsman would just run, or fight defensively if they can't run.
One thing you'd see is increased use of tassels, cords, and scarves, used to distract, bind your opponent's weapon, or block their view. Two-handed techniques would be more popular because they increase the number of probabilities that someone has to keep track of. I suspect that shuriken and throwing knives might play a role in reducing your opponent's options.
Nonetheless, it wouldn't be very interesting to watch.
