Are Jedi engaged in predictive battles utilizing some aspect of precognition to help improve their outcomes? Given what we've seen, I would say "not exactly." Are they like chessmasters considering their moves several swings ahead, using the Force to predict what would possibly work best against an opponent? Probably not. While there are Jedi precognitives, most depictions show them using their powers out of combat.
Looking at Jedi/Sith battles, it would be best to consider Jedi combat in the same fashion as you would any normal martial art here on Earth. Jedi train the body first, then sharpen the mind's connection to the Force. Force-sensitivity is enhanced so luck is no longer a factor, whatever the Jedi is good at, they will become better at. The Force can enhance fighting technique, but it seems to be more often utilized by the Sith than the Jedi. The Sith use their anger and channel the Force through it.
A bit more detail
Consider the fighting techniques of the Jedi like we would a normal martial artist. There would be three levels of consideration (four when we add the Force): Technique, Katas and Forms, Style and the Force.
Technique embodies the fundamentals of all Jedi/Sith lightsaber combat. How it works, why it works, what works, what doesn't.
Katas are the ritualized combat techniques used to help a martial artist sharpen their skills and techniques until they become second nature and can be done without thought.
Style will eventually embody particular techniques unique to the martial art. These would be specialized attacks or defenses used by practitioners of a specific discipline.
Now add the Force which offers enhancements to strength, speed, reflex time, awareness and a weapon that can, with the proper technique, slice through almost anything.
The Jedi training regimen is a challenging physical discipline honed with years of rigorous development of both the mind and the body.
Most often trained from childhood, their physical abilities even without use of the Force would make them excellent soldiers. When the Jedi fight on the field, they are often on the front lines leading and protecting their troops.
However, just like Earth based martial artists, technique can make or break any fight and the ability to read the technique of other fighters is a strong edge in any fight. The Force can act as another sense, another way to gauge your opponents connectedness and ability to harness the Force in their technique.
Use of the Force to predict blaster-fire (Form III, Soresu) is second nature to most Jedi due to their training, so it can be safe to assume they are able to, in a limited fashion attempt to read the attack style of their enemies attempting to predict their opponents attacks. This is likely more a physical training issue than just a Jedi-Force reading issue. Given the speed of lightsaber combat, there is clearly a mix of technique, reflex speed, prediction, and analysis happening simultaneously.
Some fighting styles utilize more interaction with the Force than others (Juyo/Vaapad, for example) which means a strong user of the Force is likely to get more out of that fighting style than a weaker user. But since Jedi train to find a fighting style suited to their use of the Force, most Jedi can likely read when a conflict is going to go bad for them within a few moments of fighting.
Vaapad required a constant and sizable stream of Force use from the user, with a barely contained explosion of Force power essential to all variations of Form VII as another prerequisite for its use. The form's attacks appeared to be unconnected, its motions seemingly unpolished to an untrained observer.
Does the Force, solely determine the outcome of a battle? No. The Force augments the will and the skills of the Jedi. It can make them faster, stronger, jump higher, have better reflexes, but when two Force users meet, martial training, then the connection to the Force come into play. A strong connection to the Force can make even a very old Jedi, (like Yoda) quite capable for a particular battle but it has been seen that Sith training can overcome even very good Jedi in a straight-up fight.
I would look at Jedi combat less as a battle of predictive algorithms and more as a form of reflex-enhanced dancing with deadly sword-play thrown in. There are steps, you need to know them, and despite the ease at which most Jedi appear when fighting, there is a constant assessment of the enemy both with their physical senses and with their connection to the Force.