What is the meaning of observing commandments according to a determinist?

None. Ask him.

The purpose of the commandments is to improve the person.
And just as the mechanic doesn’t require your car to have free choice, so too here.
There is no connection between free choice and improving the person.
Belief in free choice comes from pride and nothing more. (To be free. To resemble God.)

Michi, the confusion between denying free choice and the human capacity for thought and rational decision-making is a pitfall that many fine people stumble over. Even in a world that proceeds according to its natural laws (perhaps only in such a world), we are influenced by the results of our actions and plan our steps wisely so that we may earn reward and avoid loss.

Decisor, the purpose of the commandments is the service of God, not the “improvement of man,” that is, the service of man.

Best regards,

Yeshayahu Leibowitz

Does a determinist think we don’t need laws? Is he in favor of shutting down all the prisons and courts? I don’t think so.

Indeed, for a person to be improved, he has to believe that the purpose of the commandments is the service of God.
In practice, God in the Torah serves as a means, and without that role He would have no meaning at all.
The proof is simple. If God had not been mentioned in the Torah, it would not have interested anyone.

Yoav, the determinist can think that laws are needed, because that is how he is programmed to think. Beyond that, the laws are part of the constraints that dictate a person’s behavior, so even according to the determinist laws have a role. But the whole process—decision, legislation, influence—is deterministic. The question is why the Holy One, blessed be He, would create a world in which determinism reigns and mechanically carries out His purposes. In particular, it is not clear why He tells us that we have choice when we do not.
And of course prisons and courts too are a result of the deterministic mechanisms acting on us, so there is indeed reason to relate to them.

Michi. So what if it is all deterministic.

After all, no one disputes that when we taste food, that is deterministic. Why in that case don’t you say, “therefore there is no point in relating to it”? This whole argumentative approach just doesn’t hold water.
If injustice arouses anger, then the insight that this is something deterministic only strengthens it. Because then one can come and claim that this is a natural matter and not a temporary madness.

I make the same claim about those too; there is no point in bringing proof from them to our issue.
Your identification of free will with madness is precisely the misunderstanding I keep pointing out to you all the time. It was explained in detail in my book The Science of Freedom and in an article here on the site.

As one more voice in the chorus, I too will note that the point about attributing a higher probability of correctness to conclusions of “free” choice than to conclusions produced by determinism is one of the most barren rocky crags that Rabbi Michael decided to plant his flag on, all the way to entrenching himself among various kinds of doubts and skepticism.

When 2 human beings with free choice arrive at different conclusions on a certain issue, the possible ways to explain the cause of the disagreement are:

1. These are two rational people with different assumptions. Therefore, different conclusions.
2. They have the same assumptions, but one of them lacks reason, meaning he is crazy. Therefore he reached an incorrect conclusion.
3. They are both crazy.

What can’t be said? It can’t be said:
4. These are two rational people with the same assumptions, but free choice caused different conclusions.
And that is identical to madness.

In summary, the madness of belief in free choice is meant to cultivate the impulse of pride (or alternatively, to serve as an educational tool so that all kinds of donkeys won’t think they’re allowed to do whatever they want).
You never explained anything that would lead me to think of any other option.