Take the American put option with strike price K=98 as an example, the result of Monte Carlo simulation is a definite price path, such as the following:

T | t= | t=1 | t=2 | t=3

Path 1 | 1 | 97 | 13 | 15

If you compare it, But this is equivalent to knowing the future price trend when t=1.

This kind of predicting the future is not allowed in reality. You can return to the data and get the mapping relationship (or law), but you can't turn over the script and directly use the future results. Therefore, it is considered to introduce least square Monte Carlo simulation, E(Y|X)=g(X), where y is the discounted value (i.e. intrinsic value) of the future income brought by continuing to hold and not mentioning the exercise right, and x is the price of the subject matter at time t.

To deepen your understanding, you should consider the European option. Because it doesn't depend on the path, it won't exercise in advance, and only pays attention to the price of the subject matter at the expiration date t, so it can be directly simulated by Monte Carlo.