I'm working on an algorithm that predicts expected value equations of making certain moves in a probability based game. I am trying to come up with a metric that can prove that these expected value equations are accurate and the following questions I am stuck on. I have tried running these simulations comparing correct EV equations vs their one round value over a large number of rounds, but I can't come up with a metric that can quantitatively verify that the predicted EV equation is correct.
Let's say we have two vectors $p$ (probabilities) and $v$ (values) of size $n$.
Let's assume a very large amount of rounds $k$ where each round you are given a new expected value equation of EV = v · p. Is there anyway to accurately estimate net profit over $k$ rounds?
Second question. Let's say you had a way of predicting these EV equations but the only label you are given is the value of one round. Is there any metric that can be calculated that prove these predicted EV equations are accurate over a large number of rounds?