Hey heraldic2.

You will need a conditional distribution that gives a model that given a prior score, you will get a new score and this model is known as Markov Modelling. It's a fancy of saying that the next outcome only depends on the outcome that came before it and nothing else (for each outcome).

This is a more general model taking into account the performance of the last game to update the probability but if you want to consider that each probability of winning (or losing) is the same for each game then this is called a Binomial model where this gives you a probability for winning X games in N attempts.

Both are very different approaches with different assumptions and you will need to decide what those assumptions are.