Estimating probability of player playing move in the opening For position you never played, book probability is perfectly fine for me. The question starts when you already played position x-times. I'm looking for function that will update book probabilities with your style. Obviously if you play 1.d4 in 97 games out of 100 games, probability of playing 1.e4 runs close to 0%. On the other hand, if you played some late position just once, it's nowhere close to 100% you will repeat the move. I could probably make some  workaround myself, but this looks like problem data scientists must have already solved, as it is applicable to virtually any discipline where you want to predict someone's behavior.

Edit: I think there should be one parameter &lt;0;1> measuring how seriously we take book probabilities and how seriously we take players games. With one extreme being ignoring book and one being ignoring player's games.
Intuitively we should look at the player's games for early moves and book moves for later. This is because as we get further in a game, the number of possibilities increases, therefore the sample size of player games decreases. In this scheme, we are assuming that the player in question behaves as the average player does in the long run given the positions they usually seek from the opening.

You could use a rule of using the player's games if there are more than 5 to use, and using other players games otherwise.