How to sum the probabilities of an event?

Question

Mathematics

The poker player of each of the 4 stages of the game can make actions of 4 different sizes. Each size has its own probability that there is a strong or weak combination. How can we sum these probabilities over all stages in order to make a more accurate guess about the presence of a strong and weak combination after the 4th stage of the game, taking into account the statistics of his past games?
For example.
Stage 1 - small bet - shift the probability to the weak side
Stage 2 - average bet - do not shift the probability
Stage 3 - big bet - shift to the strong side
Stage 4 - big bet - shift the probability to the strong side
We conclude: -1 0 +1 + one. Most likely there is one unit stronger than usual.
How to do it mathematically? Which method to use?

Answer 1

You are not asking the question that way. Not "how to sum probabilities". And what kind of model can be built to calculate the final results of rates based on each stage. Maybe you need to add the probabilities, or maybe multiply ... That's the question. Whatever model you build, so be it. In general, everything is correct Bavashi writes to you. You need to analyze the dataset against the results and find correlations with rates at each step. By themselves, the rates do not say anything, even if they are folded, even multiplied.
UPD: In general, it seems to me that the approach is vicious. It is clear that the player's bets are affected by the behavior of other players, as well as what opens on the flop, etc., but this does not appear in your case. And what is a strong or weak hand compared to what. Those. the task is initially very multi-parametric, and not taking into account many factors leads to the construction of an incorrect statistical hypothesis.