Every match is simulated 20,000 times. Goals follow a Poisson model with separate attack and defence strength per team and a home advantage, fitted separately for each half so half-time markets fall out naturally. Corners and cards follow negative-binomial distributions whose spread is estimated from how far real matches deviate from the model's expectation.
Two hidden factors tie the legs together. A match tempo scales both goals and corners, so a bet like “over 2.5 goals and over 9.5 corners” is more likely than the product of its parts. A card heat factor is shared by both teams. This is what makes the bet builder's joint probability different from simple multiplication.
For goal markets the bookmaker's price is used as an anchor: the model's attack rates are adjusted so that its 1X2 and over/under 2.5 match the market with the margin removed. Markets for goals are efficient; we do not pretend to know better. Corners, cards and the half-time structure are left to the model.
Every league is tested walk-forward: for each month of the last seasons, the model is trained only on matches before that month and scored on that month. If a market's Brier score is not better than predicting the league average, we switch it off for that league and say so. The Track record page repeats this exam in public, on predictions stored before kick-off.
Data: football-data.co.uk. Probabilities are estimates and can be wrong. Nothing here is advice.