well I think it’s a mixture of “gut feeling” and calculations. Like from a bayesian perspective, it’s adjusting your calculations on the basis of prior knowledge and beliefs.
Savants discuss about being able to ‘see the answer’ to a mathematical calculation - so maybe it’s not like going through a process of sums or calculations that you or I might do, but instead being able to instantly see or feel the correct approach which is on the basis of being able to instantly calculate the odds and probabilities on the tables and adjust based on good memory/experience etc.
I guess what it comes to is that there’s probably a grey area between savants and players who are very good at doing mental arithmetic on the fly. The second set of people can probably train and learn those abilities to a certain level.