r/MachineLearning - [D] Decision Tree Splitting strategy

I have a dataset with 4 categorical features (Cholesterol, Systolic Blood pressure, diastolic blood pressure, and smoking rate). I use a decision tree classifier to find the probability of stroke. I am trying to verify my understanding of the splitting procedure done by Python Sklearn. Since it is a binary tree, there are three possible ways to split the first feature which is either to group categories {0 and 1 to a leaf, 2 to another leaf} or {0 and 2, 1}, or {0, 1 and 2}. What I know (please correct me here) is that the chosen split is the one with the highest information gain.