# Number of all possible splits in each node of trees in a Random Forest

The trees in a Random Forest are grown by recursive splitting the nodes, and the best split in each node is obtained by using the Gini index, I want to know if there is a possibility to know the number of all possible split-cuts? For example by knowing the dimension of data and mtry ?

• I'm not sure why this is marked as a duplicate, the question is not addressed at all in the linked 'duplicate'. – bi_scholar Jan 15 at 16:24
• My question is not answered in the link provided, I am asking about the number of all possible splits in the node, and I expect a formula or a specific explanation rather than a general explanation on mtry. – user6845158 Jan 16 at 10:09

Since the original trees in the Random Forest are build via the CART algorithm, the number of possible splits at each node is given by the sum of the carnality of each variable in the mtry subset. For example, in case three variables A, B, C are selected at a node $$i$$, with A being a binary feature, B an integer in the interval $$[1, 100]$$ and C a continuous variable taking on 200 distinct values in the current sample, the number of possible splits is $$2 + 100 + 200 = 302$$. Note that the 'local' carnality of variables gets smaller the deeper down the node is in the tree, since as the number of samples decreases, the expected number of distinct values decreases as well.