I think you’re missing what I’m saying. I’m not talking about ML. I’m taking about mixed integer programming. Minimizing the depth of the trees is the goal, not a method of getting there. Most discussion I see on this is on greedy methods that choose the first step that will maximize information gain and then the next best and so forth. But it’s possible there exists a first step that is less optimal up front but allows for more entropy on the second steps. I’m not sure if the greedy solutions are able to guarantee a three step solution for all possible words. Even if they are, it’s probable that they’re still inferior to the globally optimized answer.