Let's get a bit more details on exactly how much computation the min max algorithm has to do. If we have a game of breadth b and depth d, then evaluating a complete game with min-max would require the construction of a tree with eventual d ^b leaves. If we use a max depth of n with an evaluation function, it would reduce our tree size to n ^b. But this is an exponential equation, and even though n is as small as 4 and b as 20, you still have 1,099,511,627,776 possibilities to evaluate. The tradeoff here is that as n gets lower, our evaluation function is called at a shallower level, where it may be a lot less good than the estimated quality of the position. Again, think of chess where our evaluation function is simply counting the number of pieces left on the board. Stopping at a shallow point may miss the fact that the last move put the queen in a position where it could be taken in the following move. Greater depth always equals greater accuracy of evaluation.