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So that means that with our minimax algorithm, and if we are using a common computer, our “Artificial Intelligence” takes 1 minute at each step to decide which action to choose by computing all the possible outcomes $6$ plies in advance. Actually the minimax algorithm will certainly take a minute to look ahead 6 plies and not 2 seconds because a state expansion doesn't correspond to an atomic operation from the processor point of view That means that the minimax algorithm will take roughly $2$ seconds to determine the best next move to execute by analyzing all the possibilities $6$ plies ahead. Hence, if we use the minimax algorithm we could look ahead only about $6$ plies because a common CPU has aįrequency around $1e9$ and $1.8e9/1e9 = 1.8$ seconds. $N = 6 \rightarrow 35^6 = 1.8e9$ possibilities if we try to anticipate the moves up to $6$ steps in advance.$N = 3 \rightarrow 35^3 = 42875$ possibilities if we try to anticipate the moves up to $3$ steps in advance.
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$N = 2 \rightarrow 35^2 = 1225$ possibilities if we try to anticipate the moves up to $2$ steps in advance.$N = 1 \rightarrow 35^1 = 35$ possible moves.The branching factor allows us computing the number of states we need to expand to be able to anticipate the $N$ next moves. I have already mentioned, in the previous article, that we cannot use a naive brute force approach to solve the Chess game because it supposes we can build a Tree containing at least $10^$.