Perceptron 11 5 The Algorithms for the Problem 14 5.1 Preexisting Algorithm 14 5.1.1 Nim-sum 14 5.1.2 Nim-sum of the State 15 5.1.3 Finding the Correct Move 16 5.2 Reinforcement Learning 16 5 Time Complexity ..... 49 7.1 The Deterministic Algorithm ..... 49 7.1.1 Time-complexity of the Nim-sum Operation ..... 49 7.1.2 The Rest of the Algorithm ..... 50 7.1.3 Practically, Then? ..... 50 defined as the value of a pile in a game of Nim. $ ^{7} $ The Nimber of a game of Nim is simply the Nim-sum of the game, which will be explained later. Because of this theorem, it seems easy to conclude that