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Game Playing

Game Playing. Introduction. One of the earliest areas in artificial intelligence is game playing. Two-person zero-sum game. Games for which the state space is small enough – generate the entire space. Games for which the entire space cannot be generated. The Game NIM. 7. 6-1. 5-2. 4-3.

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Game Playing

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  1. Game Playing

  2. Introduction • One of the earliest areas in artificial intelligence is game playing. • Two-person zero-sum game. • Games for which the state space is small enough – generate the entire space. • Games for which the entire space cannot be generated.

  3. The Game NIM 7 6-1 5-2 4-3 5-1-1 4-2-1 3-2-2 3-3-1 4-1-1-1 3-2-1-1 2-2-2-1 3-1-1-1 2-2-1-1 2-1-1-1-1-1

  4. NIM- MAX Plays First MAX 7 MIN 6-1 5-2 4-3 MAX 5-1-1 4-2-1 3-2-2 3-3-1 MIN 4-1-1-1 3-2-1-1 2-2-2-1 1 . MAX 3-1-1-1 2-2-1-1 0 2-1-1-1-1-1 1 MIN

  5. NIM- MIN Plays First MIN 7 MAX 6-1 5-2 4-3 MIN 5-1-1 4-2-1 3-2-2 3-3-1 MAX 4-1-1-1 3-2-1-1 2-2-2-1 0 . MIN 3-1-1-1 2-2-1-1 1 MAX 2-1-1-1-1-1 0

  6. Minimax Algorithm Repeat • If the limit of search has been reached, compute the static value of the current position relative to the appropriate player. Report the result. • Otherwise, if the level is a minimizing level, use the minimax on the children of the current position. Report the minimum value of the results. • Otherwise, if the level is a maximizing level, use the minimax on the children of the current position. Report the maximum of the results. Until the entire tree is traversed .

  7. Minimax Applied to NIM MIN 0 7 MAX 1 6-1 0 5-2 0 4-3 0 MIN 5-1-1 0 4-2-1 0 3-2-2 3-3-1 0 MAX 4-1-1-1 1 3-2-1-1 0 2-2-2-1 0 . 0 MIN 3-1-1-1 1 2-2-1-1 MAX 2-1-1-1-1-1 0

  8. Generating the Game Tree to a Depth • In some cases the game tree will be too large to generate. • In this case the tree is generated to a certain depth or ply. • Heuristic values are used to estimate how promising a node is. • Horizon effect .

  9. Example

  10. Heuristic for Tic-Tac-Toe • h(n) = x(n) - o(n) where • x(n) is the total of MAX’s possible winning (we assume MAX is playing x) • o(n) is the total of the opponent’s, i.e. MIN’s winning lines • h(n) is the total evaluation for a state n.

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