Game Tree ( Oyun Ağaçları )

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How computer(Artificial Intelligence) choose next move. How to apply Minimax Method and Alpha & Beta Pruning step by step.

Tecnologia

Unbeatable TicTacToe (xox) Alp Çoker www.alpcoker.com [email_address] Game Tree

Game Systems Rely On ,[object Object],[object Object],[object Object],[object Object]

Why Board Games? ,[object Object],[object Object],[object Object],[object Object]

Minimax Method ,[object Object],[object Object],[object Object],[object Object]

Minimax Method ,[object Object],[object Object],[object Object]

Minimax Search Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Evaluation Function ,[object Object],[object Object],[object Object],[object Object]

Minimax ( Decide Whose Turn ) MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 12 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 12 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 12 4 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 4 12 4 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 4 3 12 7 6 3 4 18 6 15 7 24 15 12 5 18 6 7 11 7 24 1 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 7 4 3 12 7 6 3 4 18 6 15 7 24 15 12 5 18 6 7 11 7 24 1 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

Minimax ( Evaluate Funcions ) 4 3 12 6 3 4 18 6 15 24 15 12 5 18 6 11 7 24 1 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN 7 7 7 7

α-β Pruning ,[object Object],[object Object]

α-β Pruning 11 7 5 1 8 10 16 14 2 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

α-β Pruning 7 11 7 5 1 8 10 16 14 2 <7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

α-β Pruning 7 11 7 5 1 8 10 16 14 2 <7 >7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

α-β Pruning 7 11 7 5 1 8 10 16 14 2 <7 >7 <5 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

α-β Pruning 7 11 5 7 5 8 10 16 2 <7 >7 <5 In 7<x and 5>x interval there can be no x , so we don’t Need to traverse in nodes 14 and 1 1 14 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

α-β Pruning 7 11 7 5 8 MAX ( Artificial Intelligence ) MIN ( Player ) MAX 10 16 2 <7 >7 <5 1 14 <10 In 7<x and 10>x interval there can be x then continue in nodes 2 and 8

α-β Pruning 7 11 7 5 8 MAX ( Artificial Intelligence ) MIN ( Player ) MAX 10 16 2 <7 >7 <5 1 14 <2 In 7<x and 2>x interval there can be no x , so we don’t Need to traverse in node 8.

α-β Pruning 7 7 11 7 5 8 MAX ( Artificial Intelligence ) MIN ( Player ) MAX 10 16 2 <7 >7 <5 1 14 <2

Applying Minimax & α-β Pruning ,[object Object],[object Object],[object Object],[object Object],[object Object]

Applying Minimax & α-β Pruning I assume the game state is like above form. Next move will be X and that will be determined by computer using Minimax Method with α-β Pruning step by step.

-1 0 0 -1 +1 +1 0 0 MAX ( AI ) MAX ( AI ) MIN ( Opponent ) +1 +1 MIN ( Opponent ) -1 -1 0 0 α-β Pruning Computer Choses That Move

Alp Çoker www.alpcoker.com [email_address] Thanks...

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Game Tree ( Oyun Ağaçları )

1. Unbeatable TicTacToe (xox) Alp Çoker www.alpcoker.com [email_address] Game Tree

4. Board Games Tic Tac Toe,Chess,Go....

10.

11. Minimax ( Generate Tree )

12. Minimax ( Decide Whose Turn ) MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

13. Minimax ( Evaluate Funcions ) 12 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

14. Minimax ( Evaluate Funcions ) 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

15. Minimax ( Evaluate Funcions ) 12 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

16. Minimax ( Evaluate Funcions ) 12 4 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

17. Minimax ( Evaluate Funcions ) 4 12 4 12 7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

18. Minimax ( Evaluate Funcions ) 4 3 12 7 6 3 4 18 6 15 7 24 15 12 5 18 6 7 11 7 24 1 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

19. Minimax ( Evaluate Funcions ) 7 4 3 12 7 6 3 4 18 6 15 7 24 15 12 5 18 6 7 11 7 24 1 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN

20. Minimax ( Evaluate Funcions ) 4 3 12 6 3 4 18 6 15 24 15 12 5 18 6 11 7 24 1 MAX ( Artificial Intelligence ) MIN ( Player ) MAX MIN 7 7 7 7

21.

22.

23. α-β Pruning 11 7 5 1 8 10 16 14 2 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

24. α-β Pruning 7 11 7 5 1 8 10 16 14 2 <7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

25. α-β Pruning 7 11 7 5 1 8 10 16 14 2 <7 >7 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

26. α-β Pruning 7 11 7 5 1 8 10 16 14 2 <7 >7 <5 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

27. α-β Pruning 7 11 5 7 5 8 10 16 2 <7 >7 <5 In 7<x and 5>x interval there can be no x , so we don’t Need to traverse in nodes 14 and 1 1 14 MAX ( Artificial Intelligence ) MIN ( Player ) MAX

28. α-β Pruning 7 11 7 5 8 MAX ( Artificial Intelligence ) MIN ( Player ) MAX 10 16 2 <7 >7 <5 1 14 <10 In 7<x and 10>x interval there can be x then continue in nodes 2 and 8

29. α-β Pruning 7 11 7 5 8 MAX ( Artificial Intelligence ) MIN ( Player ) MAX 10 16 2 <7 >7 <5 1 14 <2 In 7<x and 2>x interval there can be no x , so we don’t Need to traverse in node 8.

30. α-β Pruning 7 7 11 7 5 8 MAX ( Artificial Intelligence ) MIN ( Player ) MAX 10 16 2 <7 >7 <5 1 14 <2

31. Tic Tac Toe

32. Tic Tac Toe Game Search

33.

34. Applying Minimax & α-β Pruning I assume the game state is like above form. Next move will be X and that will be determined by computer using Minimax Method with α-β Pruning step by step.

35. -1 0 0 -1 +1 +1 0 0 MAX ( AI ) MAX ( AI ) MIN ( Opponent ) +1 +1 MIN ( Opponent ) -1 -1 0 0 α-β Pruning Computer Choses That Move

36. ¿ Questions ?

37. Alp Çoker www.alpcoker.com [email_address] Thanks...

Game Tree ( Oyun Ağaçları )

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