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Game Tree ( Oyun Ağaçları )

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Alp Çoker
Alp Çoker

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

Technology
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Unbeatable TicTacToe (xox) Alp Çoker www.alpcoker.com [email_address] Game Tree
[object Object]
Game Systems Rely On ,[object Object],[object Object],[object Object],[object Object]
Board Games Tic Tac Toe,Chess,Go....
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],[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 ( Generate Tree )
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 ,[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
Tic Tac Toe
Tic Tac Toe Game Search
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
¿ Questions ?
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
  • 2.
  • 3.
  • 4. Board Games Tic Tac Toe,Chess,Go....
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 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
  • 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
  • 37. Alp Çoker www.alpcoker.com [email_address] Thanks...