Descripcion minimax alfabeta .

1. Juegos Nelson Becerra Correa Fundación FABBECOR-ONG

9. Como juegan las maquinas

10. Como juegan las maquinas

11. Como juegan las maquinas

12. Como juegan las maquinas

13. Como juegan las maquinas

14. DEEP-BLUE potencia de calculo

15. Función de evaluación

16. Función de evaluación

28. … MINIMAX Se tiene que e(p)=6 – 4 = 2 http://www.ocf.berkeley.edu/~yosenl/extras/alphabeta/alphabeta.html

29. Basic Algorithm

32. MINIMAX NEGAMAX ALFA/BETA FALFA/BETA

33. LALFA/BETA PALFA/BETA SCOUT

34. Max Min Max Min Starting node and labels MiniMax Search

35. Max Min Max Min Continue expand the search space

36. Max Min Max Min Continue expand the search space

37. Max Min Max Min 2 3 5 0 9 7 4 Expand the search space down 3-ply

38. Max Min Max Min 2 3 5 0 9 7 4 Propagate the leaf values backward Pick Max values at Max Level 9 0 3 7 7

39. Max Min Max Min 2 3 5 0 9 7 4 Continue propagate the values backward Pick Min values at Min Level 9 0 3 7 7 3 0

40. Max Min Max Min 2 3 5 0 9 7 4 Continue propagate the values backward Pick Max values at Max Level 9 0 3 7 7 3 0 3

41. Max Min Max Min 2 3 5 0 9 7 4 The move picked by Max 9 0 3 7 7 3 0 3

44. N = 4 K = N = 3 K = N = 2 K = N = 1 K = N = 0 K = N = 1 K = N = 2 K = N = 0 K = N = 0 K = N = 1 K = N = 0 K = N = 1 K = N = 0 K = N = 0 K = 1 2 3 3 2 1 2 1 1 1 2 1 1 N = 0 K = 1 F(S)= 0 F(S)= 0 F(S)= 0 F(S)= 1 F(S)= 1 F(S)=1 F(S)= 1 MAX MIN

45. N = 4 K = 1 N = 3 K = 0 N = 2 K = 0 N = 1 K = 1 N = 0 K = 1 N = 1 K = 0 N = 2 K = 1 N = 0 K = 1 N = 0 K = 1 N = 1 K = 0 N = 0 K = 0 N = 1 K = 1 N = 0 K = 0 N = 0 K = 0 1 2 3 3 2 1 2 1 1 1 2 1 1 N = 0 K = 1 1 F(S)=0 F(S)=0 F(S)=0 F(S)=1 F(S)=1 FFS(51791527S)=1 F(S)=1 MAX MIN Solution F(S)=1

50. Max Min Max Min Starting node and labels Alpha-Beta Prune

51. Max Min Max Min Perform a DFS

52. Max Min Max Min Continue the DFS

53. Max Min Max Min 2 3 Until reach the depth we want, i.e., 3-ply in this case

54. Max Min Max Min 2 3 3 Propagate leaf values backward

55. Max Min Max Min 2 3 3 3

56. Max Min Max Min 2 3 3 3 3

57. Max Min Max Min 2 3 3 3 3 Alpha Node Beta Node

58. Max Min Max Min 2 3 3 3 3 Alpha Beta 5 New DFS path Ended with 5

59. Max Min Max Min 2 3 3 3 3 Alpha Beta 5 5 Propagate backward

60. Max Min Max Min 2 3 3 3 3 Alpha Beta 5 5 Because 3 < 5 The branch is pruned. Beta-Prune

61. Max Min Max Min 2 3 3 3 3 Alpha Beta 5 5 New 3-ply DFS Ended with 0 0

62. Max Min Max Min 2 3 3 3 3 Alpha Beta 5 5 0 0 Propagate backward

63. Max Min Max Min 2 3 3 3 3 Alpha Beta 5 5 0 0 Propagate backward 0

64. Max Min Max Min 2 3 3 3 3 Alpha Beta 5 5 0 0 The branch is cut off Because 3 > 0 Alpha Prune 0

65. Algorithm

66. N = 4 K = N = 3 K = N = 2 K = N = 1 K = N = 0 K = N = 1 K = N = 2 K = N = 0 K = N = 0 K = N = 1 K = N = 3 K = N = 1 K = N = 0 K = N = 0 K = 1 2 3 3 2 1 2 1 1 1 2 1 1 N = 0 K = 1 F(S)=0 F(S)=0 F(S)=0 F(S)=1 F(S)=1 F(S)=1 F(S)=1 MAX MIN α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β = α = β =

67. N = 4 K = 0 1 N = 3 K = 1 0 N = 2 K = 1 0 N = 1 K = 1 N = 0 K = 1 N = 1 K = 0 N = 2 K = 1 N = 0 K = 1 N = 0 K = 1 N = 1 K = N = 3 K = 0 N = 1 K = 1 N = 0 K = N = 0 K = 0 1 2 3 3 2 1 2 1 1 1 2 1 1 N = 0 K = 1 1 F(S)=0 F(S)=0 F(S)=0 F(S)=1 F(S)=1 F(S)=1 F(S)=1 MAX MIN α = β = 1 0 α = 0 β = α = 0 β = 1 0 α = β = 0 α = 1 β = α = 0 β = 0 α = 0 β = 0 α = 0 β = 1 α = 0 β = α = 0 β = 0 α = 0 β = α = 1 β = 0 α = β = α = 1 β = 0 α = 0 β = 1