C# Project - Chair of Software...
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C# Project Assignment 1
Transcript of C# Project - Chair of Software...
C# Project
Assignment 1
Outline
Overview
of Chess
The Forsyth
notation
Requirements
of
the assignment
Computing the
next states
Evaluation
Function
MinMax
Conclusion
Questions?
Overview of Chess
tMvWlVmTOoOoOoOo+ + + +
+ + + + + + + +
+ + + + pPpPpPpPRnBqKbNr
Goal: checkmate your opponent's King
� Board: 8x8 squares
� Two players: White, Black
� 32 pieces (16w, 16b)
� ¦ Rock
� n Knight
� ¥ Bishop
� £ Queen
� ¢ King
� § Pawn
The Pawn
tMvWlVmTOoOoOoOo+ + + +
+ + + + + + + +
+ + + + pPpPpPpP
RnBqKbNr
+*+*+*+*+*+*P*+*+*+*
+*+*+*VoO*+*P*+*+*+*
Normal Move AttackInitial Move
+*+*+*+p+*+*+*+*+*+*
+*+*+*PoO*+*+*+*+*+*
The Rock
W + + + + + + + + + + +
+ + + + + + + +
+r+ +n+v+ + + +
+ + + +
R + + + + + + + + + + +
+ + + + + + + +
+ + +n+v+ + + +
+ + + +
The Knight
+ + + + + + + + + + + +
+ + V + + +o+ +
+ + +n+v+ + + +
+ + + +
+ + + + + + + + + + + +
+ + N + + +o+ +
+ + + +v+ + + +
+ + + +
The Bishop
+ + + + + + + + + + + +
+ + B + + + + +
+ + + +O + + +
+ + + +
+ + + + + + + + + + + +
+ + + + + + + +
+ + + +B + + +
+ + + +
The Queen
+ + + + + + + + + + + +
+ + Q + + + + +
+ + + ++ + + +
+ + + +
The King
+ + + + + + + + + + + +
+ + K + + + + +
+ + + ++ + + +
+ + + +
Goal of Chess: checkmate
+ + + + +l+ + + + +p+ +
+ + + + + +v+ O
+ N + Op+ + + K
T + + +
The Forsyth notation
� ¦ r
�n n
�¥ b
�£ q
�¢ k
� § p
+ + + + +l+ + + + +p+ +
+ + + + + +v+ O
+ N + Op+ + + K
T + + +
8;1K6;
4p3;8;
4B2P;
2n3Pp;7k;
R7.
Requirements of the assignment
Forsyth
Previous StateForsyth
Next StateYour Tool
• Play for the whites
• Legal Move
• MinMax
• Computation time reasonable
Recommended Model for Chess
+ + + + +l+ + + + +p+ +
+ + + + + +v+ O
+ N + Op+ + + K
+ + + +
State of the game
Next-State Computation
+ + + + +l+ + + + +p+ +
+ + + + + +v+ O
+ N + Op+ + + +
+ + K +
+ + + + +l+ + + + +p+ +
+ + + + + +n+ O
+ + + Op+ + + +
+ + K +
+ + + + +l+ + + + +p+ +
+ + + + + +n+ O
+ + + Op+ + + +
+ + K +
+ + + + +l+ + + + +p+ +
+ + + + + +n+ O
+ + + Op+ + + +
+ + K +
+ + + + +l+ + + + +p+ +
+ + + + + +n+ O
+ + + Op+ + + +
+ + K +
Evaluation Function
+ + + + +l+ + + + +p+ +
+ + + + + +n+ O
+ + + Op+ + + +
+ + K +
+ + + + +l+ + + + +p+ +
+ + + + + +v+ O
+ N + Op+ + + +
+ + K +
+ + + + +l+ + + + +p+ +
+ + + + r+ +v+ O+ N + Op+ + + +
+ + K +
¢ Infinity£ 9
¦ 5
0 3 5
n 3 ¥ 3
§ 1
Tree RepresentationScore Player 2:
0
1
-1
3
-2
1Player 1 Player 2
MinMax: minimizing the maximal lost
int minmax(node, depth)
{
if (node.IsTerminal || depth == 0)
return evaluate(node);
if (node.WePlay)
{
int e = MAXINT;
foreach child of node
e = min(e, minmax(child, depth-1)
return e
} else // It's the turn of the opponent
{
int e = MININT;
foreach child of node
e = max(e, minmax(child, depth-1))
return e
}
}
MinMax
0
-1
-2
1
Score Player 2:
0
1
-1
3
-2
1Player 1 Player 2
MinMax
0
-1
-2
1
Score Player 2:
0
1
-1
3
-2
1Player 1 Player 2
0
1
MinMax
0
0
-1
-2
1
Score Player 2:
0
1
-1
3
-2
1Player 1 Player 2
0
1
Improvements
�Exploration depth: deeper = better
Huge state space:
�Alpha-beta algorithm
�+ promising childs first
�Pruning techniques
� It’s your job to google.
Conclusion
Forsyth
File
+v+ O+ N ++ + +
+ + K
+v+ O+ N ++ + +
+ + K
+v+ O+ N ++ + +
+ + K
+v+ O+ N ++ + +
+ + K
+v+ O+ N ++ + +
+ + K
+v+ O+ N ++ + +
+ + K
+v+ O+ N +W + +
+ + K
+v+ O+ N ++ +¥+
+ + K
MinMax
Questions?
