 EXAMPLE of an evaluation function (Shannon, 1950):
 Let K, Q, R, B, N, and P denote the number of White kings, queens, rooks, bishops, knights and pawns on the board
 Let K′, Q′, R′, B′, N′, and P′ denote the number of Black kings, queens, rooks, bishops, knights and pawns on the board
 Let D, S, and I denote the double, backward or isolated White pawns
 Let D′, S′, and I′ denote the double, backward or isolated Black pawns

Function f = 200(K  K′) + 9(Q  Q′) + 5(R  R′) + 3(B  B′ + N  N′) + (P  P′) – 0.5(D  D′ + S  S′ + I  I′)

 The drosophila (or the humble fruit fly) is a good model organism in biology, neuroscience, and genetics
 Chess has been described by Alexander Kronrod as the drosophila of AI research
 How do we design an AI system to play a skilful (i.e. human expertlevel) game of chess?
 RESPONSE 1: We could rely on a set of principles
 PRINCIPLE 1: The player with greater mobility has the better game
 PRINCIPLE 2: Different PRINCIPLES apply in different phases (e.g. opening, middle game, endgame) of the game
 ⋮
 RESPONSE 2: We could rely on an evaluation function
 RESPONSE 3: We could rely on a minimax algorithm

Go

 Go (围棋 or weiqi) is a 2player sequential zerosum game with perfect information
 The aim of Go is for each player to surround more territory than the opponent
Go board

 There are 19 vertical lines and 19 horizontal lines on the Go board
 This yields 361 (or 19^{2}) points or intersections
 9 points on the board are dotted and called star points
 The point in the centre is called the central star

The rules of Go

 P1 (Black) takes the black stones and makes the first move
 P2 (White) takes the white stones and makes the next move
 P1 (Black) and P2 (White) take turns to move and only one stone can be played per move
 A stone on the Go board has 24 adjacent intersections
 Whichever of these intersections is/are unoccupied would be called liberties
 Stones adjacent to other stones of the same colour form a unit and their liberties are counted together
 When all the liberties of a stone or group of stones have been taken by the opposite colour, those stones cannot remain on the board
 The game of Go ends when both P1 and P2 agree that there will be no more moves or when either P1 or P2 resigns

Counting the score

 At the end of the game, whichever stones will inevitably be captured are dead
 Stones that cannot be captured are alive
 All dead stones of both P1 and P2 are removed from the board
 All living stones of each player are counted, including the vacant points enclosed by those stones
 Vacant points between the living stones of both P1 and P2 will be shared equally
 180½ is half the number of points on the board
 Let t denote P_{n}'s total number of living stones and enclosed vacant points
 If t > 180½, then P_{n} wins
 If t < 180½, then P_{n} loses
 If t = 180½, then the game has ended in a draw

 Go is a far more complex game than chess

Chess 
Chinese Chess 
Shogi 
Go 
Board size 
64 (8 × 8) 
90 (9 × 10) 
81 (9 × 9) 
361 (19 × 19) 
State space complexity 
10^{46} 
10^{48} 
10^{71} 
10^{172} 
Game tree complexity 
10^{123} 
10^{150} 
10^{226} 
10^{360} 
Branching factor 
35 
38 
92 
250 
