CPSC 322 Introduction to Artificial Intelligence October 22
CPSC 322 Introduction to Artificial Intelligence October 22, 2004
Things. . . Office hours today from 3: 30 to 4: 30 pm Bring me your first midterms before the second midterm if you want to be retested on problem 3 asgn 3 will be posted this evening Jessica Hodgins talk, Thursday, October 28, 1 -2 pm, Mac. Leod 214
Helpful CILOG stuff Counting elements in a list /* This works in Prolog, but not in CILOG */ length([H|T], N) <- N > 0 & N 1 is N-1 & length(T, N 1). length([], 0). /* This works in CILOG */ length([H|T], X, Y) <- X 1 is X+1 & length(T, X 1, Y). length([], X, X). cilog: ask length([a, b, c], 0, X). Answer: length([a, b, c], 0, 3).
![Helpful CILOG stuff Sorting numeric elements in a list using insertion sort insert(X, [],](http://slidetodoc.com/presentation_image_h2/ab92eae1a6424467d9e14b47d91e20b8/image-4.jpg "Helpful CILOG stuff Sorting numeric elements in a list using insertion sort insert(X, [],")
Helpful CILOG stuff Sorting numeric elements in a list using insertion sort insert(X, [], [X]). insert(X, [Y|Ys], [X, Y|Ys]) <- X =< Y. insert(X, [Y|Ys], [Y|Zs]) <- X > Y & insert(X, Ys, Zs). sort([], []). sort([X|Xu], Ys) <- sort(Xu, Zs) & insert(X, Zs, Ys).
The Joy of Hex The game of hexapawn • 3 x 3 board • 3 pawns on each side • movement of pawns: • white moves first • pawn can move straight ahead one space if that space is empty • pawn can move diagonally one space forward to capture opponent’s pawn occupying that space
The Joy of Hex The game of hexapawn • 3 ways to win: • capture all your opponent’s pawns • one of your pawns reaches the opposite end of the board • it’s your opponent’s turn but your opponent can’t move
Two Questions Second, how do you know which move to make? Use heuristic knowledge, of course! In this case, we apply this very crude board evaluation function: if you have won then board value = +10 else if opponent has won then board value = -10 else board value = number of your pawns number of opponent’s pawns The board evaluation function is applied like this. .
WWW --BBB opponent’s move --> -WW W-BBB your --> -WW responses -WW B-- WB- B-B -WW W-B BB- opp’s moves --> - - W --W -W- W-- BW- B-W WW- B-B B-B -WWBW B-B -WW --B BW- --W WWB BB- W-W BB-
WWW --BBB opponent’s -WW move --> W-BBB your --> -WW responses -WW B-- -WW WB- B-B W-B BB- opp’s moves --> - - W --W -W- W-- BW- B-W WW- B-B B-B 0 1 1 B-B -1 -10 -WWBW B-B -10 -WW --B BW 0 --W WWB BB-1 W-W BB-
WWW --BBB opponent’s -WW move --> W-BBB your --> -WW responses -WW B-- 0 -WW W B - -10 B-B W - B -10 BB- opp’s moves --> - - W --W -W- W-- BW- B-W WW- B-B B-B 0 1 1 B-B -1 -10 -WWBW B-B -10 -WW --B BW 0 --W WWB BB-1 W-W BB-
WWW --BBB opponent’s -WW move --> W-- 0 BBB your --> -WW responses -WW B-- 0 -WW W B - -10 B-B W - B -10 BB- opp’s moves --> - - W --W -W- W-- BW- B-W WW- B-B B-B 0 1 1 B-B -1 -10 -WWBW B-B -10 -WW --B BW 0 --W WWB BB-1 W-W BB-
WWW --BBB opponent’s -WW move --> W-- 0 BBB your --> -WW response B-- 0 B-B opp’s moves --> - - W --W -W- W-- BW- B-W B-B B-B 0 1 1
What if white makes an unexpected move?
not this. . . WWW --BBB opponent’s -WW move --> W-- 0 BBB your --> response -WW B-- 0 B-B opp’s move --> - - W W-B-B 0
. . . but this WWW --BBB opponent’s -WW move --> W-- 0 BBB your --> -WW response B-- 0 B-B opp’s move --> --W BWB-B 1
What if white makes a different move? Apply this search technique again to white’s move and make your next move accordingly
your move --> -WW B-B-B opponent’s --W move --> BWB-B
your -WW move --> B-B-B opponent’s --W move --> BWB-B your B-W --W responses -> - W B-B opponent’s moves --> --W BB- BWB --B B-- --- --- --W BW- BBW --B --W BW- BBW B-- W-- B-B BW- B-B
your -WW move --> B-B-B opponent’s --W move --> BWB-B your B-W --W responses -> - W - --W BB- B-B --W BB- BWB --B B-- --- --- --W 10 opponent’s moves --> BW- BBW --B 1 2 BW- BBW B-- B-1 --W 2 W--10 B-B BW-10 B-B
your -WW move --> B-B-B opponent’s --W move --> BWB-B your B-W --W responses -> - W - --W BB-1 B-B --W BB-1 B W B -10 --B B-- --- --- --W 10 opponent’s moves --> BW- BBW --B 1 2 BW- BBW B-- B-1 --W 2 W--10 B-B BW-10 B-B
your -WW move --> B-B-B opponent’s --W move --> B W - 10 B-B your B-W --W responses -> - W - --W BB-1 B-B --W BB-1 B W B -10 --B B-- --- --- --W 10 opponent’s moves --> BW- BBW --B 1 2 BW- BBW B-- B-1 --W 2 W--10 B-B BW-10 B-B
your move --> -WW B-B-B opponent’s move --> --W B W - 10 B-B your B-W response -> - W B-B 10
What if. . . ? . . . way back at the beginning there was an obvious win for you in your search space?
WWW --BBB opponent’s -WW move --> W-BBB your --> -WW responses -WW B-- -WW WB- B-B W-B BB- opp’s moves --> - - W --W -W- W-- BW- B-W WW- B-B B-B 0 1 1 B-B -1 -10 -WWBW B-B -10 -WW --B BW+10 --W WWB BB-1 W-W BB-
WWW --BBB opponent’s -WW move --> W-BBB should you move here? your --> -WW responses -WW B-- -WW WB- B-B W-B BB- opp’s moves --> - - W --W -W- W-- BW- B-W WW- B-B B-B 0 1 1 B-B -1 -10 -WWBW B-B -10 -WW --B BW+10 --W WWB BB-1 W-W BB-
WWW --BBB opponent’s -WW move --> W-BBB NOOOOO!!!! your --> -WW responses -WW B-- -WW WB- B-B W-B BB- opp’s moves --> - - W --W -W- W-- BW- B-W WW- B-B B-B 0 1 1 B-B -1 -10 -WWBW B-B -10 -WW --B BW+10 --W WWB BB-1 W-W BB-
Game search (also known as adversarial search) has these components: move (or board) generator static board evaluation function (this is the heuristic part - it doesn’t generate moves or look ahead - it’s static) minimax algorithm to alternately propagate minima and maxima upward from “bottom”
Minimax algorithm Start with the following: a) there are two players, MAX and MIN b) it’s MAX’s turn to move c) MAX has a static board evaluation function that returns bigger values if a board is favorable to MAX d) the evaluation function gets better as the game gets closer to a goal state (else why bother to generate the game space? ) e) MAX believes that MIN’s evaluation function is no better than MAX’s (if that’s not true, then MAX should at least avoid betting money on this game)
Minimax algorithm 1. 2. 3. 4. Generate the game tree to as many levels (plies) that time and space constraints allow. The top level is called MAX (as in it’s now MAX’s turn to move), the next level is called MIN, the next level is MAX, and so on. 2. 3. Apply the evaluation function to all the terminal (leaf) states/boards to get “goodness” values 3. Use those terminal board values to determine the values to be assigned to the immediate parents: a) if the parent is at a MIN level, then the value is the minimum of the values of its children b) if the parent is at a MAX level, then the value is the maximum of the values of its children 4. Keep propagating values upward as in step 3 5. When the values reach the top of the game tree, MAX chooses the move indicated by the highest value
Minimax algorithm 1. 2. 3. 4. Generate the game tree to as many levels (plies) that time and space constraints allow. The top level is called MAX (as in it’s now MAX’s turn to move), the next level is called MIN, the next level is MAX, and so on. 2. 3. Apply the evaluation function to all the terminal (leaf) states/boards to get “goodness” values 3. Use those terminal board values to determine the values to be assigned to the immediate parents: a) if the parent is at a MIN level, then the value is the minimum of the values of its children b) if the parent is at a MAX level, then the value is the maximum of the values of its children 4. Keep propagating values upward as in step 3 5. When the values reach the top of the game tree, MAX chooses the move indicated by the highest value
Minimax algorithm MAX (it’s MAX’s turn to move)
Minimax algorithm MAX (it’s MAX’s turn to move) MIN
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX MIN
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX
Minimax algorithm 1. 2. 3. 4. Generate the game tree to as many levels (plies) that time and space constraints allow. The top level is called MAX (as in it’s now MAX’s turn to move), the next level is called MIN, the next level is MAX, and so on. 2. 3. Apply the evaluation function to all the terminal (leaf) states/boards to get “goodness” values 3. Use those terminal board values to determine the values to be assigned to the immediate parents: a) if the parent is at a MIN level, then the value is the minimum of the values of its children b) if the parent is at a MAX level, then the value is the maximum of the values of its children 4. Keep propagating values upward as in step 3 5. When the values reach the top of the game tree, MAX chooses the move indicated by the highest value
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm 1. 2. 3. 4. Generate the game tree to as many levels (plies) that time and space constraints allow. The top level is called MAX (as in it’s now MAX’s turn to move), the next level is called MIN, the next level is MAX, and so on. 2. 3. Apply the evaluation function to all the terminal (leaf) states/boards to get “goodness” values 3. Use those terminal board values to determine the values to be assigned to the immediate parents: a) if the parent is at a MIN level, then the value is the minimum of the values of its children b) if the parent is at a MAX level, then the value is the maximum of the values of its children 4. Keep propagating values upward as in step 3 5. When the values reach the top of the game tree, MAX chooses the move indicated by the highest value
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX MIN 5 -3 8 -12 7 -42 13 -10 -8 MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm 1. 2. 3. 4. Generate the game tree to as many levels (plies) that time and space constraints allow. The top level is called MAX (as in it’s now MAX’s turn to move), the next level is called MIN, the next level is MAX, and so on. 2. 3. Apply the evaluation function to all the terminal (leaf) states/boards to get “goodness” values 3. Use those terminal board values to determine the values to be assigned to the immediate parents: a) if the parent is at a MIN level, then the value is the minimum of the values of its children b) if the parent is at a MAX level, then the value is the maximum of the values of its children 4. Keep propagating values upward as in step 3 5. When the values reach the top of the game tree, MAX chooses the move indicated by the highest value
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX MIN 5 -3 8 -12 7 -42 13 -10 -8 MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm MAX (it’s MAX’s turn to move) MIN MAX 5 8 7 13 -8 MIN 5 -3 8 -12 7 -42 13 -10 -8 MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm MAX (it’s MAX’s turn to move) 5 MIN MAX 7 5 -8 8 7 13 -8 MIN 5 -3 8 -12 7 -42 13 -10 -8 MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm 7 MAX (it’s MAX’s turn to move) 5 MIN MAX 7 5 -8 8 7 13 -8 MIN 5 -3 8 -12 7 -42 13 -10 -8 MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm 1. 2. 3. 4. Generate the game tree to as many levels (plies) that time and space constraints allow. The top level is called MAX (as in it’s now MAX’s turn to move), the next level is called MIN, the next level is MAX, and so on. 2. 3. Apply the evaluation function to all the terminal (leaf) states/boards to get “goodness” values 3. Use those terminal board values to determine the values to be assigned to the immediate parents: a) if the parent is at a MIN level, then the value is the minimum of the values of its children b) if the parent is at a MAX level, then the value is the maximum of the values of its children 4. Keep propagating values upward as in step 3 5. When the values reach the top of the game tree, MAX chooses the move indicated by the highest value
Minimax algorithm 7 MAX (it’s MAX’s turn to move) 5 MIN MAX 7 5 -8 8 7 13 -8 MIN 5 -3 8 -12 7 -42 13 -10 -8 MAX 5 -3 17 9 8 22 -12 4 7 -42 -9 13 36 -10 -6 -8
Minimax algorithm 7 MAX (it’s MAX’s turn to move) MIN 7
Minimax algorithm A simple but powerful technique. . . how powerful is it?
1997 Deep Blue vital statistics: • 200, 000 moves per second • 480 custom chess-playing chips
1997
1997 Deep Blue vital statistics: • 200, 000 moves per second • 480 custom chess-playing chips Garry Kasparov vital statistics: • 3 moves per • meat
1997
1997 Deep Blue defeats Garry Kasparov 3. 5 games to 2. 5 games Kasparov wins $400, 000 Deep Blue wins $700, 000 The human race is humiliated
2003 Garry Kasparov takes on Deep Junior
2003 Deep Junior and Garry Kasparov tie 3 games each Kasparov wins $500, 000 just for being there Deep Junior and Kasparov split another $500, 000 Honor of human race is restored
2003 Deep Junior and Garry Kasparov tie 3 games each Kasparov wins $500, 000 just for being there Deep Junior and Kasparov split another $500, 000 Honor of human race is restored. . . or is it?
Computer chess rankings have increased about 200 points every 5 years, due in large part to increases in CPU speed
But speed doesn’t explain Deep Junior Deep Blue vital statistics: • 200, 000 moves per second • 480 custom chess-playing chips Deep Junior vital statistics: • 3, 000 moves per second • 8 1. 6 GHz Intel processors
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