Consider the following 2-player game, X vs. Y. At each stage, an integer utility valu N is assigned to a legal move. Each of X and Y has two legal moves, respectively, as shown below. X player: Move A: new N= old N+ (old N mod 23) -11 Move B: new N= old N + 20 (old N mod 41) Y player: Move C: new N= old N+ 2*(old N mod 17)-16 Move D: new N= old N + 25- (old N mod 51) At the initial state, N = 100, and X player makes the 1st move, followed by Y player. This game played for 4 ply, i.e. X plays first, Y plays second, then X plays again, and at last Y plays. Then th game is over. Now assume the game tree is evaluated using DFS that follows the alphabetical order, i.e. Move before Move B, also Move C before Move D, and using alpha-beta to prune the tree from left to right (a) (b) Draw the game tree with alpha-beta pruning, and mark the pruned nodes (or branches). Show the utility value of each node according to the definitions above, 11 th the hottom level

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2.
Consider the following 2-player game, X vs. Y. At each stage, an integer utility value
N is assigned to a legal move. Each of X and Y has two legal moves, respectively, as shown below.
X player:
Move A: new N= old N + (old N mod 23)-11
Move B: new N= old N+ 20 - (old N mod 41)
Y player:
Move C: new N= old N + 2*(old N mod 17) -16
Move D: new N= old N+ 25 - (old N mod 51)
At the initial state, N = 100, and X player makes the 1st move, followed by Y player. This game is
played for 4 ply, i.e. X plays first, Y plays second, then X plays again, and at last Y plays. Then the
game is over.
Now assume the game tree is evaluated using DFS that follows the alphabetical order, i.e. Move A
before Move B, also Move C before Move D, and using alpha-beta to prune the tree from left to right.
(a)
(b)
(c)
Draw the game tree with alpha-beta pruning, and mark the pruned nodes (or branches).
Show the utility value of each node according to the definitions above,
Show all the utility values backpropagated from the bottom level,
Transcribed Image Text:2. Consider the following 2-player game, X vs. Y. At each stage, an integer utility value N is assigned to a legal move. Each of X and Y has two legal moves, respectively, as shown below. X player: Move A: new N= old N + (old N mod 23)-11 Move B: new N= old N+ 20 - (old N mod 41) Y player: Move C: new N= old N + 2*(old N mod 17) -16 Move D: new N= old N+ 25 - (old N mod 51) At the initial state, N = 100, and X player makes the 1st move, followed by Y player. This game is played for 4 ply, i.e. X plays first, Y plays second, then X plays again, and at last Y plays. Then the game is over. Now assume the game tree is evaluated using DFS that follows the alphabetical order, i.e. Move A before Move B, also Move C before Move D, and using alpha-beta to prune the tree from left to right. (a) (b) (c) Draw the game tree with alpha-beta pruning, and mark the pruned nodes (or branches). Show the utility value of each node according to the definitions above, Show all the utility values backpropagated from the bottom level,
A partial sample game tree with the top two levels is shown below for your reference. The numbers in
the boxes are the values of N. You need to finish the rest of the game tree, and backpropagate the
appropriate N values. Show the backpropagated N values next to the boxes, e.g. No, N1, N2.
No
100
A
N1
97
102
N2
Transcribed Image Text:A partial sample game tree with the top two levels is shown below for your reference. The numbers in the boxes are the values of N. You need to finish the rest of the game tree, and backpropagate the appropriate N values. Show the backpropagated N values next to the boxes, e.g. No, N1, N2. No 100 A N1 97 102 N2
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