Game Playing Overview, And Example Domain.pptx

Darshan Institute of Engineering & Technology, Rajkot
Unit-6:
Game Playing
gopi.sanghani@darshan.ac.in
9825621471
Computer Engineering Department
Dr. Gopi Sanghani
Artificial Intelligence (AI)
3170716

 Looping
Outline
 Overview
 MiniMax Search Procedure
 Alpha-Beta Cut-offs
 Refinements Theory

Dr. Gopi Sanghani #3170716 (AI)  Unit 6 Game Playing 3
Introduction
 Game Playing is an important domain of Artificial Intelligence.
 There are two reasons that games appeared to be a good domain.
1. They provide a structured task in which it is very easy to measure success or failure.
2. They are easily solvable by a straightforward search from the starting state to a winning
position.
 Games require only the domain knowledge such as the rules, legal moves and
the conditions of winning or losing the game.
 In a two-player game, both the players try to win the game. So, both of them try
to make the best move possible at each turn.
 To improve the effectiveness of a search based problem solving program two
things can be done.
1. Improve generate procedure so that only good moves are generated.
2. Improve test procedure so that the best move will be recognized and explored first.

Introduction
 If we use legal-move generator then the test procedure will have to look at each
of them, because the test procedure must look at so many possibilities and it
must be fast.
 The depth of the resulting tree or graph and its branching factor will be too
large.
 Instead of legal-move generator we can use plausible-move generator in which
only some small numbers of promising moves are generated.
 As the number of legal available moves increases it becomes increasingly
important in applying heuristics to select only those moves that seem more
promising.
 The performance of overall system can be improved by adding heuristic
knowledge into both the generator and the tester.
 It is possible to search tree only ten or twenty moves deep then in order to
choose the best move, the resulting board positions must be compared to
discover which is most advantageous.

Introduction
 This is done using static evaluation function, which uses whatever information it
has to evaluate individual board position by estimating how likely they are to
lead eventually to a win.
 The most common search technique in game playing is Minimax search
procedure.
MAX
(player)
MIN
(opponent)
3 14 12 27 17 2 6 21 14 3 5 1
MAX
(player)
MIN
(opponent)
17
14 27 17 21 14 5
14 17 5

The MINIMAX Search Procedure
 The Minimax search is a depth first and depth limited procedure.
 The idea is to start at the current position and use the plausible-move generator
to generate the set of possible successor positions.
 Now we can apply the static evaluation function to those positions and simply
choose the best one.
 After doing so, we can back that value up to the starting position.
 Here, we assume that static evaluation function returns larger values to indicate
good situations for us.
 So our goal is to maximize the value of the static evaluation function of the next
board position.
 The opponents’ goal is to minimize the value of the static evaluation function.

The MINIMAX Search Procedure
 The alternation of maximizing and minimizing at alternate ply when evaluations
are to be pushed back up corresponds to the opposing strategies of the two
players is called MINIMAX.
 It is recursive procedure that depends on two procedures :
1. MOVEGEN(position, player)— The plausible-move generator, which returns a list of nodes
representing the moves that can be made by Player in Position.
2. STATIC(position, player) -- static evaluation function, which returns a number representing
the goodness of Position from the standpoint of Player.
 To decide when recursive procedure should stop, variety of factors may
influence the decision such as,
 Has one side won?
 How many ply have we already explored? Or how much time is left?
 How stable is the configuration?

Minimax – Algorithm
 Given a game tree, the optimal strategy can be determined from the minimax
value of each node, which we write as MINIMAX(n).
 The minimax algorithm computes the minimax decision from the current state.
 It uses a simple recursive computation of the minimax values of each successor
state, directly implementing the defining equations.
 The recursion proceeds all the way down to the leaves of the tree, and then the
minimax values are backed up through the tree as the recursion unwinds.

 The minimax value of a node is the utility (for MAX) of being in the
corresponding state, assuming that both players play optimally from there to
the end of the game.
 The algorithm first recuses down to the three bottom left nodes and uses the
UTILITY function on them to discover that their values are 3 and 14 respectively.
 Then it takes the maximum of these values, 14, and returns it as the backed up
value of parent node.
 A similar process gives the backed-up values of 27, 17, 21, 14 and 5 respectively.

 Then it takes the minimum of these values 14, 17 and 5 respectively.
 Finally, we take the maximum of 14, 17, and 5 to get the backed-up value of 17
for the root node.
 The minimax algorithm performs a complete depth-first exploration of the
game tree.
 During every ply MAX prefers to move to a state of maximum value, whereas
MIN prefers a state of minimum value.

Alpha-Beta Pruning
 Alpha-beta pruning is a modified version of the Minimax algorithm. It is an
optimization technique for the Minimax algorithm.
 In the Minimax search algorithm, the number of game states to be examined
can be exponential in the depth of a tree.
 Hence there is a technique by which without checking each node of the game
tree we can compute the correct Minimax decision, and this technique is called
pruning.
 This involves two threshold parameter Alpha and beta for future expansion, so
it is called alpha-beta pruning. It is also called as Alpha-Beta Algorithm.
 Alpha-beta pruning can be applied at any depth of a tree, and sometimes not
only it prunes the tree leaves but also entire sub-tree.

Alpha-Beta Pruning
 Alpha-beta pruning technique maintains two bounds:
1. Alpha ( ):
𝜶 The best (highest-value) choice we have found so far at any point along the
path of Maximizer. The initial value of alpha is - . A lower bound on best, i.e., Max
∞
2. Beta ( ):
𝜷 The best (lowest-value) choice we have found so far at any point along the path
of Minimizer. The initial value of beta is + . An upper bound on what the opponent can
∞
achieve
 The Search proceeds maintaining and
𝜶 𝜷
 Whenever _ , or _ ,
𝜶 ≥ 𝜷 𝒉𝒊𝒈𝒉𝒆𝒓 𝜷 ≤ 𝜶 𝒉𝒊𝒈𝒉𝒆𝒓 searching further at this node
is irrelevant.
 In conclusion, Minimax with alpha beta pruning is a faster algorithm than the
Minimax algorithm.

Minimax with Alpha-beta Pruning – Example 1
4 5 6
3 4
3 8
Max
Min
Max
A
B C D
E F G H
M
K
L
7 9
J
O
I
≤ 𝟒
≥ 𝟒
≤ 𝟔
≥ 𝟑 𝟒
≤𝟒
≤ 𝟑
N

2 3 5 9 1 0 7 4 2 1 5 6
Max
Min
Max
≤ 𝟑
≥ 𝟐
≥ 𝟑
≥ 𝟓 ≥ 𝟏
≤ 𝟏
≥ 𝟐
≤ 𝟐
𝟑
A
B C D
E F G H J
I

6
3 6 5
5 3 6 7 5 8
MAX
(player)
MIN
(opponent)
5 4 3 6 6 7 5 8 6
MAX
(player)
MIN
(opponent)
3 7 5
7
6
5 4 5 9
6
6 6
8
9 MAX
(player)

Game Refinement Theory
 Game theory is a discipline which stands from the game player’s point of view
with a focus on how to win a game.
 However, game designers would consider another important aspect: how to
make a game more attractive.
 With such motivation, a new game theory from the game designer’s point of
view, called game refinement theory was proposed in the early 2000s.
 Von Neumann was a pioneer who formed the foundation for the modern game
theory, which has widely been applied in various fields.
 One direction with game theory was to find the best move in a game or to
ensure the possibility of winning the game based on the understanding of
current positions.
 Another direction with game refinement theory was to assess the attractiveness
or sophistication of a game.

Game Refinement Theory
 In particular, game refinement theory gives a measure to quantify the
sophistication of a game.
 This enables to obtain the deep insight into the current game and improve the
quality of the game.
 The measure of game refinement can also be used to obtain the deep insight
into the history of games.
 It also gives a reasonable look on the evolution of specific game variants.
 Game refinement theory has been widely applied to many different types of
games with the promising results.
 We can extend the idea of game refinement into the other domains in human
life such as sports games, video games, education or business.
 In many activities of human, the engagement is used as one of the important
standards to evaluate the effectiveness of those activities.

Game Playing Overview, And Example Domain.pptx

More Related Content

Similar to Game Playing Overview, And Example Domain.pptx

Recently uploaded

Game Playing Overview, And Example Domain.pptx