The minimum maximum analysis method of game tree

A summary of the game

Game features:

(1) The initial pattern of the game is the initial node

(2) In the game tree, the "or" and "and" are alternately present. The extension node of one's own side is the "or" relationship, and the node that the other side expands is the "and" relationship. Both sides expand the nodes in turn.

(3) The final of all of their own wins is the original problem, the corresponding nodes are solvable nodes, all of which make the other side of the final victory is considered to be non-solvable points.

Suppose there is a two-party game, if a first go to the odd depth of the node should be a walk, all even level should be by B.

A game tree is a tree of "and or", and we have to look at the angle of an object. We should eventually search the tree and the trees until the best results are reached.

Second, minimum maximum analysis method

Static Valuation:

Standing on one side, estimating the score of the current game tree node, when the pattern is favorable to each other, the estimated value of the function is small

* If P is a winning chess game, then E (p) =+ Infinity

* If P is the winning chess game of B, then E (p) =-Infinity

* If P is an undecided game, then E (P) =e (+p)-E (-p)

where e (+p) means that the game p may make X a three-line number E (-p) indicates that the game P may make o a number of three sub-lines

So for the static valuation of the game, if you stand on the x side, most want to be which chess game.

A hypothesis needs to be made:

1, a first moves, stand on the position of a

2, the game tree only expand two layers at a time, (a, b) each step

3. Two chess games with symmetry count as a chess game

The best result for x in the picture above is S3, and when x goes S3, O will definitely go S4, because it is the most unfavorable for X.

Maximum Minimum analysis method:

When a has more than one action plan at present, a always chooses the most advantageous action for oneself

When B is in action, a must fully estimate the other person's most adverse actions against them.