Winning strategy of a game A winning strategy for a player is a strategy that enables the player to win no matter what moves his or her opponent makes. If a game can end in a draw,then we can also speak of drawing strategy. A drawing strategy is a strategy which does not guarantee a win for a particular player,but guarantees that he or she does not lose
Winning strategy of a game A winning strategy for a player is a strategy that enables the player to win no matter what moves his or her opponent makes. If a game can end in a draw, then we can also speak of drawing strategy. A drawing strategy is a strategy which does not guarantee a win for a particular player, but guarantees that he or she does not lose
Zermelo's Theorem We have just proven that Hex must have a winner. To show that one of the players has a winning strategy,we shall apply the so- called Zermelo's Theorem which is an important result about finite two-person game of perfect information
Zermelo’s Theorem We have just proven that Hex must have a winner. To show that one of the players has a winning strategy, we shall apply the socalled Zermelo ’s Theorem which is an important result about finite two-person game of perfect information
Finite and Perfect Information Game -A finite game is one that must necessarily terminate in a finite number of moves. A perfect information game is a game in which the players are aware at all times of all aspects of the structure of the games
Finite and Perfect Information Game A finite game is one that must necessarily terminate in a finite number of moves. A perfect information game is a game in which the players are aware at all times of all aspects of the structure of the games
Finite and Perfect Information Game In a perfect information game,each player knows,at any point in the game, what moves have been made prior to that point as well as what moves the opponent will be able to make in response to any possible move
Finite and Perfect Information Game In a perfect information game, each player knows, at any point in the game, what moves have been made prior to that point as well as what moves the opponent will be able to make in response to any possible move
Zermelo's Theorem Zermelo's Theorem says that in any finite two-person game of perfect information in which the players move alternatively and in which chance does not affect the decision making process, if the game cannot end in a draw,then one of the two players must have a winning strategy
Zermelo’s Theorem Zermelo ’s Theorem says that in any finite two-person game of perfect information in which the players move alternatively and in which chance does not affect the decision making process, if the game cannot end in a draw, then one of the two players must have a winning strategy