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The Minimax algorithm helps AI make decisions in games with two players. One player, the maximizer, tries to get the best possible outcome for themselves. The other player, the minimizer, tries to get the worst outcome for the maximizer. The algorithm helps find the best move by considering both players' goals.
Imagine playing a game of Tic-Tac-Toe. If it's your turn, you want to choose a move that either wins the game or prevents your opponent from winning. The Minimax algorithm helps you make this choice by looking at all possible future moves.
Minimax looks at all possible moves in a game and evaluates which move gives you the best result assuming your opponent is also playing optimally. It calculates the best move by looking at each possible outcome and picking the one that offers the highest minimum gain, considering your opponent will always try to minimize your gains.
In a game of Chess, Minimax would look at all possible moves you could make, and for each move, it would estimate the best move your opponent could make in response. It then chooses the move that has the best worst-case outcome.
Minimax assumes that both players are making the best possible moves. It uses this assumption to calculate the optimal strategy. If the opponent does not play optimally, the problem becomes simpler because you only need to account for less-than-perfect moves.
If you are playing Checkers and your opponent makes a poor move, Minimax will still help you make the best move, but in a simpler scenario where your opponent isn’t always making the best choices.
In Minimax, a game is represented as a tree where each node represents a game state and each branch represents a possible move. This tree helps visualize all possible moves and outcomes, making it easier to implement the Minimax algorithm.
Think of a game of Connect Four. The game tree starts with the current board and branches out to show all possible moves for both players, creating a complete picture of the game’s potential progress.
Even if a game state is not the end of the game, Minimax can evaluate it to decide the best move. This is useful in games like Chess, where you might be many moves away from a win or loss.
In a game of Go, Minimax evaluates the current board position even if it’s not the final state to determine which move will lead to the best outcome in the long run.
Minimax can be slow when dealing with games that have very large trees of possible moves. To handle this, you might limit the depth of the tree you examine or use shortcuts to find good enough solutions quickly.
In a game of Poker with many possible hands and moves, Minimax might only look a few moves ahead instead of every possible outcome to make quick and practical decisions.
Alpha-beta pruning is a technique used to speed up the Minimax algorithm. It cuts off branches of the game tree that don't need to be explored, reducing the number of calculations needed and making the algorithm faster.
In Chess, using alpha-beta pruning means you don’t explore every possible move and counter-move but only those that are most promising, which speeds up the decision-making process.
In alpha-beta pruning, you keep track of two values: alpha and beta. Alpha represents the best score that the maximizer can guarantee, and beta represents the best score that the minimizer can guarantee. These values are updated as you explore the game tree to decide which parts of the tree can be skipped.
During a game of Othello, if you find a move where the score is already better than what you can achieve with other moves, you can skip evaluating less promising moves thanks to alpha-beta pruning.
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