using minimax, implement an ai to play 2048 optimally in matlab

To implement an AI that plays 2048 optimally using minimax, we need to first understand the basics of these concepts.

2048 is a simple game where the player slides numbered tiles on a grid to combine them and create a tile with the number 2048. The game ends when the player cannot make any more moves.

Minimax is a decision-making algorithm often used in games. It works by recursively considering all possible moves and their outcomes to determine the best move for the current player. This algorithm assumes that the opponent will also choose their best move, leading to a game tree that evaluates all possible outcomes.

To implement an AI that plays 2048 optimally using minimax, we need to define the game state, possible moves, evaluation function, and recursion to evaluate all possible outcomes.

Here's an example code for implementing a minimax AI for 2048 in Matlab:


function [bestMove, score] = minimax(grid, depth, alpha, beta, maximizingPlayer)
  if depth == 0
    score = evaluate(grid);
    bestMove = -1;
    return
  end
  if maximizingPlayer
    bestScore = -Inf;
    bestMove = -1;
    moves = getMoves(grid);
    for i = 1:numel(moves)
      newGrid = executeMove(grid, moves(i));
      [moveValue, ~] = minimax(newGrid, depth - 1, alpha, beta, false);
      if moveValue > bestScore
        bestScore = moveValue;
        bestMove = moves(i);
      end
      alpha = max(alpha, bestScore);
      if beta <= alpha
        break;
      end
    end
    score = bestScore;
  else
    emptyTiles = getEmptyTiles(grid);
    tileValues = [2, 4];
    bestScore = Inf;
    for i = 1:numel(emptyTiles)
      for j = 1:numel(tileValues)
        r = emptyTiles(i);
        c = mod(emptyTiles(i), size(grid,1)) + 1;
        newGrid = placeTile(grid, r, c, tileValues(j));
        [moveValue, ~] = minimax(newGrid, depth - 1, alpha, beta, true);
        if moveValue < bestScore
          bestScore = moveValue;
        end
        beta = min(beta, bestScore);
        if beta <= alpha
          break
        end
      end
      if beta <= alpha
          break;
      end
    end
    score = bestScore;
  end
end

function [value] = evaluate(grid)
  % Evaluate the grid after a move
  % Here we use simple heuristics
  sum = 0;
  for i = 1:size(grid,1)
    for j = 1:size(grid,2)
      sum = sum + grid(i,j);
    end
  end
  value = sum;
end

function [moves] = getMoves(grid)
  % Return a list of possible moves
  % Moves are represented as integers: 1 = up, 2 = down, 3 = left, 4 = right
  moves = [];
  if canMoveUp(grid)
    moves = [moves, 1];
  end
  if canMoveDown(grid)
    moves = [moves, 2];
  end
  if canMoveLeft(grid)
    moves = [moves, 3];
  end
  if canMoveRight(grid)
    moves = [moves, 4];
  end
end

function [newGrid] = executeMove(grid, move)
  % Execute a move on the grid
  % Returns the new grid after the move
  newGrid = grid;
  switch move
    case 1 % Up
      newGrid = moveUp(newGrid);
    case 2 % Down
      newGrid = moveDown(newGrid);
    case 3 % Left
      newGrid = moveLeft(newGrid);
    case 4 % Right
      newGrid = moveRight(newGrid);
  end
end

function [emptyTiles] = getEmptyTiles(grid)
  % Return a list of empty tiles
  emptyTiles = find(grid == 0);
end

function [newGrid] = placeTile(grid, r, c, value)
  % Place a new tile on the grid
  % Returns the new grid with the new tile placed
  newGrid = grid;
  newGrid(r,c) = value;
end
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This code implements a recursive minimax function that evaluates all possible moves up to a certain depth. At each level, the algorithm alternates between maximizing and minimizing player. The function returns the best move and the score of that move. The evaluate function computes the score for the current state of the game. The getMoves function returns a list of possible moves. The executeMove function executes a given move on the grid. The getEmptyTiles function returns a list of empty tiles on the grid. The placeTile function places a new tile on the grid.

Note that this code does not guarantee an optimal solution, as 2048 is a game with a high branching factor that makes evaluating all possible outcomes impractical. Therefore, additional heuristics and optimizations would need to be applied to create an AI that can consistently score high on 2048.

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related categories

minimax

2048

artificial intelligence

game theory

matlab