LLMMCTS/examples/chess_game.jl

# Chess-like Game Example - MCTS for Game Playing

This example demonstrates MCTS for a simplified chess-like game where the goal is to capture the opponent's pieces.

```julia
using LLMMCTS

# Simple game state
# board: Dict mapping positions to pieces
# turn: :white or :black
struct GameState
    board::Dict{String, String}  # position => piece
    turn::Symbol
    piece_count::Int
end

# Initialize a simple board
function init_board()
    board = Dict{String, String}()
    
    # Place some pieces
    board["e1"] = "K"  # White King
    board["e8"] = "k"  # Black King
    
    # Random pieces
    board["d4"] = "P"  # White Pawn
    board["d5"] = "p"  # Black Pawn
    
    return board
end

# Check if position is on board
function on_board(pos::String)
    cols = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h']
    rows = ['1', '2', '3', '4', '5', '6', '7', '8']
    length(pos) == 2 && 
    pos[1] in cols && 
    pos[2] in rows
end

# Game transition function
function chess_transition(state::Dict, args::NamedTuple)
    current_step = get(state, :step, 0)
    board = state[:board]
    turn = state[:turn]
    
    if current_step >= args.max_moves
        # Max moves reached, end game
        newstate = Dict(
            :step => current_step + 1,
            :board => board,
            :turn => turn,
            :reward => 0.0,
            :isterminal => true
        )
        return Dict(
            :newNodeKey => "max_moves",
            :newstate => newstate,
            :progressvalue => 5.0
        )
    end
    
    # Generate possible moves
    possible_moves = String[]
    
    # Find all pieces of current turn's color
    turn_prefix = turn == :white ? "upper" : "lower"
    
    # Simple move generation: try moving each piece
    for (pos, piece) in board
        if !isempty(piece)
            # Try moving to adjacent positions
            for dx in [-1, 0, 1]
                for dy in [-1, 0, 1]
                    if dx == 0 && dy == 0
                        continue
                    end
                    
                    # Simple coordinate conversion
                    col = pos[1]
                    row = parse(Int, pos[2])
                    
                    new_col = col + dx
                    new_row = row + dy
                    
                    if new_col >= 'a' && new_col <= 'h' && 
                       new_row >= 1 && new_row <= 8
                        new_pos = string(new_col, new_row)
                        if on_board(new_pos)
                            push!(possible_moves, pos * new_pos)
                        end
                    end
                end
            end
        end
    end
    
    if isempty(possible_moves)
        # No moves available, game over
        newstate = Dict(
            :step => current_step + 1,
            :board => board,
            :turn => turn,
            :reward => turn == :white ? 10.0 : -10.0,
            :isterminal => true
        )
        return Dict(
            :newNodeKey => "game_over",
            :newstate => newstate,
            :progressvalue => turn == :white ? 10.0 : 0.0
        )
    end
    
    # LLM would select the best move
    # For this example, pick a random valid move
    move_idx = (current_step - 1) % length(possible_moves) + 1
    move = possible_moves[move_idx]
    
    # Simulate the move (simplified)
    from_pos = move[1:2]
    to_pos = move[3:4]
    
    new_board = copy(board)
    piece = get(new_board, from_pos, "")
    new_board[to_pos] = piece
    delete!(new_board, from_pos)
    
    # Calculate reward based on capture
    reward = 0.0
    if !isempty(get(new_board, to_pos, ""))
        reward = 5.0  # Capture!
    end
    
    # Progress value: estimate of game state quality
    progressvalue = 5.0 + reward  # Capturing is good
    
    # Switch turns
    new_turn = turn == :white ? :black : :white
    
    newstate = Dict(
        :step => current_step + 1,
        :board => new_board,
        :turn => new_turn,
        :reward => reward,
        :isterminal => false
    )
    
    return Dict(
        :newNodeKey => "move_$current_step",
        :newstate => newstate,
        :progressvalue => progressvalue
    )
end

# Initial state
initialstate = Dict(
    :step => 0,
    :board => init_board(),
    :turn => :white,
    :reward => 0,
    :isterminal => false
)

# Transition arguments
transitionargs = (
    max_moves = 10,
)

# Run MCTS
result = runMCTS(
    initialstate,
    chess_transition,
    transitionargs;
    maxiterations = 30,
    explorationweight = 2.0,  # More exploration for game playing
    maxSimulationDepth = 4,
    horizontalSampleExpansionPhase = 5
)

# Display results
println("Chess-like Game MCTS")
println("====================")
println()
println("Best move sequence:")
println("  Initial board state")
println("  → ", result.bestTerminalState[:step], " moves")
println()
println("Final board has ", length(result.bestTerminalState[:board]), " pieces")
println("Root node visits: ", result.root.visits)
println("High value states: ", length(result.highValueStateList))
```