// Recursive part of iterative deepening Expectimax
private Tuple<Move, Boolean> IterativeDeepeningExpectimax(State state, int depth, double timeLimit, Stopwatch timer, WeightVector weights)
{
Move bestMove;
if (depth == 0 || state.IsGameOver())
{
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER)
{
bestMove = new ComputerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true);
}
else throw new Exception();
}
if (state.Player == GameEngine.PLAYER) // AI's turn
{
bestMove = new PlayerMove();
double highestScore = Double.MinValue, currentScore = Double.MinValue;
List<Move> moves = state.GetMoves();
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
currentScore = IterativeDeepeningExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = move;
}
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = highestScore;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
}
bestMove.Score = highestScore;
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER) // computer's turn (the random event node)
{
bestMove = new ComputerMove();
// return the weighted average of all the child nodes's scores
double average = 0;
List<Cell> availableCells = state.GetAvailableCells();
List<Move> moves = state.GetAllComputerMoves(availableCells);
int moveCheckedSoFar = 0;
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
average += StateProbability(((ComputerMove)move).Tile) * IterativeDeepeningExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;
moveCheckedSoFar++;
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = average / moveCheckedSoFar;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
}
bestMove.Score = average / moves.Count;
return new Tuple<Move, Boolean>(bestMove, true);
}
else throw new Exception();
}
// Recursive part of iterative deepening Expectimax with star 1 pruning
private Tuple<Move, Boolean> RecursiveIterativeDeepeningExpectimaxWithStar1(State state, double alpha, double beta, int depth,
int timeLimit, Stopwatch timer, WeightVector weights)
{
Move bestMove;
if (depth == 0 || state.IsGameOver())
{
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER)
{
bestMove = new ComputerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true); ;
}
else throw new Exception();
}
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove();
double highestScore = Double.MinValue, currentScore = Double.MinValue;
List<Move> moves = state.GetMoves();
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
currentScore = RecursiveIterativeDeepeningExpectimaxWithStar1(resultingState, alpha, beta, depth - 1, timeLimit, timer, weights).Item1.Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = move;
}
alpha = Math.Max(alpha, highestScore);
if (beta <= alpha)
{ // beta cut-off
break;
}
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = highestScore;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
}
bestMove.Score = highestScore;
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER) // computer's turn (the random event node)
{
bestMove = new ComputerMove();
List<Cell> availableCells = state.GetAvailableCells();
List<Move> moves = state.GetAllComputerMoves(availableCells);
int numSuccessors = moves.Count;
double upperBound = AI.GetUpperBound(weights);
double lowerBound = AI.GetLowerBound(weights);
double curAlpha = numSuccessors * (alpha - upperBound) + upperBound;
double curBeta = numSuccessors * (beta - lowerBound) + lowerBound;
double scoreSum = 0;
int i = 1;
foreach (Move move in moves)
{
double sucAlpha = Math.Max(curAlpha, lowerBound);
double sucBeta = Math.Min(curBeta, upperBound);
State resultingState = state.ApplyMove(move);
double score = StateProbability(((ComputerMove)move).Tile) *
RecursiveIterativeDeepeningExpectimaxWithStar1(resultingState, sucAlpha, sucBeta, depth - 1, timeLimit, timer, weights).Item1.Score;
scoreSum += score;
if (score <= curAlpha)
{
scoreSum += upperBound * (numSuccessors - i);
bestMove.Score = scoreSum / numSuccessors;
return new Tuple<Move, Boolean>(bestMove, true); // pruning
}
if (score >= curBeta)
{
scoreSum += lowerBound * (numSuccessors - i);
bestMove.Score = scoreSum / numSuccessors;
return new Tuple<Move, Boolean>(bestMove, true); // pruning
}
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = scoreSum / i;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
curAlpha += upperBound - score;
curBeta += lowerBound - score;
i++;
}
bestMove.Score = scoreSum / numSuccessors;
return new Tuple<Move, Boolean>(bestMove, true);
}
else throw new Exception();
}
// Classic Expectimax search
public Move ExpectimaxAlgorithm(State state, int depth, WeightVector weights)
{
Move bestMove;
if (depth == 0 || state.IsGameOver())
{
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return bestMove;
}
else if (state.Player == GameEngine.COMPUTER)
{
bestMove = new ComputerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return bestMove;
}
else throw new Exception();
}
if (state.Player == GameEngine.PLAYER) // AI's turn
{
bestMove = new PlayerMove();
double highestScore = Double.MinValue, currentScore = Double.MinValue;
List<Move> moves = state.GetMoves();
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
currentScore = ExpectimaxAlgorithm(resultingState, depth - 1, weights).Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = move;
}
}
bestMove.Score = highestScore;
return bestMove;
}
else if (state.Player == GameEngine.COMPUTER) // computer's turn (the random event node)
{
bestMove = new ComputerMove();
// return the weighted average of all the child nodes's scores
double average = 0;
List<Cell> availableCells = state.GetAvailableCells();
List<Move> moves = state.GetAllComputerMoves(availableCells);
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
average += StateProbability(((ComputerMove)move).Tile) * ExpectimaxAlgorithm(resultingState, depth - 1, weights).Score;
}
bestMove.Score = average / moves.Count;
return bestMove;
}
else throw new Exception();
}
// Expectimax with Star2 pruning
// NB: DO NOT USE - way too slow
private Move Star2Expectimax(State state, double alpha, double beta, int depth, WeightVector weights)
{
Move bestMove;
if (depth == 0 || state.IsGameOver())
{
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.Evaluate(state);
return bestMove;
}
else if (state.Player == GameEngine.COMPUTER)
{
bestMove = new ComputerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.Evaluate(state);
return bestMove;
}
else throw new Exception();
}
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove();
double highestScore = Double.MinValue, currentScore = Double.MinValue;
List<Move> moves = state.GetMoves();
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
currentScore = Star2Expectimax(resultingState, alpha, beta, depth - 1, weights).Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = move;
}
alpha = Math.Max(alpha, highestScore);
if (beta <= alpha)
{ // beta cut-off
break;
}
}
bestMove.Score = highestScore;
return bestMove;
}
else if (state.Player == GameEngine.COMPUTER) // computer's turn (the random event node)
{
bestMove = new ComputerMove();
List<Cell> availableCells = state.GetAvailableCells();
List<Move> moves = state.GetAllComputerMoves(availableCells);
int numSuccessors = moves.Count;
double upperBound = AI.GetUpperBound(weights);
double lowerBound = AI.GetLowerBound(weights);
double curAlpha = numSuccessors * (alpha - upperBound);
double curBeta = numSuccessors * (beta - lowerBound);
double sucAlpha = Math.Max(curAlpha, lowerBound);
double[] probeValues = new double[numSuccessors];
// probing phase
double vsum = 0;
int i = 1;
foreach (Move move in moves)
{
curBeta += lowerBound;
double sucBeta = Math.Min(curBeta, upperBound);
State resultingState = state.ApplyMove(move);
probeValues[i - 1] = Probe(resultingState, sucAlpha, sucBeta, depth - 1, weights);
vsum += probeValues[i - 1];
if (probeValues[i - 1] >= curBeta)
{
vsum += lowerBound * (numSuccessors - i);
bestMove.Score = vsum / numSuccessors;
return bestMove; // pruning
}
curBeta -= probeValues[i - 1];
i++;
}
// search phase
vsum = 0;
i = 1;
foreach (Move move in moves)
{
curAlpha += upperBound;
curBeta += probeValues[i - 1];
sucAlpha = Math.Max(curAlpha, lowerBound);
double sucBeta = Math.Min(curBeta, upperBound);
State resultingState = state.ApplyMove(move);
double score = StateProbability(((ComputerMove)move).Tile) * Star2Expectimax(resultingState, sucAlpha, sucBeta, depth - 1, weights).Score;
vsum += score;
if (score <= curAlpha)
{
vsum += upperBound * (numSuccessors - i);
bestMove.Score = vsum / numSuccessors;
return bestMove; // pruning
}
if (score >= curBeta)
{
vsum += lowerBound * (numSuccessors - i);
bestMove.Score = vsum / numSuccessors;
return bestMove; // pruning
}
curAlpha -= score;
curBeta -= score;
i++;
}
bestMove.Score = vsum / numSuccessors;
return bestMove;
}
else
{
throw new Exception();
}
}
// Expectimax search with Star1 pruning and forward pruning
private Move Star1WithUnlikelyPruning(State state, double alpha, double beta, int depth, int lastSpawn, WeightVector weights)
{
Move bestMove;
if (depth == 0 || state.IsGameOver())
{
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return bestMove;
}
else if (state.Player == GameEngine.COMPUTER)
{
bestMove = new ComputerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return bestMove;
}
else throw new Exception();
}
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove();
double highestScore = Double.MinValue, currentScore = Double.MinValue;
List<Move> moves = state.GetMoves();
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
currentScore = Star1WithUnlikelyPruning(resultingState, alpha, beta, depth - 1, lastSpawn, weights).Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = move;
}
alpha = Math.Max(alpha, highestScore);
if (beta <= alpha)
{ // beta cut-off
break;
}
}
bestMove.Score = highestScore;
return bestMove;
}
else if (state.Player == GameEngine.COMPUTER) // computer's turn (the random event node)
{
bestMove = new ComputerMove();
List<Cell> availableCells = state.GetAvailableCells();
List<Move> moves = state.GetAllComputerMoves(availableCells);
int numSuccessors = moves.Count;
double upperBound = AI.GetUpperBound(weights);
double lowerBound = AI.GetLowerBound(weights);
double curAlpha = numSuccessors * (alpha - upperBound) + upperBound;
double curBeta = numSuccessors * (beta - lowerBound) + lowerBound;
double scoreSum = 0;
int i = 1;
foreach (Move move in moves)
{
int value = ((ComputerMove)move).Tile;
if (value == 4 && lastSpawn == 4) continue; // unlikely event pruning (2 4-spawns in sequence only has 1% chance)
double sucAlpha = Math.Max(curAlpha, lowerBound);
double sucBeta = Math.Min(curBeta, upperBound);
State resultingState = state.ApplyMove(move);
double score = StateProbability(((ComputerMove)move).Tile) * Star1WithUnlikelyPruning(resultingState, sucAlpha, sucBeta, depth - 1, value, weights).Score;
scoreSum += score;
if (score <= curAlpha)
{
scoreSum += upperBound * (numSuccessors - i);
bestMove.Score = scoreSum / numSuccessors;
return bestMove; // pruning
}
if (score >= curBeta)
{
scoreSum += lowerBound * (numSuccessors - i);
bestMove.Score = scoreSum / numSuccessors;
return bestMove; // pruning
}
curAlpha += upperBound - score;
curBeta += lowerBound - score;
i++;
}
bestMove.Score = scoreSum / numSuccessors;
return bestMove;
}
else throw new Exception();
}
// Recursive part of ^^ iterative deepening Expectimax with Star1, move ordering and transposition table
private Tuple<Move, Boolean> RecursiveTTStar1(State state, double alpha, double beta, int depth, double timeLimit, Stopwatch timer, WeightVector weights)
{
Move bestMove;
if (depth == 0 || state.IsGameOver())
{
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER)
{
bestMove = new ComputerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true);
}
else throw new Exception();
}
if (state.Player == GameEngine.PLAYER) // AI's turn
{
DIRECTION bestDirection = (DIRECTION)(-1);
bestMove = new PlayerMove();
double highestScore = Double.MinValue, currentScore = Double.MinValue;
// transposition table look-up
long zob_hash = GetHash(state);
if (transposition_table.ContainsKey(zob_hash) && transposition_table[zob_hash].depth > depth)
{
Move move = new PlayerMove(transposition_table[zob_hash].direction);
move.Score = transposition_table[zob_hash].value;
return new Tuple<Move, Boolean>(move, true);
}
// move ordering - make sure we first check the move we believe to be best based on earlier searches
else if (transposition_table.ContainsKey(zob_hash))
{
bestDirection = transposition_table[zob_hash].direction;
State resultingState = state.ApplyMove(new PlayerMove(bestDirection));
currentScore = RecursiveTTStar1(resultingState, alpha, beta, depth - 1, timeLimit, timer, weights).Item1.Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = new PlayerMove(bestDirection);
}
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = highestScore;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
}
// now check the rest of moves
List<Move> moves = state.GetMoves();
foreach (Move move in moves)
{
if (((PlayerMove)move).Direction != bestDirection)
{
State resultingState = state.ApplyMove(move);
currentScore = RecursiveTTStar1(resultingState, alpha, beta, depth - 1, timeLimit, timer, weights).Item1.Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = move;
}
alpha = Math.Max(alpha, highestScore);
if (beta <= alpha)
{ // beta cut-off
break;
}
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = highestScore;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
}
}
bestMove.Score = highestScore;
// add result to transposition table
TableRow row = new TableRow((short)depth, ((PlayerMove)bestMove).Direction, bestMove.Score);
transposition_table.AddOrUpdate(zob_hash, row, (key, oldValue) => row);
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER) // computer's turn (the random event node)
{
bestMove = new ComputerMove();
int moveCheckedSoFar = 0;
List<Cell> availableCells = state.GetAvailableCells();
List<Move> moves = state.GetAllComputerMoves(availableCells);
int numSuccessors = moves.Count;
double upperBound = AI.GetUpperBound(weights);
double lowerBound = AI.GetLowerBound(weights);
double curAlpha = numSuccessors * (alpha - upperBound) + upperBound;
double curBeta = numSuccessors * (beta - lowerBound) + lowerBound;
double scoreSum = 0;
int i = 1;
foreach (Move move in moves)
{
double sucAlpha = Math.Max(curAlpha, lowerBound);
double sucBeta = Math.Min(curBeta, upperBound);
State resultingState = state.ApplyMove(move);
double score = StateProbability(((ComputerMove)move).Tile) * RecursiveTTStar1(resultingState, sucAlpha, sucBeta, depth - 1, timeLimit, timer, weights).Item1.Score;
scoreSum += score;
moveCheckedSoFar++;
if (score <= curAlpha)
{
scoreSum += upperBound * (numSuccessors - i);
bestMove.Score = scoreSum / numSuccessors;
return new Tuple<Move,bool>(bestMove, true); // pruning
}
if (score >= curBeta)
{
scoreSum += lowerBound * (numSuccessors - i);
bestMove.Score = scoreSum / numSuccessors;
return new Tuple<Move, bool>(bestMove, true); // pruning
}
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = scoreSum / moveCheckedSoFar;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
curAlpha += upperBound - score;
curBeta += lowerBound - score;
i++;
}
bestMove.Score = scoreSum / numSuccessors;
return new Tuple<Move, bool>(bestMove, true);
}
else throw new Exception();
}
// Recursive part of iterative deepening Expectimax with transposition table
private Tuple<Move, Boolean> RecursiveTTExpectimax(State state, int depth, double timeLimit, Stopwatch timer, WeightVector weights)
{
Move bestMove;
if (depth == 0 || state.IsGameOver())
{
if (state.Player == GameEngine.PLAYER)
{
bestMove = new PlayerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER)
{
bestMove = new ComputerMove(); // dummy action, as there will be no valid move
bestMove.Score = AI.EvaluateWithWeights(state, weights);
return new Tuple<Move, Boolean>(bestMove, true);
}
else throw new Exception();
}
if (state.Player == GameEngine.PLAYER) // AI's turn
{
// transposition table look-up
long zob_hash = GetHash(state);
if (transposition_table.ContainsKey(zob_hash) && transposition_table[zob_hash].depth > depth)
{
Move move = new PlayerMove(transposition_table[zob_hash].direction);
move.Score = transposition_table[zob_hash].value;
return new Tuple<Move, Boolean>(move, true);
}
bestMove = new PlayerMove();
double highestScore = Double.MinValue, currentScore = Double.MinValue;
List<Move> moves = state.GetMoves();
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
currentScore = RecursiveTTExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;
if (currentScore > highestScore)
{
highestScore = currentScore;
bestMove = move;
}
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = highestScore;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
}
bestMove.Score = highestScore;
// add result to transposition table
TableRow row = new TableRow((short)depth, ((PlayerMove)bestMove).Direction, bestMove.Score);
transposition_table.AddOrUpdate(zob_hash, row, (key, oldValue) => row);
return new Tuple<Move, Boolean>(bestMove, true);
}
else if (state.Player == GameEngine.COMPUTER) // computer's turn (the random event node)
{
bestMove = new ComputerMove();
// return the weighted average of all the child nodes's scores
double average = 0;
List<Cell> availableCells = state.GetAvailableCells();
List<Move> moves = state.GetAllComputerMoves(availableCells);
int moveCheckedSoFar = 0;
foreach (Move move in moves)
{
State resultingState = state.ApplyMove(move);
average += StateProbability(((ComputerMove)move).Tile) * RecursiveTTExpectimax(resultingState, depth - 1, timeLimit, timer, weights).Item1.Score;
moveCheckedSoFar++;
if (timer.ElapsedMilliseconds > timeLimit)
{
bestMove.Score = average / moveCheckedSoFar;
return new Tuple<Move, Boolean>(bestMove, false); // recursion not completed, return false
}
}
bestMove.Score = average / moves.Count;
return new Tuple<Move, Boolean>(bestMove, true);
}
else throw new Exception();
}
