/*
* Calculates the expected value over all possible states that could result from
* taking the given action in the given state.
*/
private double ExpectedValue(GameState state, Action action, IDepthLimit searchLimit)
{
state.ApplyAction(action);
double placementProbability = 1.0 / state.EmptyCells;
double probability2 = placementProbability * Constants.TILE_PROBABILITY_2;
double probability4 = placementProbability * Constants.TILE_PROBABILITY_4;
double expectedValue = 0;
// Tries all possible placements of '2' and '4' tiles, calculating the
// value of each outcome and aggregating values into the expected value.
foreach (var cell in state.GetEmptyCells())
{
var tile2 = new Tile(cell, 2);
state.AddTile(tile2);
expectedValue += MaxValue(state, searchLimit) * probability2;
state.RemoveTile(cell);
var tile4 = new Tile(cell, 4);
state.AddTile(tile4);
expectedValue += MaxValue(state, searchLimit) * probability4;
state.RemoveTile(cell);
}
return(expectedValue);
}
/*
* Returns the maximum value over all states reachable from the given state.
*/
private double MaxValue(GameState state, IDepthLimit searchLimit)
{
if (state.IsWin)
{
return(100.0);
}
else if (state.IsLoss)
{
return(0);
}
else if (searchLimit.Done())
{
return(Evaluate(state));
}
double maxValue = NO_VALUE;
foreach (var action in ShuffledLegalActions(state))
{
searchLimit.IncreaseDepth();
double expectedValue = ExpectedValue(new GameState(state), action, searchLimit);
searchLimit.DecreaseDepth();
if (expectedValue > maxValue)
{
maxValue = expectedValue;
}
}
return(maxValue);
}
/// <summary>
/// Returns the list of legal actions in a game state with their corresponding
/// expected values.
/// </summary>
/// <param name="state">the game state</param>
/// <param name="searchLimit">a depth limit for the search algorithm</param>
public IEnumerable <ActionValue> GetPolicies(GameState state, IDepthLimit searchLimit)
{
foreach (var action in ShuffledLegalActions(state))
{
searchLimit.IncreaseDepth();
double value = ExpectedValue(new GameState(state), action, searchLimit);
searchLimit.DecreaseDepth();
yield return(new ActionValue()
{
Action = action,
Value = value
});
}
}
/// <summary>
/// Returns the best action to take in a game state using the given depth limit.
/// If no actions are legal, NoAction is returned.
/// </summary>
/// <param name="state">the game state</param>
/// <param name="searchLimit">the depth limit</param>
public Action GetPolicy(GameState state, IDepthLimit searchLimit)
{
return(GetPolicies(state, searchLimit).Best());
}
