Minimum Winning Attacking Troops Cache

Core/Cache/MinimumAttackerWinCache.cs

@@ -0,0 +1,141 @@
+using System.Collections.Concurrent;
+
+namespace Risk.Dice;
+
+public static class MinimumAttackerWinCache
+{
+    /// <summary>
+    /// For a particular game, <see cref="RoundConfig"/> and <see cref="BalanceConfig"/>
+    /// will not change, so this is effectively an (int) key. This should
+    /// result in very efficient lookups for the vast majority of rolls throughout the game,
+    /// as a single attack early against a particular stack of defenders (say, one) will
+    /// provide an O(1) solution for that defender stack size for the remainder of the game.
+    /// </summary>
+    private static readonly ConcurrentDictionary<(
+        int defenders,
+        RoundConfig round,
+        BalanceConfig balance), int> Cache
+        = [];
+
+    /// <summary>
+    /// Gets the minimum number of attackers required to destroy the defending troops with 100% certainty
+    /// if such a solution exists. 
+    /// </summary>
+    /// <exception cref="ArgumentNullException">Only supports balanced blitz; balanceConfig required.</exception>
+    public static int? Get(int defenders, RoundConfig roundConfig, BalanceConfig balanceConfig)
+    {
+        // True random not supported
+        if (balanceConfig == null)
+        {
+            throw new ArgumentNullException(nameof(balanceConfig), 
+                "MinWinAttackerCache requires Balanced Blitz configuration.");
+        }
+
+        // RoundConfig must be augmented, we'll need the attacking/defending DiceAugments
+        if (roundConfig.AppliedAttackDiceAugment is null ||
+            roundConfig.AppliedDefenseDiceAugment is null)
+        {
+            throw new ArgumentException("RoundConfig must be augmented.");
+        }
+
+        // Avoid trivial case
+        if (defenders <= 0)
+        {
+            return 1;
+        }
+
+        return Cache.TryGetValue((defenders, roundConfig, balanceConfig), out var minimumAttackers)
+            ? minimumAttackers
+            : Compute(defenders, roundConfig, balanceConfig);
+    }
+
+    /// <summary>
+    /// Populate the cache for 1..maxDefenders under a particular balanced-blitz setting.
+    /// Builds a single WinChanceInfo table and scans each column once.
+    /// </summary>
+    private static int? Compute(int maxDefenders, RoundConfig roundConfig, BalanceConfig balanceConfig)
+    {
+        // Certain dice augments need more or fewer attacking dice to find a 100% win probability
+        var multiplier = GetMaxAttackerMultiplier(
+            roundConfig.AppliedAttackDiceAugment.Value,
+            roundConfig.AppliedDefenseDiceAugment.Value);
+        var maxAttackers = (int)Math.Ceiling(multiplier * maxDefenders) + 10;
+
+        // Calculate the solution using the existing WinChanceInfo logic
+        var winChanceInfo = WinChanceCache.Get(Math.Max(maxAttackers, maxDefenders) + 1, roundConfig, balanceConfig);
+        winChanceInfo.Calculate();
+
+        // Populate the cache until the winning percentage drops below one
+        for (var d = 1; d <= maxDefenders; d++)
+        {
+            // Short-circuit if no solutions exist or if we've already calculated the solution
+            if (winChanceInfo.WinChances[maxAttackers, d] < 1.0f - 1e-6f)
+            {
+                continue;
+            }
+
+            // Protects against refactoring that no longer uses the Cache.Get pattern
+            if (Cache.TryGetValue((d, roundConfig, balanceConfig), out var attackers))
+            {
+                if (d == maxDefenders)
+                {
+                    return attackers;
+                }
+
+                continue;
+            }
+
+            // Work up from the fewest available attacking troops.
+            for (var a = 1; a <= maxAttackers; a++)
+            {
+                if (winChanceInfo.WinChances[a, d] >= 1.0f - 1e-6f)
+                {
+                    _ = Cache.TryAdd((d, roundConfig, balanceConfig), a);
+                    if (d == maxDefenders)
+                    {
+                        return a;
+                    }
+
+                    break;
+                }
+            }
+        }
+
+        // Fail-safe, current behavior
+        if (maxDefenders > 0 
+            && winChanceInfo.WinChances[maxAttackers, maxDefenders] >= 1.0f)
+        {
+            return maxAttackers;
+        }
+
+        return null;
+    }
+
+    private static double GetMaxAttackerMultiplier(DiceAugment attackDiceAugment, DiceAugment defenseDiceAugment)
+    {
+        var multiplier = 1.0;
+
+        if (defenseDiceAugment.HasFlag(DiceAugment.OnCapital))
+        {
+            multiplier += 1.0;
+        }
+
+        if (defenseDiceAugment.HasFlag(DiceAugment.IsBehindWall))
+        {
+            multiplier += 1.0;
+        }
+
+        if (defenseDiceAugment.HasFlag(DiceAugment.IsZombie))
+        {
+            multiplier -= 0.5;
+        }
+
+        if (attackDiceAugment.HasFlag(DiceAugment.IsZombie))
+        {
+            multiplier += 0.5;
+        }
+
+        // Floor so we don't go below 1x
+        return Math.Max(multiplier, 1.0); 
+    }
+}

Core/Config/RoundConfig.cs

@@ -41,6 +41,8 @@ public struct RoundConfig : IEquatable<RoundConfig>
         [SerializeField] private int _attackDiceCount;
         [SerializeField] private int _defendDiceCount;
         [SerializeField] private bool _favourDefenderOnDraw;
+        [SerializeField] private DiceAugment? _appliedAttackDiceAugment;
+        [SerializeField] private DiceAugment? _appliedDefenseDiceAugment;
 
         public int DiceFaceCount => _diceFaceCount;
         public int AttackDiceCount => _attackDiceCount;
@@ -51,6 +53,9 @@ public struct RoundConfig : IEquatable<RoundConfig>
 
         public static RoundConfig Default => new RoundConfig(6, 3, 2, true);
 
+        public DiceAugment? AppliedAttackDiceAugment => _appliedAttackDiceAugment;
+        public DiceAugment? AppliedDefenseDiceAugment => _appliedDefenseDiceAugment;
+
         public RoundConfig (int diceFaceCount, int attackDiceCount, int defendDiceCount, bool favourDefenderOnDraw)
         {
 #if UNITY_ASSERTIONS
@@ -75,6 +80,9 @@ public void SetMaxAttackDice (int maxAttackDice)
 
         public void ApplyAugments (DiceAugment attackAugment, DiceAugment defendAugment)
         {
+            _appliedAttackDiceAugment = attackAugment;
+            _appliedDefenseDiceAugment = defendAugment;
+
             if ((attackAugment & DiceAugment.IsZombie) != 0)
             {
                 _attackDiceCount = Math.Max(_attackDiceCount - 1, 1);