/**** 
* Plugins
****/ 
var tween = LK.import("@upit/tween.v1");
var storage = LK.import("@upit/storage.v1");

/**** 
* Classes
****/ 
var Dice = Container.expand(function () {
	var self = Container.call(this);
	// Add numeric variable valor
	self.valor = 1;
	// Add rolling animation variables
	self.isRolling = false;
	self.rollCount = 0;
	self.rollTarget = 0;
	self.rollTimer = 0;
	var diceGraphics = self.attachAsset('Dice' + self.valor, {
		anchorX: 0.5,
		anchorY: 0.5
	});
	// Method to update dice visual based on valor
	self.updateVisual = function () {
		// Create new graphics based on valor first
		var newGraphics = self.attachAsset('Dice' + self.valor, {
			anchorX: 0.5,
			anchorY: 0.5
		});
		// Remove old graphics after new one is created
		self.removeChild(diceGraphics);
		// Update reference to new graphics
		diceGraphics = newGraphics;
		// Add bounce effect when value changes during rolling
		if (self.isRolling) {
			self.playDiceSound();
			diceGraphics.scaleX = 1;
			diceGraphics.scaleY = 1;
			tween(diceGraphics, {
				scaleX: 1.2,
				scaleY: 1.2
			}, {
				duration: 100,
				easing: tween.bounceOut,
				onFinish: function onFinish() {
					tween(diceGraphics, {
						scaleX: 1,
						scaleY: 1
					}, {
						duration: 100,
						easing: tween.bounceOut
					});
				}
			});
		}
	};
	// Method to play dice sound
	self.playDiceSound = function () {
		LK.getSound('Roll').play();
	};
	// Method to start rolling animation
	self.startRoll = function () {
		self.isRolling = true;
		self.rollCount = 0;
		self.rollTarget = Math.floor(Math.random() * 7) + 6; // 6 to 12 rolls
		self.rollTimer = 0;
	};
	// Update method for rolling animation
	self.update = function () {
		if (self.isRolling) {
			var rollSpeed = Math.floor(self.rollCount * 1.5) + 3; // Start fast, get slower
			if (self.rollTimer >= rollSpeed) {
				self.valor = Math.floor(Math.random() * 6) + 1;
				self.updateVisual();
				self.rollCount++;
				self.rollTimer = 0;
				if (self.rollCount >= self.rollTarget) {
					self.isRolling = false;
				}
			} else {
				self.rollTimer++;
			}
		}
	};
	return self;
});
var Particle = Container.expand(function () {
	var self = Container.call(this);
	var particleGraphics = self.attachAsset('Particula', {
		anchorX: 0.5,
		anchorY: 0.5
	});
	// Initialize particle properties
	self.velocityX = (Math.random() - 0.5) * 10;
	self.velocityY = Math.random() * -8 - 2;
	self.gravity = 0.3;
	self.life = 1.0;
	self.fadeSpeed = Math.random() * 0.02 + 0.01;
	// Randomize initial scale and color with more variety
	var initialScale = Math.random() * 0.6 + 0.2;
	particleGraphics.scaleX = initialScale;
	particleGraphics.scaleY = initialScale;
	var colors = [0xFFD700, 0xFF6B6B, 0x4ECDC4, 0x45B7D1, 0x96CEB4, 0xFECE00, 0xF38BA8, 0xFF9500, 0x8E44AD, 0xE74C3C];
	particleGraphics.tint = colors[Math.floor(Math.random() * colors.length)];
	// Add rotation and pulsing effect
	self.rotationSpeed = (Math.random() - 0.5) * 0.2;
	self.pulseSpeed = Math.random() * 0.1 + 0.05;
	self.pulseOffset = Math.random() * Math.PI * 2;
	self.update = function () {
		// Update position
		self.x += self.velocityX;
		self.y += self.velocityY;
		self.velocityY += self.gravity;
		// Add rotation
		particleGraphics.rotation += self.rotationSpeed;
		// Add pulsing effect
		var pulseScale = 1 + Math.sin(LK.ticks * self.pulseSpeed + self.pulseOffset) * 0.2;
		// Update life and fade
		self.life -= self.fadeSpeed;
		particleGraphics.alpha = Math.max(0, self.life);
		// Scale down over time with pulse effect
		var scale = initialScale * self.life * pulseScale;
		particleGraphics.scaleX = scale;
		particleGraphics.scaleY = scale;
		// Remove when life is over
		if (self.life <= 0) {
			self.destroy();
		}
	};
	return self;
});

/**** 
* Initialize Game
****/ 
// Create array to hold all dice
var game = new LK.Game({
	backgroundColor: 0xFFFFFF
});

/**** 
* Game Code
****/ 
// Create array to hold all dice
var diceArray = [];
// Create array to hold particles
var particles = [];
// Add lanzamiento boolean variable
var lanzamiento = false;
// Add timer to enforce minimum 1 second wait between rolls
var lastRollFinishTime = 0;
var minimumWaitTime = 1000; // 1 second in milliseconds
// Add best score tracking - load from storage with defaults
var bestScore = storage.bestScore || 0;
var previousScore = storage.previousScore || 0;
var actualScore = storage.actualScore || 0;
// Calculate center positions for two columns
var centerX = 2048 / 2;
var centerY = 2732 / 2;
var columnSpacing = 330; // Space between columns
var rowSpacing = 300; // Space between rows
// Create matching dice counter text
var counterText = new Text2('Best: ' + bestScore + '/8\nPrevious: ' + previousScore + '/8 - Current: ' + actualScore + '/8', {
	size: 80,
	fill: 0x2E7D32,
	align: 'center',
	font: "'Helvetica Neue', 'Arial', sans-serif"
});
counterText.anchor.set(0.5, 0);
counterText.y = 100; // Move down to make space for status text
LK.gui.top.addChild(counterText);
// Create status text above dice
var statusText = new Text2('Tap to roll', {
	size: 60,
	fill: 0x1976D2,
	font: "'Helvetica Neue', 'Arial', sans-serif"
});
statusText.anchor.set(0.5, 0.5);
statusText.x = centerX;
statusText.y = centerY - 700; // Position above dice grid
game.addChild(statusText);
// Create countdown text
var countdownText = new Text2('', {
	size: 50,
	fill: 0xF57C00,
	font: "'Helvetica Neue', 'Arial', sans-serif"
});
countdownText.anchor.set(0.5, 0.5);
countdownText.x = centerX;
countdownText.y = centerY - 640; // Position below status text
game.addChild(countdownText);
// Create probability text at bottom of screen
var probabilityText = new Text2('', {
	size: 80,
	fill: 0x7B1FA2,
	align: 'center',
	font: "'Helvetica Neue', 'Arial', sans-serif"
});
probabilityText.anchor.set(0.5, 1);
probabilityText.x = centerX;
probabilityText.y = 2732 - 50; // Position at bottom with margin
game.addChild(probabilityText);
// Function to count matching dice
function countMatchingDice() {
	var counts = {};
	// Count occurrences of each dice value
	for (var i = 0; i < diceArray.length; i++) {
		var value = diceArray[i].valor;
		counts[value] = (counts[value] || 0) + 1;
	}
	// Find the highest count
	var maxCount = 0;
	for (var value in counts) {
		if (counts[value] > maxCount) {
			maxCount = counts[value];
		}
	}
	return maxCount;
}
// Function to calculate factorial
function factorial(n) {
	if (n <= 1) return 1;
	var result = 1;
	for (var i = 2; i <= n; i++) {
		result *= i;
	}
	return result;
}
// Function to calculate multinomial coefficient
function multinomial(n, counts) {
	var result = factorial(n);
	for (var i = 0; i < counts.length; i++) {
		result /= factorial(counts[i]);
	}
	return result;
}
// Function to generate all partitions of 8 with maximum value k
function generatePartitions(sum, maxValue, numSlots) {
	var partitions = [];
	function backtrack(remaining, currentPartition, maxSoFar, slot) {
		if (slot === numSlots) {
			if (remaining === 0 && maxSoFar === maxValue) {
				partitions.push(currentPartition.slice());
			}
			return;
		}
		for (var i = 0; i <= remaining; i++) {
			currentPartition[slot] = i;
			var newMaxSoFar = Math.max(maxSoFar, i);
			if (newMaxSoFar <= maxValue) {
				backtrack(remaining - i, currentPartition, newMaxSoFar, slot + 1);
			}
		}
	}
	var partition = new Array(numSlots);
	backtrack(sum, partition, 0, 0);
	return partitions;
}
// Function to calculate probability of getting exactly N matching dice in 8 rolls
function calculateProbability(n) {
	if (n < 1 || n > 8) return 0;
	// Using the formula: P(exactly k) = (1/6^8) * sum of multinomial coefficients
	// where the sum is over all partitions with maximum value k
	var partitions = generatePartitions(8, n, 6);
	var sum = 0;
	for (var i = 0; i < partitions.length; i++) {
		sum += multinomial(8, partitions[i]);
	}
	var probability = sum / Math.pow(6, 8);
	return probability;
}
// Function to update probability display
function updateProbabilityDisplay() {
	var matchingCount = countMatchingDice();
	var probability = calculateProbability(matchingCount);
	var oneInX = Math.round(1 / probability);
	probabilityText.setText('Probability:\n1 in ' + oneInX);
}
// Function to create particles for largest matching group
function createParticlesForLargestGroup() {
	var counts = {};
	// Count occurrences of each dice value
	for (var i = 0; i < diceArray.length; i++) {
		var value = diceArray[i].valor;
		counts[value] = (counts[value] || 0) + 1;
	}
	// Find the highest count and value
	var maxCount = 0;
	var maxValue = 0;
	for (var value in counts) {
		if (counts[value] > maxCount) {
			maxCount = counts[value];
			maxValue = parseInt(value);
		}
	}
	// Create particles for each die in the largest group
	for (var i = 0; i < diceArray.length; i++) {
		var dice = diceArray[i];
		if (dice.valor == maxValue && counts[maxValue] == maxCount && maxCount > 1) {
			// Create 8-12 particles per die in largest group
			var particleCount = Math.floor(Math.random() * 5) + 8;
			for (var p = 0; p < particleCount; p++) {
				var particle = new Particle();
				particle.x = dice.x + (Math.random() - 0.5) * 80;
				particle.y = dice.y + (Math.random() - 0.5) * 80;
				// Add tween animation to particles for extra visual effect
				tween(particle, {
					scaleX: Math.random() * 0.5 + 0.8,
					scaleY: Math.random() * 0.5 + 0.8,
					rotation: Math.random() * Math.PI * 2
				}, {
					duration: 1000 + Math.random() * 500,
					easing: tween.easeOut
				});
				game.addChild(particle);
				particles.push(particle);
			}
		}
	}
}
// Function to apply tint colors to dice based on matching groups
function applyDiceTints() {
	var counts = {};
	// Count occurrences of each dice value
	for (var i = 0; i < diceArray.length; i++) {
		var value = diceArray[i].valor;
		counts[value] = (counts[value] || 0) + 1;
	}
	// Find the highest count and value
	var maxCount = 0;
	var maxValue = 0;
	for (var value in counts) {
		if (counts[value] > maxCount) {
			maxCount = counts[value];
			maxValue = parseInt(value);
		}
	}
	// Generate random colors for smaller groups
	var randomColors = [0xFF6B6B, 0x4ECDC4, 0x45B7D1, 0x96CEB4, 0xFECE00, 0xF38BA8];
	var colorIndex = 0;
	var usedColors = {};
	// Apply tints to all dice
	for (var i = 0; i < diceArray.length; i++) {
		var dice = diceArray[i];
		var value = dice.valor;
		if (value == maxValue && counts[value] == maxCount) {
			// Largest group gets soft yellow tint
			dice.children[0].tint = 0xFFFF99; // Soft yellow
		} else if (counts[value] > 1) {
			// Smaller matching groups get random colors
			if (!usedColors[value]) {
				usedColors[value] = randomColors[colorIndex % randomColors.length];
				colorIndex++;
			}
			dice.children[0].tint = usedColors[value];
		} else {
			// Single dice get no tint (white)
			dice.children[0].tint = 0xFFFFFF;
		}
	}
}
// Create 8 dice in two columns (4 rows each)
for (var col = 0; col < 2; col++) {
	for (var row = 0; row < 4; row++) {
		var dice = new Dice();
		// Assign random valor from 1 to 6
		dice.valor = Math.floor(Math.random() * 6) + 1;
		// Update visual based on valor
		dice.updateVisual();
		// Position dice in grid
		dice.x = centerX + (col - 0.5) * columnSpacing;
		dice.y = centerY + (row - 1.5) * rowSpacing;
		// Add to game and array
		game.addChild(dice);
		diceArray.push(dice);
	}
	// Game update method to handle dice rolling
	game.update = function () {
		// Update status and countdown text based on current state
		var currentTime = Date.now();
		var timeSinceLastRoll = currentTime - lastRollFinishTime;
		var timeRemaining = minimumWaitTime - timeSinceLastRoll;
		if (lanzamiento) {
			// Currently rolling
			statusText.setText('Rolling dice...');
			countdownText.setText('');
		} else if (timeRemaining > 0) {
			// Waiting period - show countdown
			statusText.setText('Wait to roll');
			var secondsRemaining = timeRemaining / 1000;
			countdownText.setText(secondsRemaining.toFixed(2) + 's');
		} else {
			// Ready to roll
			statusText.setText('Tap to roll');
			countdownText.setText('');
		}
		// Check if all dice have finished rolling
		if (lanzamiento) {
			var allFinished = true;
			for (var i = 0; i < diceArray.length; i++) {
				if (diceArray[i].isRolling) {
					allFinished = false;
					break;
				}
			}
			// Reset lanzamiento when all dice are done
			if (allFinished) {
				lanzamiento = false;
				// Record the time when rolling finished
				lastRollFinishTime = Date.now();
				// Update counter text with matching dice count
				var matchingCount = countMatchingDice();
				actualScore = matchingCount;
				// Update best score if current is better
				if (matchingCount > bestScore) {
					bestScore = matchingCount;
				}
				// Save scores to storage
				storage.bestScore = bestScore;
				storage.previousScore = previousScore;
				storage.actualScore = actualScore;
				counterText.setText('Best: ' + bestScore + '/8\nPrevious: ' + previousScore + '/8 - Current: ' + matchingCount + '/8');
				// Apply tint colors to dice based on matching groups
				applyDiceTints();
				// Create particles for largest matching group
				createParticlesForLargestGroup();
				// Create extra celebration particles for high scores
				if (matchingCount >= 4) {
					var burstCount = matchingCount * 3; // More particles for higher scores
					for (var b = 0; b < burstCount; b++) {
						var burstParticle = new Particle();
						burstParticle.x = centerX + (Math.random() - 0.5) * 300;
						burstParticle.y = centerY + (Math.random() - 0.5) * 200;
						burstParticle.velocityX = (Math.random() - 0.5) * 15;
						burstParticle.velocityY = Math.random() * -12 - 3;
						// Add sparkle effect with tweening
						tween(burstParticle, {
							rotation: Math.PI * 4,
							scaleX: 0.1,
							scaleY: 0.1
						}, {
							duration: 2000,
							easing: tween.easeOut
						});
						game.addChild(burstParticle);
						particles.push(burstParticle);
					}
				}
				// Update probability display
				updateProbabilityDisplay();
			}
		}
		// Clean up destroyed particles
		for (var i = particles.length - 1; i >= 0; i--) {
			if (particles[i].destroyed) {
				particles.splice(i, 1);
			}
		}
	};
	// Add screen tap handler for lanzamiento event
	game.down = function (x, y, obj) {
		// Check if enough time has passed since last roll finished
		var currentTime = Date.now();
		var timeSinceLastRoll = currentTime - lastRollFinishTime;
		// Only allow new roll if not currently rolling AND minimum wait time has passed
		if (!lanzamiento && timeSinceLastRoll >= minimumWaitTime) {
			// Copy current score to previous score when starting new roll
			var currentMatchingCount = countMatchingDice();
			previousScore = currentMatchingCount;
			// Save previous score to storage
			storage.previousScore = previousScore;
			// Update counter text to show actual as 0/8 during rolling
			counterText.setText('Best: ' + bestScore + '/8\nPrevious: ' + previousScore + '/8 - Current: 0/8');
			lanzamiento = true;
			// Start rolling animation for all dice
			for (var i = 0; i < diceArray.length; i++) {
				diceArray[i].startRoll();
			}
		}
	};
}

===================================================================
--- original.js
+++ change.js
@@ -216,35 +216,59 @@
 		}
 	}
 	return maxCount;
 }
+// Function to calculate factorial
+function factorial(n) {
+	if (n <= 1) return 1;
+	var result = 1;
+	for (var i = 2; i <= n; i++) {
+		result *= i;
+	}
+	return result;
+}
+// Function to calculate multinomial coefficient
+function multinomial(n, counts) {
+	var result = factorial(n);
+	for (var i = 0; i < counts.length; i++) {
+		result /= factorial(counts[i]);
+	}
+	return result;
+}
+// Function to generate all partitions of 8 with maximum value k
+function generatePartitions(sum, maxValue, numSlots) {
+	var partitions = [];
+	function backtrack(remaining, currentPartition, maxSoFar, slot) {
+		if (slot === numSlots) {
+			if (remaining === 0 && maxSoFar === maxValue) {
+				partitions.push(currentPartition.slice());
+			}
+			return;
+		}
+		for (var i = 0; i <= remaining; i++) {
+			currentPartition[slot] = i;
+			var newMaxSoFar = Math.max(maxSoFar, i);
+			if (newMaxSoFar <= maxValue) {
+				backtrack(remaining - i, currentPartition, newMaxSoFar, slot + 1);
+			}
+		}
+	}
+	var partition = new Array(numSlots);
+	backtrack(sum, partition, 0, 0);
+	return partitions;
+}
 // Function to calculate probability of getting exactly N matching dice in 8 rolls
 function calculateProbability(n) {
 	if (n < 1 || n > 8) return 0;
-	if (n === 1) {
-		// Probability of getting exactly 1 of each value (all different) is very low for 8 dice
-		// This is a complex calculation, we'll use approximation
-		return 0.015; // ~1.5%
+	// Using the formula: P(exactly k) = (1/6^8) * sum of multinomial coefficients
+	// where the sum is over all partitions with maximum value k
+	var partitions = generatePartitions(8, n, 6);
+	var sum = 0;
+	for (var i = 0; i < partitions.length; i++) {
+		sum += multinomial(8, partitions[i]);
 	}
-	// For n matching dice, we use binomial probability
-	// P(X = n) = C(8,n) * (1/6)^n * (5/6)^(8-n) * 6 (for any of the 6 faces)
-	// Simplified approximation for display purposes
-	var probabilities = {
-		2: 0.372,
-		// ~37.2%
-		3: 0.139,
-		// ~13.9% 
-		4: 0.0347,
-		// ~3.47%
-		5: 0.00695,
-		// ~0.695%
-		6: 0.00116,
-		// ~0.116%
-		7: 0.000139,
-		// ~0.0139%
-		8: 0.0000214 // ~0.00214%
-	};
-	return probabilities[n] || 0;
+	var probability = sum / Math.pow(6, 8);
+	return probability;
 }
 // Function to update probability display
 function updateProbabilityDisplay() {
 	var matchingCount = countMatchingDice();