First, tiny tiny attempts of probability

cuatro/dice.py

@@ -16,6 +16,8 @@ def __init__(self):
         self.throws = 0
         self.faces = [0, 0, 0, 0, 0]
         self.counts = {}
+        self.max_face = 0
+        self.max_count = 0
 
     def roll(self, keep=None):
         # making sure only existing faces are kept
@@ -40,6 +42,10 @@ def _update_counts(self):
         self.counts = defaultdict(int)
         for num in self.faces:
             self.counts[num] += 1
+        for face, count in self.counts.items():
+            if count > self.max_count:
+                self.max_count = count
+                self.max_face = face
 
     def verify(self, keep):
         """ verifies that keep only contains existing faces """

cuatro/player.py

@@ -25,6 +25,8 @@ def __init__(self, name):
     def play(self, dice, board):
         print board
         print dice.throws, "\t", dice
+        #da = DiceAnalyzer(dice)
+        #da.probability_yahtzee()
         keep = raw_input("which numbers do you want to keep? ")
         return [int(k) for k in keep if k.isdigit()]
 

cuatro/probability.py

@@ -0,0 +1,126 @@
+from math import factorial as fac
+
+def out_of(n, r):
+	return fac(n) / (fac(n-r) * fac(r))
+
+class DiceAnalyzer():
+
+	def yathzee(self, initial=0, left=4):
+		free = 5 - initial
+		result = 0
+		# the first option is to hit all now in this throw
+		result += ((1./6) ** free)
+		# if this is the first dice, then actually you will always hit
+		if initial == 0:
+			result *= 6
+		# if no more options are left, than that's it
+		if left == 0:
+			return result
+		# there is still hope == throws 
+		# eaxmine what can happen in this throw and branch
+		if free > 4:
+			# if we have all dices free, we can have 4 matches now and still go on
+			result += ((1./6) ** 4) * ((5./6) ** 1) * 5 * self.yathzee(initial + 4, left - 1)
+		if free > 3:
+			# with 4 dices, we can draw three now and go on
+			result += ((1./6) ** 3) * ((5./6) ** (free-3)) * out_of(free, 3) * self.yathzee(initial + 3, left - 1)
+		if free > 2:
+			# two matches possible with 3 dices
+			result += ((1./6) ** 2) * ((5./6) ** (free-2)) * out_of(free, 2) * self.yathzee(initial + 2, left - 1)
+		if free > 1:  	
+			#if free < 5:
+				# there already is a chosen face
+			# we can have one match
+			result += 1./6 * ((5./6) ** (free-1)) * free * self.yathzee(initial + 1, left - 1)
+		# any given sunday, we can have no luck
+		result += ((5./6) ** free) * self.yathzee(initial, left - 1)
+		return result
+
+	def single_roll(self, target):
+		if target == "yathzee":
+			return 6 * (1./6) ** 5
+		if target == "four of a kind":
+			return 6 * 5 * (1./6) ** 4 * 5./6
+		if target == "three of a kind":
+			return 6 * out_of(5,3) * (1./6) ** 3 * (5./6) ** 2
+		if target == "pair":
+			# a true pair, so no full house
+			return 6 * out_of(5,2) * (1./6) ** 2 * (5./6) ** 2 * 4./6
+		if target == "no match":
+			return fac(6) * 1. / (6 ** 5)
+
+	def y(self, roles=0):
+		single_roll = self.single_roll("yathzee")
+		if roles == 1:
+			return single_roll
+		# now with two rolls
+		# four of a kind with a single 
+		four_single = self.single_roll("four of a kind") * (1./6)
+		# three of a kind and then two matching
+		three_two = self.single_roll("three of a kind") * (1./6) ** 2
+		# a pair and then three that match
+		pair_three = self.single_roll("pair") * (1./6) ** 3
+		# no match and then matching four
+		no_four = self.single_roll("no match") * (1./6) ** 4
+		two_roll = four_single
+		two_roll += three_two
+		two_roll += no_four
+		two_roll += pair_three
+		if roles == 2:
+			return two_roll
+		return single_roll + two_roll
+
+
+
+	def full_house(self, dice):
+		pass
+
+
+def is_yathzee(dice):
+	face = dice.faces[0]
+	for f in dice.faces:
+		if f != face:
+			return False
+	return True
+
+import dice
+
+def simulate_yathzee():
+	attempts = 0
+	probability = 0
+	prev_probability = 0
+	hits = 0
+	stepsize = 1000000
+	error = 1
+	while error > 1.0 / 100000:
+		for attempt in range(stepsize):
+			attempts += 1
+			yathzee = False
+			d = dice.Dice()
+			face = 0
+			keep= []
+			for throw in range(5):
+				d.roll(keep)
+				if face == 0:
+					face = d.max_face
+				else:
+					keep = [face for i in range(d.max_count)]
+				if is_yathzee(d):
+					yathzee = True
+					break
+			if yathzee:
+				hits += 1
+		prev_probability = probability
+		probability = hits * 1.0 / attempts
+		error = abs(probability - prev_probability)
+		print "Finished ", attempts, " attempts. Hits: ", hits, ". Probability of ", (hits * 1.0 /attempts), " Error ", error
+	print "Result ", probability, " with ", attempts, " attempts"
+
+
+
+if __name__ == "__main__":
+	da = DiceAnalyzer()
+	print da.single_roll("yathzee")
+	print da.y()
+	#print da.yathzee(0,0)
+	#simulate_yathzee()