Initial data commit

Task/Dice-game-probabilities/Python/dice-game-probabilities-1.py

@@ -0,0 +1,19 @@
+from itertools import product
+
+def gen_dict(n_faces, n_dice):
+    counts = [0] * ((n_faces + 1) * n_dice)
+    for t in product(range(1, n_faces + 1), repeat=n_dice):
+        counts[sum(t)] += 1
+    return counts, n_faces ** n_dice
+
+def beating_probability(n_sides1, n_dice1, n_sides2, n_dice2):
+    c1, p1 = gen_dict(n_sides1, n_dice1)
+    c2, p2 = gen_dict(n_sides2, n_dice2)
+    p12 = float(p1 * p2)
+
+    return sum(p[1] * q[1] / p12
+               for p, q in product(enumerate(c1), enumerate(c2))
+               if p[0] > q[0])
+
+print beating_probability(4, 9, 6, 6)
+print beating_probability(10, 5, 7, 6)

Task/Dice-game-probabilities/Python/dice-game-probabilities-2.py

@@ -0,0 +1,26 @@
+from __future__ import print_function, division
+
+def combos(sides, n):
+    if not n: return [1]
+    ret = [0] * (max(sides)*n + 1)
+    for i,v in enumerate(combos(sides, n - 1)):
+        if not v: continue
+        for s in sides: ret[i + s] += v
+    return ret
+
+def winning(sides1, n1, sides2, n2):
+    p1, p2 = combos(sides1, n1), combos(sides2, n2)
+    win,loss,tie = 0,0,0 # 'win' is 1 beating 2
+    for i,x1 in enumerate(p1):
+        # using accumulated sum on p2 could save some time
+        win += x1*sum(p2[:i])
+        tie += x1*sum(p2[i:i+1])
+        loss+= x1*sum(p2[i+1:])
+    s = sum(p1)*sum(p2)
+    return win/s, tie/s, loss/s
+
+print(winning(range(1,5), 9, range(1,7), 6))
+print(winning(range(1,11), 5, range(1,8), 6)) # this seem hardly fair
+
+# mountains of dice test case
+# print(winning((1, 2, 3, 5, 9), 700, (1, 2, 3, 4, 5, 6), 800))

Task/Dice-game-probabilities/Python/dice-game-probabilities-3.py

@@ -0,0 +1,24 @@
+from __future__ import division, print_function
+from itertools import accumulate # Python3 only
+
+def combos(sides, n):
+    ret = [1] + [0]*(n + 1)*sides # extra length for negative indices
+    for p in range(1, n + 1):
+        rolling_sum = 0
+        for i in range(p*sides, p - 1, -1):
+            rolling_sum += ret[i - sides] - ret[i]
+            ret[i] = rolling_sum
+        ret[p - 1] = 0
+    return ret
+
+def winning(d1, n1, d2, n2):
+    c1, c2 = combos(d1, n1), combos(d2, n2)
+    ac = list(accumulate(c2 + [0]*(len(c1) - len(c2))))
+
+    return sum(v*a for  v,a in zip(c1[1:], ac)) / (ac[-1]*sum(c1))
+
+
+print(winning(4, 9, 6, 6))
+print(winning(5, 10, 6, 7))
+
+#print(winning(6, 700, 8, 540))