Problem 121

Problem 121/Problem 121.py

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+from fractions import Fraction
+from math import ceil
+
+def prob_of_win(discs, last_probability, blues_selected, n):
+    #Chance of blue is 1 / discs
+    #Multiply by the last probabilty as events are independent as we replace
+
+    #Taken n discs out
+    if discs == n + 1:
+        #They have won if over half are blue
+        if blues_selected > n // 2:
+            return last_probability
+
+        #Otherwise this branch was a loss
+        return 0
+
+    #Put another disc in
+    discs += 1
+
+    #Pick a blue
+    blues_selected += 1
+    #P(blue) = 1 / discs
+    blue_last = last_probability * Fraction(1, discs)
+
+    #Pick a red, P(red) = (discs - 1) / discs
+    red_last = last_probability * Fraction(discs - 1, discs)
+
+    #Recursively calculate the probability of winning until they reach the maximum number of discs
+    return prob_of_win(discs, blue_last, blues_selected, n) + prob_of_win(discs, red_last, blues_selected - 1, n)
+
+def solve(turns):
+    prob = prob_of_win(1, 1, 0, turns)
+    #P(wins) = 1/x then x = expected number of times to play before winning
+    #So 1/P(wins) = x so x - 1 is should be the maximum prize pool to at least break even
+    print("After", turns, "turns, the chance of winning is:", prob, "which is", round(float(prob * 100), 4), "%")
+    print("The maximum prize fund should be: £", ceil(prob ** -1) - 1, sep = '')
+
+solve(15)
+