coin

from random import randint
"""
Written by Nick Bowling

I made this simulation based on just 3 simple equations:

l-d = b
b/l = p
k = m * (2*p - 1)

Where:
      l = length of boundary space in one dimension
      d = diameter of circular object in one dimension
      b = length of space where center of circular object can
          exist, in one dimension, without crossing the boundary space
      p = probability that circular object will randomly appear without
          crossing the boundary space
      m = your current betting bankroll
      k = Kelly equation, used to compute the amount of your bankroll you
          should bet to maximize your return in a long term, multiple,
          betting situation
"""

#Initial Parameters:

              # length of each side of hypercube is 10
              # length of diameter of hypersphere is 4

              # Volume of hypercube = 10^4
              # Volume of hypersphere's hypercube boundary = 4^4

inside = []   # Volume where center of hypersphere can exist while
              # keeping hypersphere in bounds of hypercube = 10^4-4^4 = 6^4

outside = []  # Volume where center of hypersphere can exist where
              # edge of hypersphere crosses boundary of hypercube = 10^4-6^4


              # Ratio of center inside volume to hypercube volume is 6^4/10^4 = 81/625
              # Probability that hypersphere will not cross boundary of hypercube is p = 12.96%


coin_in = 0
coin_out = 0
money = 0
count = 0
for i in range(1, 82):  # Produces number list for volumes
    inside.append(i)
for i in range(82, 626):
    outside.append(i)
def coin(z):
    global count
    global coin_in
    global coin_out
    global money
    money = float(bank_roll)
    wager = money * (2 * 0.8704 - 1)   # 2*(1-p)-1 <--Kelly equation betting that hypersphere
                                       # will cross hypercube boundary
    for i in range(int(z)):
        count += 1
        wager = money * (2 * 0.8704 - 1)
        x = randint(1, 625)  # Creates random placement of center of hypersphere inside
        if x in inside:      # hypercube
            coin_in += 1
            money -= wager
        elif x in outside:
            coin_out += 1
            money += wager  # Makes a bet that hypersphere WILL cross boundary of hypercube
        if money < 0:
            break

print()
print()
print('This program will simulate a 4^4 hypersphere randomly appearing in a 10^4')
print('hypercube space, while you bet, in succession, a Kelly amount of your bankroll that the')
print('hypersphere will cross the boundary of the hypercube space.')
print()
print()
z = input('Number of simulations to run: ')
print()
bank_roll = input('How much money do you have to bet with?: $')
wager1 = float(bank_roll) * 0.7408  # Initial Kelly value based on probability
print()
print('Based on the Kelly Criterion you should initially wager 74.08% of your bankroll, which '
      'is $', float(wager1))
print()
print()
coin(z)
print('Simulations: ', count)  # Number of simulations
print('Hypersphere inside boundary (lose) :', coin_in)  # Number of times hypersphere in bounds of hypercube
print('Hypersphere crossed boundary (win) :', coin_out)  # Number of times hypersphere crossed boundary of hypercube
money = int(money)
print('Bankroll : $', money)  # Your current bankroll