lotto.py

#############################################################
# lotto.py
#############################################################
# Description: Compare avg return of 2018-10-23
# mega million lottery compared to number of tickets bought.
# Note: this script doesn't appear to implement the correct 
# behavior for doing so. I think my math is off. Oh well, it
# was fun trying.
#############################################################

import np
import matplotlib.pyplot as plt
import matplotlib as mpl
mpl.use('Agg')

# earnings, 1: odds
odds = [
  [1.6e9,   302526350],
  [1e6,      12607306],
  [1e4,        931001],
  [1e2,         38792],
  [2e2,         14547],
  [10,            606],
  [10,            693],
  [4,              89],
  [2,              37],
]

# multiplier, 1: odds
mpOdds = [
  [2, 3],
  [3, 2.5],
  [4, 5],
  [5, 15],
]

# normal, multiplier
cost = [2, 3]
def initChances(odds, n):
  chances = []
  for odd in odds:
    weight = odd[0]
    ratio = odd[1]
    chance = np.true_divide(np.longdouble(n), np.longdouble(ratio))
    chances.append([weight, chance])
    # verify precision, if you'd like
    # print ratio * chance + "~= 1"
  return chances  

def weightedAvg(chances):
  avgs = []
  for odd in chances:
    weight = odd[0]
    chance = odd[1]
    avg = np.multiply(weight, chance)
    avgs.append(avg)
  return avgs

def multiplierAvgs(avgs, mpOdds):
  mpAvgs = []
  for winnings in avgs:
    wAvg = 0
    for mpOdd in mpOdds:
      multiplier = mpOdd[0]
      ratio = mpOdd[1]
      chance = np.true_divide(np.longdouble(1), np.longdouble(ratio))
      wOdd = np.multiply(multiplier, winnings)
      wAvgReturn = np.multiply(chance, wOdd)
      wAvg += wAvgReturn
    mpAvgs.append(wAvg)
  return mpAvgs

def normalRet(odds, numTickets, cost):
  chances = initChances(odds, numTickets)
  avgs = weightedAvg(chances)
  avgRet = np.sum(avgs)
  gross = avgRet - cost
  return gross
      
def multRet(odds, mpOdds, numTickets, cost):
  chances = initChances(odds, numTickets)
  avgs = weightedAvg(chances)
  jackpotAvgs = avgs[0:1]
  restAvgs = avgs[1:]
  mpAvgs = multiplierAvgs(restAvgs, mpOdds)
  multAvgs = jackpotAvgs + mpAvgs
  avgMulRet = np.sum(multAvgs)
  multGross = avgMulRet - cost
  return multGross

# return avg return in general
def avgReturn(x, cost, odds, mpOdds):
  return x*multRet(odds, mpOdds, x, cost)

# get avgReturn for normal ticket
def normal(x):
  return avgReturn(x, 2, odds, [[1,1]])

# get avgReturn for multi ticket
def multi(x):
  return avgReturn(x, 3, odds, mpOdds)


fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111)
  
# total num tickets
N = 302526350
N = 40
r = range(1, N+1)
cost = [2*n for n in r]
ret = [normal(n) for n in r]
ax.plot(cost, color='r', label='cost')
ax.plot(ret, color='g', label='avg return')
ax.legend()
fig.savefig('graph.png')