Hi,

I read this interesting article: http://people.math.gatech.edu/~shenk/OptionsClub/kellyOptionTalk1.pdf

where a coin parlor game that pays 2x your bet when you win, and -1x has an optimal bet of 1/4 of your bank role. I tried replicating this with Python, but my results, don't match the theory.

My approach is this. I test bet ratios from 0% to 99% of my bank roll. Then for each bet ratio, I generate N simulations, where for each simulation, I flip the coin N times. Below In my set up, heads is a win which pays 2x the bet, and tails is a loss which pays -1x the bet. According to the document above, the ideal bet is .25. My distrubtion say .6x.

Could someone see where my Python code is astray?

I read this interesting article: http://people.math.gatech.edu/~shenk/OptionsClub/kellyOptionTalk1.pdf

where a coin parlor game that pays 2x your bet when you win, and -1x has an optimal bet of 1/4 of your bank role. I tried replicating this with Python, but my results, don't match the theory.

My approach is this. I test bet ratios from 0% to 99% of my bank roll. Then for each bet ratio, I generate N simulations, where for each simulation, I flip the coin N times. Below In my set up, heads is a win which pays 2x the bet, and tails is a loss which pays -1x the bet. According to the document above, the ideal bet is .25. My distrubtion say .6x.

Could someone see where my Python code is astray?

Python:

```
import random
import matplotlib.pyplot as plt
import pandas as pd
#this program simulates a parlor coin game. You flip a coin N times. You always pick Heads. If you bet heads and win
#your return is 2x your bet. If you bet heads and lose, you lost your bet (not double your bet)
coin_value = ['H','T']
simulations = 100 #number of simulations of the N coin toss game
coin_tosses = 100 #number of times you flip a coin per simulation
game_result = []
for x in range(0,100): #i loop through bet percentages.
bet_size = (x/100) #set the bet percentage
for sim in range(0, simulations): #we run N simulations, which play N coin tosses per simulation
bank_roll = 100 #starting bank roll for each simulation
for coin_toss in range(0, coin_tosses): #we toss the coin N times
outcome = random.choice(coin_value)
if outcome == 'H': #if Heads, you win.
profit_loss = 2 * (bet_size * bank_roll) #Double your bet and add that to bankroll
result = 'W'
elif outcome == 'T': #if tails you lose.
profit_loss = -(bet_size * bank_roll) #Loss your bet and add that to bankroll
result = 'L'
bank_roll = bank_roll + profit_loss
#below I create a dataframe which has columns below
game_result.append([bet_size, result, bank_roll, sim, coin_toss])
df = pd.DataFrame(game_result, columns = ['Bet_Size','result','Bankroll', 'sim', 'coin_toss'])
df = df[df['coin_toss'] == (coin_tosses - 1)] #this selects the last coin toss for each simulation. Effectively, this
#is your ending balance after N coin tosses.
x = df.groupby(['Bet_Size'])['Bankroll'].mean() #calculated E[V] by bet size by averaging the simulations based on
#bet size
```