billionaire.py

# project euler #267
# You are given a unique investment opportunity.

# Starting with £1 of capital, you can choose a fixed proportion, f, of your capital to bet 
# on a fair coin toss repeatedly for 1000 tosses.

# Your return is double your bet for heads and you lose your bet for tails.

# For example, if f = 1/4, for the first toss you bet £0.25, and if heads comes up 
# you win £0.5 and so then have £1.5. You then bet £0.375 and if the second toss is tails, 
# you have £1.125.

# Choosing f to maximize your chances of having at least £1,000,000,000 after 1,000 flips, what is 
# the chance that you become a billionaire?

# All computations are assumed to be exact (no rounding), but give your answer rounded to 12 digits 
# behind the decimal point in the form 0.abcdefghijkl.

from fractions import *
from decimal import *
import random

def gamble():
	acct = Decimal('1')
	rounds = 10000
	proportion = Decimal('0.5')

	for i in range(rounds):
		if random.choice([True, False]):
			acct += (acct * proportion) * 2
			print(f"acct after win: {acct}")
		else:
			acct -= (acct * proportion)
			print(f"acct after loss: {acct}")

	print(acct)

# gamble()

# well, by tweaking the number, it's easy to see that you don't bet more than half, which makes sense.
# I assume the next is to simlify this into a particular probability.