## ================================ SETUP ================================
##
## I play a game against an infinitely rich opponent.  I have MONEY=10
## pennies at the beginning of the game.
##
## The game consists in tossing a coin NTRIALS=100 times.  If the outcome
## of an individual toss is "heads" I get one penny from the opponent.
## If the outcome is "tails", I have to pay my opponent 1 penny.
## 
## What is the probability that I become broke?
##
## To get an accurate estimate, I use NREPS=10 repetitions of the game
## (you may think of a repetition as a separate game).
##
##========================================================================


## Number of repetitions
nreps <- 100
## Number of trials, i.e. coin tosses in a single game
ntrials <- 1000
## The amount of money I start with
money <- 10
s <- vector(length=nreps)
for(i in 1:nreps) {
  s[i] <- min(cumsum(sample(c(1,-1), ntrials,replace=T)))
};
print(length(which(s<= -money))/nreps)