## Plot the winnings of a simple H&T game
## where you win or lose 1 penny each time
n <- 1000
ev <- sample(c(1,-1), n, replace=T)
winnings <- cumsum(ev);
plot(winnings, type='l')


## Count the number of games during which
## the winnings exceed 5 pennies
ngames <- 10
goalAchieved <- vector(length=ngames)
for(k in 1:ngames) {
  winnings <- cumsum(sample(c(1,-1), n, replace=T))
  goalAchieved[k] <- any(winnings>=5)
}
timesGoalAchieved <- length(which(goalAchieved))
probGoalAchieved <- timesGoalAchieved / ngames