# 
# A function to calculate ruin probabilities.
# Function illusttrate  the ifelse flow control structure.
# It considers the case of the fair coin toss separately 
# from the biased coin toss.
# It contains no error checking, say to test that 
# p is between 0 and 1, but this you can add with more "if statements."
#


# win(p, A, B)
#
# The probability of winning A dollars before losing B dollars given that you 
# have a probability of winning of p on each round of betting.

win<-function(p, A, B){
if (p==0.5) return(B/(A+B))
else {
q=1-p;
N=(q/p)^(B)-1;
D=(q/p)^(A+B)-1;
return(N/D)}
}

# Incidentally there are some things you might want to explore 
# using this code. For example, what happned if you let p be very close to 0.5
# do you recover the simpler formula for ruin in a fair game?