Two gamblers, A and B, bet on the outcomes of successive flips of a coin. On each flip, if the coin comes up heads, A collects from B one unit, whereas if it comes up tails, A pays to B one unit. They continue to do this until one of them runs out of money. If it is assumed that the successive flips of the coin are independent and each flip results in a head with probability p, what is the probability that A winds up with all the money if A starts with i units and B starts with Ni units?