the coin is returned with an additional $1 coin, otherwise the original coin is

lost. The probability of winning is 1/2 unless the previous play has resulted

in a win, in which case the probability is p < 1/2. If the cost of maintaining

the machine averages $c per play (with c < 1/3), give conditions on the value

of p that the owner of the machine must arrange in order to make a prot in

the long run.