### An Easy One This Week

Remy wants to buy a car for *C* pounds, but he only has *x* < *C* pounds. He decides to play a gambling game in the hopes of raising his money to *C* pounds. The rules are as follows:

Remy chooses how much to pay, then *n* fair dice are thrown. If the sum is even then he gets double his money back, if it is odd he gets nothing. He can play as many times as he likes.

Remy bets all his money if he has less than half of *C*, otherwise he bets enough to make his total up to exactly *C* if he wins.

Determine *f*(*x*), the probability that he reaches *C* before going bankrupt.