#puzzle38

Charlie wants to buy a car for 2C dollars, but he only has x < 2C dollars. He decides to play a gambling game in the hopes of raising his money to 2C. The rules are as follows:

Charlie 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.

Charlie bets all his money if he has less than C, otherwise he bets enough to make his total up to exactly 2C if he wins.

Determine the probability that Charlie reaches 2C before going bankrupt, as a function of x.