In a board game, players roll a six-sided die to advance on a path. The path has 30 spaces, and players win by reaching or exceeding the 30th space. Players start on space 1. If a player rolls an even number, they move forward by that number of spaces. If they roll an odd number, they move back by that number of spaces unless they are already on space 1, in which case they stay on space 1. What is the probability that a player will win the game within their first 10 rolls? Let's think step by step and output the final answer within \boxed{}.
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