# Gambling With Rich Friends

Yudhisthira is a habitual gambler and gambles at every opportunity he can find. One day, he enters in a casino with 1 rupee in his pocket and starts betting. At each bet, he is likely to win 1 rupee with probability $$0.1$$ and likely to lose 1 rupee with probability $$0.9$$. Yudhisthira also has a super-supportive rich friend, Krishna, who always provides with 1 rupee to keep him betting whenever Yudhisthira's total earning becomes zero.

What is the probability that Yudhisthira will eventually earn 1 million rupees from the gambling?

Note: If $$q_t$$ denotes the amount of money that Yudhisthira's has after $$t$$ bets, we have $q_{t+1}= \max(1,q_t+G_t),$ where $$G_t$$ is an independent random variable where $$G_t=+1$$ with probability $$0.1$$ and $$G_t=-1$$ with probability $$0.9$$.

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