Imagine you have $k$ dollars in your pocket and you are gambling with a wealthy man (with infinitely much money). The rule is repeatedly tossing a coin and you win $\$1$ if it's a head, otherwise you lose $\$1$. Now, what's the probability that you get broke eventually?
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This is a very common question in stochastic processes known as Gambler's ruin problem.
the answer is :If coin is fair,gambler will go broke with probability $1$.
Also it should be noted that if the coin is biased,i.e, probability of gambler winning is greater that $0.5$, then there is strictly positive probabilty that Gambler is never broke.