# What's the probability of losing a coin tossing gambling with a wealthy man?

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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–  Ragib Zaman Oct 6 '12 at 7:18
The probability is $1$. –  Rasmus Oct 6 '12 at 7:19

The probability is $1$. This is the gambler’s ruin problem, and see also one-dimensional random walks.
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.