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?
What's the probability of losing a coin tossing gambling with a wealthy man?
2
$\begingroup$
probability
-
0The probability is $1$. – 2012-10-06
2 Answers
1
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.
-
0Which is 1-((1-p)/p)^g where g is Gambler's initial fortune and p>.5 is the probability that Gambler wins a single toss. – 2012-10-06
1
The probability is $1$. This is the gambler’s ruin problem, and see also one-dimensional random walks.