1. ## Coin flip explanation

Hi, I have been wondering about a probability question.

Suppose you have a 50% chance of winning \$1 when you flip a coin. You also have a 50% chance of losing \$1 when you flip a coin. You keep flipping the coin as many times as necessary until someone is up \$5 or someone is down \$5. What is your probability of winning \$5 dollars, what is your probability of losing \$5. I feel like the obvious answer is 0.5. However, I am interested in the way to actually prove this answer is correct or show it is correct with math. Can anyone please help? Thanks!

Also, what is your probability of winning \$5 in the same situation, except you have 51% chance of winning the flip and a 49% chance of losing the flip. Thank you so much in advance!

2. ## Re: Coin flip explanation

Before we discuss in details, I suggest you to have some basic readings on Markov Chain, Random walk and Gambler Ruin's problem first. See, e.g.

https://en.wikipedia.org/wiki/Gambler%27s_ruin

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