## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# Bet you a dollar

Senior Member

• Members
• 1828 posts
• Gender:Female

Posted 21 October 2013 - 10:26 PM

Starting with 0 dollars, you repeatedly flip a fair coin, earning \$1 each time heads appears, and losing \$1 each time tails appears. When your net cash reaches either A or -B, you stop gambling.

As a function of A and B, compute the expected number of flips until the game stops.

Now consider the unstopped version of this process, in which you gamble indefinitely regardless of your current profit or debt. Prove that the expected time till your net cash is +\$1 is infinite. Likewise, the expected time till your net cash is -\$1 is also infinite.

note that one of these two events must occur upon the first coin flip!

• 0

### #2 phil1882

phil1882

Senior Member

• Members
• 560 posts

Posted 23 October 2013 - 05:04 AM

Spoiler for false

• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users