Let's consider this simple dice game: A coin is faked so it has p
chance to land on heads, and 1-p
chance to land on tails. Every round costs 1
, and gives you 2
if you win (for a total of +1
).
Assume you're starting with n
. What are your odds to "go infinite" - be able to play the game forever? This sounds like Markov Chains 101, it's just been ages since I read anything about Markov Chains.
Also - given any constant m
, what are the odds of ever reaching $m
in this game?