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
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?