topspin
03-17-2005, 06:39 PM
Any math majors that might be able to help me out?
I was reading this post (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=micro&Number=1935848) the other day, and I got to thinking that given a starting bankroll and a goal of reaching X BB, you should be able to approximate the probability of busting out before reaching your goal by a random walk with two thresholds.
Specifically, if we start at 0BB, play poker with win rate mu and variance var per hand, what is the probability that we reach alpha BB without reaching beta BB first, where alpha > 0 while beta < 0?
I tried setting this up using the first two derivatives of Wald's Identity evaluated at zero, which gave me an equation in terms of the relevant quantities that I could solve numerically. My numbers seemed a bit wonky though. Can anyone point me towards a solution, or explain how to calculate this?
I was reading this post (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=micro&Number=1935848) the other day, and I got to thinking that given a starting bankroll and a goal of reaching X BB, you should be able to approximate the probability of busting out before reaching your goal by a random walk with two thresholds.
Specifically, if we start at 0BB, play poker with win rate mu and variance var per hand, what is the probability that we reach alpha BB without reaching beta BB first, where alpha > 0 while beta < 0?
I tried setting this up using the first two derivatives of Wald's Identity evaluated at zero, which gave me an equation in terms of the relevant quantities that I could solve numerically. My numbers seemed a bit wonky though. Can anyone point me towards a solution, or explain how to calculate this?