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Message: [QUOTE="primrose, post: 7181068, member: 1036998"] In discussion on Poker Bankroll, people often cite a "risk of ruin", which presumably is the chance that, following these instructions, you eventually lose your entire bankroll. E.g., Jonathan Little has [URL='https://pokercoaching.com/blog/the-bankroll-bible/']this article[/URL] where he recommands a certain number of BBs (depending on your winrate) and then adds that But what does a 3% chance to go broke mean? I can think of two very different interpretations of what it could mean: [LIST=1] [*]If you play with this starting bankroll and then literally never touch the bankroll for the rest of your life, then the chance of it hitting 0 if you play forever is 3%. (Note that in this case, if you start with 3000BB, you will probably have 10.000BB eventually; your bankroll grows indefinitely) [*]If you use poker for income, so you deduct winnings from your bankroll, [I]but only ever do it if you're above the recommended amount [/I](so if you start with 3000BB, you only ever take out money if you're currently above 3000BB, and if you're below, you keep playing until you're back at 3000BB), then over the course of a lifetime, there's a 3% chance of hitting 0. [/LIST] These two interpretations are completely different! The first is a well-defined and studied math problem (see e.g. [URL='https://en.wikipedia.org/wiki/Gambler%27s_ruin#Unfair_coin_flipping']here[/URL], it's not exactly the same because poker isn't like flipping a single biased coin repeatedly, but it's pretty close), whereas the second one isn't well-defined because it depends on how long you're playing. The second one also gives you a theoretical 100% risk of ruin if you played for an infinite amount of time. (Essentially each year has the same chance to be a catastrophic downswing, so if you keep adding years, you keep increasing the risk.) So the first is easier to calculate, but the second is clearly more relevant to real players. So, which is it? Which of those two do people mean when they say "risk of ruin"? I've asked Claude (the LLM) and it claimed that poker players just use the term inconsistently. I hope that's not true. I've never read a proper book that discussed bankroll in depth, so maybe at least some good authors are precise? [/QUOTE]

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