What Actually is Risk of Ruin?

primrose

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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 this article where he recommands a certain number of BBs (depending on your winrate) and then adds that

Playing with these numbers will give you a 3% chance to go broke.

But what does a 3% chance to go broke mean? I can think of two very different interpretations of what it could mean:

  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)
  2. If you use poker for income, so you deduct winnings from your bankroll, but only ever do it if you're above the recommended amount (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.
These two interpretations are completely different! The first is a well-defined and studied math problem (see e.g. here, 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?
 
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fundiver199

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"Risk of Ruin" in BRM terms is under the assumption, that you dont withdraw money from your poker bankroll, and that you also continue playing the same game with the same winrate indefinitely. For people, who depends on poker income to pay their bills, this is very far from their actual situation. If their monthly spending is higher than their average monthly winnings from poker, then the "Risk of Ruin" is obviously 100%, unless they manage to change either side of the equation, before its to late. Presumably this is part of the reason, why there are so many professional poker players, who end up going broke, being in debt etc.
 
Goggelheimer

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Here is what "gemini" says about Risk of Ruin and going broke.


What is Risk of Ruin in Bankroll or Poker Bankroll Management







In poker and bankroll management, the Risk of Ruin (RoR) is a statistical measure of the probability that a player will lose their entire bankroll. It's a critical concept for anyone who takes poker seriously, as it helps them understand the financial risk they are taking and how to mitigate it.


Even a skilled, winning player can experience a series of losing sessions (a "downswing") due to the inherent element of luck and variance in poker. Risk of Ruin quantifies the likelihood that such a downswing will completely deplete a player's designated poker funds, forcing them to stop playing.



Key Factors Affecting Risk of Ruin​


The Risk of Ruin is not a fixed number; it's a dynamic probability that depends on several key factors:
  1. Bankroll Size: This is the total amount of money a player has set aside specifically for poker. A larger bankroll acts as a cushion against losing streaks. The smaller your bankroll relative to the stakes you are playing, the higher your risk of ruin.




  2. Win Rate (Edge): This is a measure of a player's profitability over the long term. In poker, it's often expressed in terms of big blinds per 100 hands (BB/100). A higher win rate means a player has a larger skill advantage over their opponents, which significantly reduces the risk of ruin. A player with a negative win rate (a losing player) has a 100% risk of ruin over the long run, regardless of their bankroll size.


  3. Variance (Standard Deviation): This measures the volatility of a player's results. Higher variance means a greater likelihood of wild swings in fortune, both up and down. Some game types, like tournaments, have much higher variance than cash games, and therefore require a larger bankroll to maintain a similar risk of ruin.




  4. Stakes Played: The size of the bets you are playing is a direct factor. Playing at stakes that are too high for your bankroll dramatically increases your risk of ruin. This is why a core tenet of bankroll management is to move down in stakes if your bankroll shrinks.



How to Mitigate Risk of Ruin​


The primary purpose of understanding RoR is to manage it effectively. Here are the core strategies:
  • Proper Bankroll Management: This is the most crucial defense. It involves setting strict rules for the amount of money you risk at any one time. Common guidelines include having a certain number of buy-ins for the stakes you play (e.g., 20-40 buy-ins for cash games or 100-200 for tournaments).




  • Game Selection: Choose games where you have a clear skill advantage over your opponents. Playing against weaker players will increase your win rate and lower your variance.
  • Improving Your Skill: The better you are at poker, the higher your win rate will be. This is the most effective way to permanently lower your risk of ruin.


  • Tracking Your Results: Keeping detailed records of your play (hands played, winnings/losses, and standard deviation) allows you to accurately calculate your win rate and variance, giving you a better understanding of your true risk. Many poker tracking software tools and online calculators can help with this.


In essence, the Risk of Ruin is a mathematical concept that explains why even a skilled player needs a well-managed bankroll. It highlights the importance of being financially disciplined to survive the inevitable downswings and ensure long-term profitability.











What does going broke in poker terms mean?



Option A
In poker, the term "going broke" has a very specific and often harsh meaning: it refers to the situation where a player has lost their entire poker bankroll.
It's not just about losing money; it's about losing all the money you have designated for poker, to the point where you no longer have the funds to play at your desired stakes.
Here's a breakdown of what "going broke" in poker terms entails:
  • Loss of the Bankroll: This is the core of the definition. Your bankroll is the money you have set aside specifically for playing poker. When you go broke, that bankroll is completely depleted, leaving you with zero funds for poker.
  • The End of the Road (for now): For a serious or professional player, going broke means they can no longer play poker for a living or as a significant source of income. They are "out of the game" until they can either save up more money to rebuild a bankroll or find a backer (an investor who provides the money for them to play).
  • A Consequence of Poor Bankroll Management: While a bad run of luck (known as a downswing or high variance) can be a contributing factor, the primary reason a winning player goes broke is almost always due to poor bankroll management. This means they were playing at stakes that were too high for the size of their bankroll, leaving them vulnerable to a losing streak.
  • "Down to the Felt": A related poker slang term is "down to the felt," which literally means you have lost all your chips and all your money on the table, leaving you with nothing but the felt of the poker table in front of you. This is the ultimate symbol of going broke.

Going Broke vs. Losing a Session​


It's important to distinguish between "going broke" and simply losing a session.
  • Losing a session is a normal part of poker. Even the best players have losing days, weeks, or even months. As long as they have an adequate bankroll, these losses are just temporary fluctuations that they can recover from.
  • Going broke is the failure to manage those fluctuations. It means you have failed to protect your bankroll, and now you have no more money to play with.
In short, "going broke" is the worst-case scenario in poker bankroll management. It's the point where the inherent risks of the game, combined with a lack of financial discipline, lead to a total and often career-ending loss of poker funds.



Option B
In poker terms, "going broke" means a player has lost their entire bankroll and therefore no longer has the funds to play at their current stakes, or sometimes, at any stakes at all.
It is the ultimate failure in bankroll management and signifies a complete depletion of the money that was set aside specifically for playing poker.
Here's a breakdown of what it implies:
  1. Losing the Poker Bankroll: It means the player's designated poker funds have been reduced to zero or so close to zero that they can no longer afford the minimum buy-in for the games they were playing.
  2. Forced Hiatus: The player must stop playing immediately, or dramatically move down to much lower stakes (often called "micro stakes") to try and rebuild.
  3. The Result of Poor Management or High Variance: While even a skilled player can "run bad" due to high variance and experience massive downswings, going entirely broke is most often the direct result of poor bankroll management (e.g., playing stakes that are too high for their bankroll) or a negative long-term win rate (i.e., they are a losing player).
  4. Down to the Felt: A related slang term is being "down to the felt," which means a player has lost all their chips in the current session and has no more cash to buy back in. "Going broke" is the more general, long-term state of this condition.
In essence, "going broke" is the realization of the Risk of Ruin (RoR), where the probability of losing the entire bankroll becomes reality. It's a professional setback that every serious poker player works hard to avoid through strict financial discipline.
 
eberetta1

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You summed that up pretty nicely fundiver199
 
primrose

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"Risk of Ruin" in BRM terms is under the assumption, that you dont withdraw money from your poker bankroll, and that you also continue playing the same game with the same winrate indefinitely. For people, who depends on poker income to pay their bills, this is very far from their actual situation. If their monthly spending is higher than their average monthly winnings from poker, then the "Risk of Ruin" is obviously 100%, unless they manage to change either side of the equation, before its to late. Presumably this is part of the reason, why there are so many professional poker players, who end up going broke, being in debt etc.
It's much worse than that though because even if you do it the way I describe in #2 (i.e. never withdraw too much) it's still not the same as #1. So even if you do everything right and have manageable expenses, it would just flat out be the wrong number. It's what happens with an ever-increasing rather than a capped bankroll, it just computes the wrong thing.

I hope that you're either not correct that this is standard usage or that good guides also calculate it the other way. Otherwise it's just misleading.
 
primrose

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"hey here's your risk of ruin. It doesn't represent the risk that you end up ruined and doesn't even upper bound it, but it's 3%. Ok glhf :sneaky:"
 
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