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Whichever poker format is your favourite, if you want to grow as a player and develop your poker career, you need to understand variance's influence on your winnings and, subsequently, how you should approach your bankroll management.
Variance is a word that frightens many poker players. We can’t blame them, as whenever the bad run gets you, it feels like there’s not much you can do about it. But is such a situation really so hopeless? Let's find out.
The first step to minimizing the negative influence of variance on your winnings and mental state is understanding how it works. Therefore, in this article, we’ll look at how bad (or good) you can expect to run when playing PLO, what you should be prepared for, and how big your poker bankroll should be.
Why and when do we talk about variance in poker?
Variance is a phrase derived from statistics, and in simple terms, it measures how far a set of numbers is spread out from their average value. When it comes to poker, variance describes how lucky or unlucky you can get under certain conditions.
The most practical use of variance in poker is estimating the possible outcomes of playing a set number of hands (in cash games) or tournaments. Knowing how much money you can win or lose playing your regular games allows you to decide how big your poker bankroll should be so you can play comfortably without fear of bankruptcy.
Be aware that the human mind has trouble comprehending many probability-related issues. Due to our natural tendencies, we fall prey to various cognitive biases. As a result, we often underestimate or overestimate the influence of luck on the results of our actions, especially when we talk about poker.
How do we combat these difficulties with understanding how variance works? With the help of poker tools. One such tool is a primedope's Poker Variance Calculator. It allows you to simulate the possible outcomes of your plays under specific circumstances. With the help of the Variance Calculator, you can study various potential dependences, such as how your win rate, the number of hands you play, and the format you choose influence each other.
Let’s dive deeper and see what the range of possible outcomes is.
Firstly, to get results to analyze, you need to input a few variables: your assumed win rate in BB/100 hands (if your poker room allows hand tracking, you’ll find your win rate in your tracking software - Hold'em Manager or Poker Tracker), observed win rate (which you can omit), standard deviation (it’s another term from statistics; there are a few predefined values to choose from) and the number of hands to simulate.
Let’s see the results for the assumed win rate of 5 BB/100 hands, with a standard deviation set to 140 after 10,000 hands.
How do we study this data? The graph above shows the results of 20 theoretical samples, covering different possible outcomes.
The light blue line shows the best possible outcome; in our case, it’d be winning roughly 5,400 Big Blind (which equals 54 stacks, an insane result for 10k hands if you think about it). The brown line refers to the worst possible outcome, which equals minus 4,100 BBs. The dark green lines represent the 95% interval, meaning that 95% of the time, your results will be in this range. In our case, they span from plus 2,300 BB and minus 1,900 BB. Lastly, the light green lines represent the 70% interval, which analogically means that 70% of the time, your results will fall into this area (plus 1,900 BB and minus 900 BB).
You can find all of these (with some additional information) in the chart below.
The two most important pieces of information in the table are the probability of loss after a set number of hands and the minimum bankroll to avoid bankruptcy. In our case, that’s 36% and 5,872 BBs, respectively.
How do we interpret those numbers? These results, as with many things in poker, are very contextual. The best way to get a better understanding of how variance works is by running the same simulation with a different set of data. In other words, toy with those values yourself and determine how the results change if your win rate gets higher or lower. What about simulating 5, 10 or 25 as many hands?
After running a few different simulations, it will be much easier to estimate how big your swings can be, what to expect when playing a certain amount of hands, and how big your bankroll should be.
What sample size should you choose considering Pot Limit Omaha?
It heavily depends on a few variables that differ from player to player. How many hands do you play daily, weekly, or monthly?
Being a winning player means little when it comes to small sample sizes. We strongly recommend running simulations with 100k+ hands to get reliable results. To get a better perspective, after changing 10k hands to 100k hands (leaving other input unchanged), the probability of loss drops from 36% to 13%, and when set to 500k hands, you will lose money in only 0.6% of cases.
Summarizing this part, Pot Limit Omaha is a game in which variance significantly influences your results. Working with the Variance Calculator will help you better understand how "luck" can influence you in PLO.
How can you take advantage of all of this data?
A few things to consider for every aspiring poker player are their playing routines.
How much time a week do you spend playing?
Are you a player that focuses on quality or quantity?
How many tables do you play at once?
Many players try to play as many tables as possible, but that reflects their win rate.
If player A (let’s call him Daniel) plays only four tables with a win rate of 10BB/100 and 50k hands per month, he can expect to win as much as player B (Phil), who plays twice as many hands (100k) on twice as many tables (8) with only half as much of a win rate (5BB/100).
While the result may be the same, the overall experience will differ for both players. Phil is much more likely to play in a so-called autopilot mode with much less time to think about the present hands, facing multiple decisions simultaneously. On the other hand, Daniel plays in a less stressful environment; he has more time to think about his choices and can apply new concepts while thinking about his opponent's tendencies.
What might be surprising for some is that Daniel is much less threatened by bankruptcy (around 5.5% assuming 50k hands with a 10BB/100 win rate) than Phil (around 13% assuming 100k hands with a 5BB/100 rate) despite having the same expected winnings of 5,000 BB. At the same time, achieving a higher win rate keeps Daniel’s mindset healthier and makes the game feel like less of a grind, while Phil will likely play more to pursue the winnings he expects to achieve.
So, what bankroll is suitable for you to play PLO?
The beauties of poker formats lie in the intricacies and nuances which result in a lack of one-size-fits-all solutions. Putting their play patterns aside, what will work for Daniel won’t necessarily work for Phil and vice versa. With that in mind, how should you perceive your bankroll management when playing Pot Limit Omaha?
In our opinion, the best (and by that, we mean conservative) starting point is the 100 buy-in per limit rule. It assumes that you start with a 100 BI (i.e. $1,000 for PLO10) and move up when you achieve 100 BI on the higher limit (i.e. $2,500 for PLO25). After some time, you’ll find out what works best for you and whether you should keep even stricter bankroll management or you can play your best game with only 50BI.
Whatever your opinion on this topic is, it always helps to find out what other poker players take. The PLO Genius discord is a great place to do so, where you can find other PLO community members striving to improve!