How to Use a Poker Variance Calculator

How to Use a Poker Variance Calculator

What is a Poker Variance Calculator?

A poker variance calculator is a tool which allows you to measure the variance, or uncertainty (also referred to as ‘swings’) that you can expect to experience in poker.

This is particularly useful for those who are looking to determine what they can expect to win or lose over a given period, allowing one to make more informed decisions about the minimum bankroll requirements for a given game.

A poker variance calculator also allows you to do things like determine downswing extents (measured in both number of hands and big blinds), probability of loss after a given time period, as well as hourly rate for cash games and return on investment (ROI) for tournaments.

In short, it’s an incredibly powerful tool.

How to Use a Poker Variance Calculator

My goal with the blog is to help you use a poker variance calculator to have better poker bankroll management. In short, you should be extrapolating the data to make inferences about the extent of your downswings so you can ensure you have enough capital to withstand them.

By getting clear on how many hands you’re playing, your ROI and/or win rate and the average tournament field size, you’ll be able to make predictions about the swings you can expect.

In the video below, as well as in this blog, I provide you with the tools you need to use the program to empower you to do this process on your own. You’ll be able to predict things like your longest downswing extent, both in terms of big blinds and hands played. It’s powerful stuff, and when applied appropriately, can help you to build an extremely solid business plan.

That said, it’s a delicate process. Get it wrong and it could the difference between success and failure. I know some of you would like guidance during this process to help ensure you get it right. After all, you’re planning for your poker future and will make big decisions based on these numbers.

I have worked with numerous clients (whose case studies you can read about at the link below) to help them create solid business plans, ensuring they maximize their return and minimize their risk of ruin.

At the end of our time together, you’ll have a solid understanding of the risks involved, be able to withstand any downswings you will face, and even be able to project future earnings so you can plan for your poker future.

To apply to work with me, simply click here.

Poker Variance in Tournament Poker

There were four people left at the final table of the World Poker Tour at the Bellagio: Erik Seidel, Faraz Jaka, Justin Smith and me. Not only was there nearly a $1,000,000 difference between 1st and 4th, there was a bracelet at stake. Let’s be honest, nobody remembers the player who got second.

I found myself all-in with Ace-Queen against the pocket tens of Alexandre Gomez. If I win, I have 70% of the chips in play and practically guaranteed to get top 2; if I bust, I’m out.

I replay that hand in my head, from time-to-time, and always pause at the moment when the dealer taps the table, right before she flips the river card up. I glance one more time at the board: Kc Jc 8h 5c.

“Ace, Queen, Ten, Club,” I hear my section of the rail shouting.
It didn’t come.

It’s been a decade since the river blanked off, but it still feels like yesterday. I don’t compete in tournaments often, so I still haven’t got the chance to rewrite that history with a different result.

The truth is, unless you grind the circuit full time, play small field high-rollers, or, frankly, are on the positive side of variance more than your fair share, you may not either.

It’s something I understood conceptually as a professional, but until I lived it, I couldn’t fully grasp the nature of tournaments, and to a larger extent, poker in general.

It’s not just winning your coin flips, where one experiences the luck. Variance comes in many forms in poker: You may get coolered with the second nuts to the nuts, or your opponent may draw out on you.

But variance also comes in hidden forms: a bad turn card that kills your action; or positional variance, such as getting aces under the gun instead of on the button; or situational variance, by merely being in the right place at the right time to get into a great game, which earns you a fortune.

While these things will, in theory, even out over the long run, poker players, too often, don’t realize just how long that long run is. In the meantime, they go broke in the name of expectation, never reaching the point where their skill trumps the luck.

Just how long does it take?

In a sentence, much longer than you think.

In tournament poker, evening out the variance can take a lifetime or two.
This explains the phenomenon of how the world’s best players can go years without winning a major event. Conversely, there will always be a fortunate few who go on to win multiple events in a short period of time.

Most people will associate this hot streak solely with skill; when, in fact, luck was the principle contributor to someone winning on any given day.

This is not to say that all successful tournament professionals are merely benefactors of good fortune; some are truly phenomenal players. But it’s important to remember that for every one superstar, there are likely 100 players of equal caliber who just haven’t caught the right breaks, never won an event, and thus never had the opportunity to further pursue their tournament career.

This harsh reality doesn’t mean that winners are good, and losers are bad, or that there’s no skill for those who win. It just means that luck supersedes everything else, in the short term, which as you’ll see in a moment, isn’t all that short.

But just when you want to curse your fortune, blaming bad luck for your losses, remember this one thing. Poker is unique in that it’s the most competitively played game where luck plays a significant factor in the final outcome (other sports have variance–the best football team doesn’t always win–but it’s much less significant than in poker).

And thank God for it.

As Phil Hellmuth famously states, “If there were no luck involved, I’d win every time.” Some may question his assurance, but the implications of his idea are telling. No professional truly wishes there were less luck involved. If there were, poker would be like chess and the action would dry up.

You may be thinking I’m exaggerating, and that luck really isn’t as big of a factor as I make it out to be. Well, let’s look at what the math says. I love numbers, because they never lie.

Here is a simple variance calculator program that I use to get a grip on just how profound the role of luck is in poker tournaments.

How to Use a Poker Variance Calculator in Tournaments

Above are the metrics which you can manually input in order to run simulations. I always prefer to be extremely conservative so that I know what to expect, and plan for the worst. After all, this information should be used to manage your bankroll.

My goal was to illustrate the variance a winning professional who plays tournaments regularly can expect to incur.

I estimated that the average tournament has 300 players and that 36 places or 12% of the field were paid. I set the buy in to $500 and the industry standard $30 fee for rake, and gave our hypothetical professional 20% return on investment (ROI), which will put him in the top 1% of poker players worldwide.

(For reference, most experts believe the very best players–maybe 10-20 in the world–have a consistent 100% ROI in large field, soft live poker tournaments. Chris Moorman, the most winning tournament player in online poker history, has a 36% ROI and cashes between 13-17%).

Lastly, I ran a sample size of 10,000 to give us the most accurate results and assumed our professional played 50 major tournaments a year, or one per week.

It’s also important to consider that this is a theoretical ROI, meaning that our professional must be playing his absolute “A-game,” during each-hand-of-each-day-of-each-event, which, as anyone can attest, is a very difficult standard to achieve.

This is all to say, the following sample should get me the best-case scenario for a solid winning pro. Be modest when estimating your own results to ensure you’re planning for the worst case scenario.

How to Use a Poker Variance Calculator in Tournaments

Above is a breakdown of the possibilities one can expect, given the metrics we entered in the poker variance calculator. 

The most important stat is the probability of loss is a staggering 50%!

This means that even our theoretical pro will still lose every other year.

Let’s be honest. As nice as it is to show a profit on any given year, what draws people to tournaments is the glory. Nobody remembers the player who came in second. (Quick: who was the runner-up in the 2014 main event? Or not so long ago, the 2018 main event?)

And if the probability of having a losing year is 50%, you can easily grasp that the probability of actually coming in 1st is a small fraction of that. Run a few standard deviations below average and you’ll go your entire poker career without winning a major live event.

(Despite being some of the best known tournament players in history, Dan Smith, Jason Koon and Isaac Haxton, each with a 10-year or more career of playing live poker still haven’t won a WSOP bracelet).

The confidence intervals (also measured in standard deviations) are the probability that Hero’s results will fall within a given range. A 99.7% confidence interval (3 standard deviations) means that 99.7% of the time our Hero’s results will fall between the given amount, in this case minus $24,250 to plus $88,925.

In other words, it’s virtually impossible, after a year of playing, for Hero’s result to fall outside this range.

As you can see, the variance in tournament poker is insane, which is why I recommend my clients to use caution when allocating money toward tournaments and ensure their bankroll can withstand the inevitable swings they will face.

How to Use a Poker Variance Calculator for Cash Games

In cash games, the variance is reduced dramatically for several reasons:

1. The deeper stack games allow the edges to be much bigger. This is due, in part, because more decisions are made on the river, when there is literally no more luck involved and your equity is either 100% or 0%. Deeper stacks also one has more tools at their disposal, offering more opportunities to outplay their opponents.

2. Stable blind structure doesn’t force the action.

3. You control more of the variables, which leads to bigger long-term profit. Feeling tired after 3 hours? Want to lock up the win? Simply pick up and go as you please.

4. You play more table hours with the same players because there are no table changes, giving better players the chance to gain more information about their opponents, and still have ample time to make adjustments.

5. The game generally plays faster, so more hands per hour means you will reach the long run sooner. For example, fewer people are hollywooding and nobody is stalling to wait for others to bust in order to make the money.

6. Game selection allows you to always ensure you are playing with players who are worse than you. Since you can easily pick up, switch tables, or come back tomorrow, one could always have a significant edge in the games they’re playing.

The numbers speak for themselves. Here’s a sample using PokerDope from the same equivalent pro, and what he can expect after a year of playing live cash games.

How to Use a Poker Variance Calculator in Cash Games

Win rates in cash games are measured in BB/100, or big blinds won per 100 hands.

If you win at 20BB/100 in a $2/$5 game, then you will win $5 x 20 per 100 hands of poker, or $100. I aimed to simulate the equivalent win rate I used for tournaments (using players of the same skill level).

That said, higher win rates are possible. Many pros I know and clients of mine have achieved equivalent or higher win rates for years, playing live poker, up to 40BB/100 and beyond.

Pro Tip: You can easily calculate your hourly rate on the assumption you will play 25 hands per hour. To get an approximate hourly rate, simply divide your BB/100 win rate by 4. In this case, $100/4 = $20 per hour.

More simply, you can add up the total amount won or lost over the course of the year, and then divide it by the number of hours played.

Then, estimate how many hours you play per annum, and multiply that by 25 to get your hands per year. You can use the same standard deviation of 100. As you’ll see from doing the simulations on your own, the variance in cash games is much lower which is why I recommend players allocate their finances accordingly.

The third line, standard deviation, is determined based on one’s playing style. The looser more aggressive style of play will have a higher standard deviation; while, conversely, a more solid, conservative player will have a lower standard deviation.

Since I am always conservative in my estimates, I ran this simulation using a higher than suggested standard deviation of 100 (meaning, our pro is likely to incur the most amount of variance. PrimeDope suggests using 60-80).

Lastly, I estimated that our pro plays a very modest 10,000 hands per year (plays 25 hands per hour x 8 hours per week x 50 weeks per year). Again, I aimed to simulate the opportunity cost between cash games and tournaments, as in the previous example, one who plays 50 tournaments a year will play one per week and average roughly 8 hours of poker.

Here are the results from the poker variance calculator.

How to Use a Poker Variance Calculator in Cash Games

You can see in the screenshot above that the professional’s probability of loss is roughly 2%, compared to 50% in tournaments. That’s massive.

For most people, this reason alone is compelling enough to spend most of their time playing cash games.

That said, I see the value in playing tournaments, both for the sheer thrill and the fact that one has a disproportionate reward for their risk. That’s why I typically advise my clients to take a balanced approach, allocating the majority of their money toward cash, with a small portion for tournaments.

This mimics basic investing strategy that you’d find in a stock portfolio, with a mix between high risk investments with higher returns and low risk investments with lower returns.

The right balance of course will depend highly on your specific situation, bankroll and motivation for playing, which is why my individual recommendations are always highly personalized.

These numbers explain why, while many of my colleagues were at the World Series of Poker, I spent my summers grinding high stakes cash games in Macau. It’s a lot less glamorous, but it’s a lot more sustainable.

If you’d like help with putting together a poker bankroll that’s customized to your needs which gives you the best chance of not only winning, but maximizing your overall returns, while simultaneously mitigating your risk, you can apply to work with me here.

I’ve worked with countless clients over the years to help them get clear on their goals and put a business plan in place based on their personal situation. It’s a process I have a lot of experience in, deeply enjoy and will help you build a solid foundation upon which you can build your poker future.

If you prefer a DIY approach to bankroll management, check out our Membership at Conscious Poker and take our Mini Course on the subject.

If you enjoyed this post on how to calculate variance in tournaments and cash games, please share it with someone who would benefit.

Thanks for your attention.
Alec

Alec Torelli
Welcome! I'm Alec Torelli, founder of Conscious Poker, a training site dedicated to transforming good players into great ones by providing the best poker strategy and mindset content. I've been a professional poker player for 15 years and have over $1,500,000 in tournament winnings and millions more in both live and online cash games. On this site, I share the lessons I learned during my poker career to help you crush the games, optimize your bankroll, make winning decisions and achieve your poker goals.

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