Can you outrun variance?

Every Thursday, I do an AMA about tournament poker in my Facebook group.


Here's a question I got recently:


"At what point do results outrun variance? How much consistent winning and deep runs before we say OK we must be doing some things well and it isn't just good variance?"


Now I think this is a great question because I normally receive questions about running bad and how long it will last. Here, though, is a part-time tournament poker player who wants to know when he can be confident that his results match his expectation.


One of the best tools to help us answer this question is the tournament variance calculator over at https://www.primedope.com/tournament-variance-calculator/


Once you load the page, you'll see you have to enter some tournament data:

# of players is the number of entrants

Places paid should be pretty self explanatory

Buyin - make sure to include the part of the buyin that goes into the prizepool

Rake - this is the amount kept by the poker site/company

Return on Investment is what you estimate your ROI to be (more on this later)

How many are you going to play? basically how many of these tournaments are you going to play or want to run the simulation for - if you play 100 games per month, you could be 100 in here, or 1200 if you want to simulate for the whole year

Sample size and Bankroll - you can leave it on the default


Then just click Calculate.


Here are the simulated confidence intervals for the spot above where we want to look at playing 1200 $22 MTTs with 1000 runners, 150 paid, and an estimated ROI of 25%:

Let's take the 95% confidence interval - over 1200 games you can see that the spread of profit/loss is pretty big. Even with an estimated 25% ROI, you could play 1200 games and lose about $6k. You could also win about $21k. And yet your EV is $6k (1200 x $20 * 0.25).


Your ROI could be anywhere between -24% all the way up to 87%.


And yet we estimated our ROI to be around 25%.


So you could be a winning player, but have a losing year (if you play 1200 games in a year).


1200 games is clearly not a big enough sample in MTTs.


It's also tough to estimate your ROI.


Let's say you looked at your results on Sharkscope and saw that in 2021 you played 1200 MTTs at an average buy-in (ABI) of $22 and an average field size (AFS) of 1000. Your profit was $20,847 and your ROI was a whopping 86.86%. So for 2022 you decide to play 2400 MTTs at the same ABI and AFS and use 86.86% as your estimated ROI.


You're playing twice as many games, so you expect lower variance. Your EV is around $42k.


Here are the results:

Looking at the 95% confidence interval again, there's still a huge spread in profit and ROI. You might only make half of what you expected, or you could make 50% more... and everything in between.


But what if 2021 you just ran really well and finished at the very top end of the expected profit and ROI for the year like the first sim we ran? What if you luckboxed a huge field MTT and the rest of the year nothing exciting happened?


You're going to have a false idea of your ROI and your expectation.


And that's why it's tough to estimate your ROI.


It's also why it's important to understand what a variance calculator is actually telling you.


If you're a part-time player you probably don't have a big enough sample size yet (read: you haven't played enough MTTs) to feel confident that your results match your true ability. You could have run well. You could have run terribly. Some great poker players have losing years - you could be one of them! But it's tough for you to get enough of a meaningful sample size if you play part-time.