Variance and Poker Pt. 2: The Secret to Controlling Online Downswings

Variance and Poker Pt. 2: The Secret to Controlling Online Downswings

09-09-2014, 09:16

It's a very different story for online poker players.

In particular there's one major elephant in the room that needs to be approached with caution: win-rate.

Catch up with Part 1 of our series on Variance and Poker for live cash-game players; continue on with a look at variance for online poker players below.

By Arved Klöhn

Obviously there are a bunch of differences between live poker and online poker (and some people might even go so far as to call it a completely different game).

The most important for us related to variance are:

dwan swings
Variance is a major factor for the best players online.

1. Online poker is played much faster. A (semi) professional online player plays more than one table and will average from 200 to more than 1,000 hands per hour (the live player usually never sees more than 35 hands per hour).

2. Online poker usually has a lower standard deviation per 100 hands. Live players need three hours to play 100 hands and can experience the wildest swings over this period. Online you might only need 10 minutes to play 100 hands and will usually experience fewer swings over this period (partly due to the fact that the games are tighter in general).

3. The most important point: online poker players usually have much lower win rates than live poker players. While low-stakes live players might be able to beat their limit by 25 big blinds per 100 hands those win rates are unheard of nowadays in the online poker world. The competition is much better and win rates of five big blinds per 100 hands are already considered to be excellent.

While the first two points (more hands, lower standard deviation) might indicate that online poker has lower overall variance than live poker, the third point (lower win rates) ensures that variance is a major factor online.

Variance is a Big Deal in Online Poker

To show how major this variance-factor is, let’s return to John for a moment.

John – our live poker grinder from our previous examples – just discovered the online poker world and he’s as decent online as he is in his local casino.

Let’s say he beats the $0.50/$1 No-Limit Hold’em tables online with a win rate of five big blinds per 100 hands (which is already way above average for decent players).

His standard deviation is 100 big blinds per 100 hands (that’s a usual standard deviation for six-max tables online).

Live, John plays 4,000 hands per month, so let’s see how he does online over this period. Again we head over to the variance calculator, enter the three parameters (win rate, standard deviation and number of hands) and take a look at the results:


See what’s happening here? Those samples go wild!

Over 4,000 hands John can expect to win 200 Big Blinds (which corresponds to $200 at the $0.50/$1 tables) on average, but he will encounter plenty of very hefty swings.

Gus Hansen2
You might need thousands (maybe even tens of thousands) of hands to recover from your downswings online.

Let’s go through some numbers:

The probability of John losing money over 4,000 hands is 38% There’s a 2.5% chance (once every 40 trials) that John will lose more than $1,000 (10 or more buy-ins) over 4,000 hands In fact more than 30% of the time John will be stuck in a downswing for more than $2,000

Compare those numbers to John’s live poker performance. Live, his chances of losing money over 4,000 hands were only about 9%.

So why is variance so devastating online?

Variance is a Bitch

The reason why variance has such a huge impact was already given above: win rate.

A decent online player might win five big blinds per 100 hands -- maybe 8-10BB per 100 if he’s really brilliant and playing at a relatively low level.

While in theory that’s a nice number, it’s only a tiny fraction of this player’s standard deviation over 100 hands.

This means that variance will kick you in the butt every now and then and there is not much you can do about it. Your win rate is simply too low to negate a big downswing within a couple of hundred hands.

You might need thousands (maybe even tens of thousands) of hands to recover from your downswings.

Funny hat guy
Another obstacle? Your online opponents are sober. And probably pretty good.

If you sit down at an online poker table and expect to roll over it and come out ahead like you might in your local casino, you will be in for a nasty surprise:

Your online opponents are usually not half-drunk locals or tourists Your online opponents are (mostly) sober and usually know what they are doing Your online opponents might have hundreds of thousands hands worth of experience and grind the tables for a living

So even if you’re winning, you’re winning by a much smaller margin than live. And a smaller win rate leads to bigger downswings and significantly increased (negative) variance

More Hands, Less Variance

Let’s take a look a look at how to counter this variance problem.

The key to getting your variance under control is to play more hands. Almost all professional online grinders play tens of thousands of hands per month – some even play more than 100,000 hands (each month and every month).

If you are a winning player, accumulating more hands will inevitably reduce the impact of any short-term variance. The downswings wont just vanish, but you’ll out-win them eventually.

So let’s – again – return to John from our previous examples. He decided to give online poker a real shot and started playing 20 days per month, averaging 2,000 hands per day (playing 4 to 6 hours per day).

Per month he’s playing 40,000 hands. He plays $0.50/$1 No-Limit Hold’em and averages a win rate of five big blinds per 100 hands. His standard deviation is 100 big blinds per 100 hands.

What results can John expect for one month of playing? Well, let’s enter those numbers into the variance calculator:


While still looking quite wild, this simulation does not look too bleak.

There’s only a 16% chance that John will end up with a losing month There’s a 5% chance that John will either lose more than $2,000 or win more than $6,000 in one month

After 40,000 hands variance still is a factor, but it’s already a much smaller one than over only 4,000 hands.

We can also simulate John’s possible results over 400,000 hands (which is 10 months worth of play for John):

The chance of losing money over 10 months (400,000 hands) is tiny: 0.08% The chance of winning an amount somewhere between $7,350 and $32,650 is 95% The chance of being stuck in a $2,000 downswing at any given time is slightly over 30% The chance of being stuck in a $5,000 downswing (that’s 50 buy ins!) at any given time is around 4%

While those numbers might still look intimidating, unfortunately that’s the best one can come up with.

Playing well, avoiding tilt and amassing plenty of hands is the only way to deal with downswings.

And those numbers also show: if you’re a decent (meaning: winning) player, you can negate negative variance by playing the necessary volume.

Let Variance Be Your Bitch

We've already established that variance is a bitch and there’s one way online poker certainly does not work: You cannot just play one or two tables a couple of hours per week and expect to consistently make money.

If those are your hopes and expectations, online poker is probably not for you.

Jamie Gold
It’s always possible to land a lucky punch in poker. Winning consistently online is another matter.

You either work on your game and play a decent volume or you learn to live with the fact that variance is a huge factor and whether you have a winning or losing month is mostly determined by luck.

You also should not overvalue upswings or downswings too much. They will happen more frequently and on a larger scale than you expect anyway.

Just because you won 10 buy-ins in a couple of hours you’re not the second coming of Vanessa Selbst. And just because you dumped 10 buy-ins over two evenings you’re not necessarily a bad player.

Even players at low stakes and who play mostly for competitive reasons (and not to pay their bills) should become accustomed to the fact that they will need a lot of endurance to consistently beat their limit.

But this does not mean variance cannot be your bitch, once and for all. Yes, everybody can run badly. But on the other hand everybody can run well, too.

It’s known to happen that sub-par players score huge in big tournaments (think Jamie Gold or Darwin Moon hitting 1st and 2nd place in the WSOP Main Event).

It’s always possible to land a lucky punch in a poker tournament ... but it's a completely different story to take poker seriously and learn to win consistently.