Introduction to Poker Variance

By Alton Hardin

Introduction

Many people involved in poker will have heard the term variance as it is thrown around a lot but many people do not always understand what it actually is. As we all know poker is a game of statistical distribution; every hand we play is at the mercy of probability and what all poker players aim to do is to make decisions that put that probability in their favor. But of course it is always possible for you to make a good decision and lose or a bad decision and win. It is also possible for these things to happen over and over again over a period of time. This is variance.

Variance Defined

Therefore, poker variance is essentially the upswings and downswings in poker, in other words, negative and positive variance. More definitely, it is the difference between individual results in the short term and the average set of results we expect to see in the long term.

Negative & Positive Variance

Most people when talking about variance are talking about negative variance, when they have been losing hands they shouldn’t be over long period, but there is also such a thing as positive variance. Positive variance is what people talk about when they say a player is on a “heater”. It is where they are maybe getting dealt more premium hands than they should be or they are hitting more draws than they should etc and as a result this has a positive effect on their win rate over that period.

Experiencing Variance

Even the best players in the world experience variance of both the positive and negative kind. Good players can expect to potentially lose 10 buy-ins or more in cash game variance downswings. It is not unheard of for people to go on downswings in excess of 20 to 30 buy-ins in the case of extremely bad variance. This is normal and should be expected as we play larger sample sizes.

These stretches of variance can vary in length and we never know how long they will last. Sometimes they happen over a small sample size of only 1,000 or 2,0000 hands and then you go back to winning like you were and at other times you can be losing pots consistently for 10k hands or more and feel as if it will never end. It is not unheard of for players to have break-even samples sizes of 100k hands due to negative variance.

On the flipside, players can go on positive variance heater runs over a small sample size of 1,000 to 5,000 hands where they are winning at rates excessive of 30bb/100. So when we think of variance, we must not only focus on cooler sessions, but also heater sessions.

What Causes Variance?

Luck causes variance, nothing else.

Understanding Variance: The Coin Flip Example

With a coin flip, we expect to have it land on heads 50% of the time and tails 50% of the time. In other words, in a sample size of 1,000 flips we would expect it to land on heads 500 times and tails 500 times. However, we do not know the order in which this will happen.

Assume you take a coin flip bet with your friend. The terms of the bet are every time the coin lands on tails you win $2.00 and every time it lands on tails you lose $1.50. You both agree to flip the coin 50 times.

So according to a basic EV calculation: (50% win rate x $2.00) – (50% lose rate x $1.50) = $1 – $0.75 = $0.25 net profit on each flip. So with each flip you expect to win $0.25 on the average with this +EV bet. With 50 flips, you expect to win 50 x $0.25 = $12.50 on the average

So lets do a sample run using the virtual coin flipper from random.org (http://www.random.org/coins):

We will break the coin flips down into 10 flip samples:

Flips Heads Tails Net Winnings
1 – 10 5 5 $2.50
11 – 20 4 6 $6.00
21 – 30 4 6 $6.00
31 – 40 6 4 -$1.00
41 – 50 2 8 $13.00
Total 21 (42%) 29 (58%) $26.50

As you can see, due to short-term positive variance, when you expected to win an average of $12.50 in this bet, you actually won $26.50 because the coin flipped in your favor in the short-term. In this same, you won 8% more of the time than you would have expected in the long term. We can account this as short-term positive variance luck.

So what is long term? Well, lets look at some larger sample sizes:

Flips Heads Tails
500 261 (52.2%) 239 (47.8%)
1,000 473 (47.3%) 527 (52.7%)
2,000 979 (48.9%) 1021 (51.1%)
3,000 1515 (50.5%) 1485 (49.55%)
4,000 1988 (49.7%) 2012 (50.3%)
5,000 2487 (49.8%) 2513 (50.2%)

As you can see, the variance minimizes as our sample size increases. We still see a small percentage of variance at 2,000 coin flips but by the time we hit 4,000 coin flips we are very close to the 50/50 flip percentage that we would expect in the long term.

Dealing with Variance

If you do find yourself in the midst of negative variance it’s hard to stop yourself from getting frustrated that everyone is sucking out on you, or maybe you start to doubt that you are a winning player. You have to try to keep a level head and reduce variance as much as possible. Don’t shove those marginal flush draws or take a flip as often as you would normally. This will reduce your variance and hopefully help you keep a level head until you pull out of it.

It is common for players to tilt off some money during a downswing, which compounds the effects of the variance. Don’t let this happen. If you find yourself frustrated at the table just get up. Even if it’s only for a short time, clear your head and come back fresh. No need to lose extra money when you are already losing lots due to variance.

Embrace Variance

More importantly, we can minimize our tilt by embracing variance. We must embrace variance as an essential aspect of the game and understand that luck may happen in the short-term causing either positive or negative variance, but in the long-run variance (luck) will be minimized and the affect of cooler, suck out sessions will be minimized. Furthermore, the same goes for our lucky heater sessions. In the long run our true win rate will be realized. This is why in the long-term skill always beats out luck.

Do Not Be Results Oriented

We must also not be results oriented, as short-term session-by-session results are a factor of variance. If we embrace variance, we know that fish will suck out on us for bad beats and we will also go on heater session of our own where we cannot lose. So rather than focusing on results, we should be focusing on +EV long-term plays knowing we are making the best profitable play that will average out to winning situations in the long run.

Remember, if there were no river, there would be no fish. And if there were no fish sucking out, there would be no sharks left in the water to gobble them up.

Summing Up

Remember, variance is an essential aspect to the game of poker and we must understand the following:

  • The element of luck in poker causes short-term variance
  • We will experience larger variance upswings and downswings in small sample sizes
  • Losing in the short-term doesn’t mean you are necessarily playing bad
  • Conversely, winning in the short-term doesn’t mean you are playing well
  • Variance (luck) minimizes as we play a larger sample size
  • Therefore, never rely on your short-term results to determine if you are a winning player
  • A large sample size of 50k or greater hands will give you a fairly confident win rate
  • Lastly embrace variance, don’t be results oriented and try your best not to tilt!