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Holdemace486's complete beginner guide to variance.

Holdemace486's complete beginner guide to variance. - Thu May 09, 2013, 09:12 AM
holdemace486's Avatar
Since: Nov 2011
Posts: 1,760
What is variance?.

Variance is what we experience when we sometimes lose on the better hand. I say sometimes, because sometimes we lose by playing the best hand badly.

We experience variance in everyday life, variance is more than just poker terminology.

Example - This week you may have a variation in your shopping budget.

This would be variance in your regular budget.

Looking at variance, variance is an invisible force that we can not see.
We know it exists, and we see the effect, ''but we can never see it coming or leaving''.

The definition of variance is-

''In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean (expected value). In particular, the variance is one of the moments of a distribution. In that context, it forms part of a systematic approach to distinguishing between probability distributions. While other such approaches have been developed, those based on moments are advantageous in terms of mathematical and computational simplicity.

The variance is a parameter describing in part either the actual probability distribution of an observed population of numbers, or the theoretical probability distribution of a sample (a not-fully-observed population) of numbers. In the latter case a sample of data from such a distribution can be used to construct an estimate of its variance: in the simplest cases this estimate can be the sample variance''.

The Wikipedia quote above means nothing to the average person.

Diagram VAR1- Imagine variance has an infinite line, if not altered by disruption it will continue to travel straight.

Diagram VAR2-We change our infinite line into an infinite circle.

Diagram VAR3- WE add players, we create infinite disruption

Diagram VAR4-Different styles, different skill level,different thought, different variations of play.

Diagram VAR5-Random thought along a random variance line.

Attached Images
File Type: jpg var1.jpg (19.6 KB, 9 views)
File Type: jpg var2.jpg (10.4 KB, 8 views)
File Type: jpg var3.jpg (19.5 KB, 7 views)
File Type: jpg var4.jpg (27.4 KB, 7 views)
File Type: jpg var5.jpg (27.6 KB, 8 views)

Last edited by holdemace486; Thu May 09, 2013 at 09:23 AM..
Thu May 09, 2013, 09:43 AM
ArtySmokesPS's Avatar
Since: Oct 2011
Posts: 7,355
The way I'd explain variance in poker to a complete beginner would be something like this:

Variance describes how our results differ from expectation over a particular sample size, and this variance will be caused by random luck. Variance (or "luck" if you prefer to use that term) is the reason why your stacksize or overall bankroll will not grow/shrink at a constant rate. It will deviate from the average over a given sample size. In games with high variance (which can mean big upswings as well as big downswings) your actual results will vary widely from expectation. In low variance formats, your results will not fluctuate so wildly.
In games with high variance, larger sample sizes are required for the average expectation (such as your long-term winrate) to be established. In games with low variance, a smaller sample size can be "trusted", as the swings will not usually be so large.

Note that variance doesn't just apply to winning or losing one particular hand as a favourite. It also applies to how you're running in general. If you're card dead for a long period (e.g. not getting aces and kings as often as "expected"), then you're experiencing a bad run of variance. If you run super-hot and get aces and kings several times (and win every time) in one particular tournament, then you experienced some short-run "good variance".

Bracelet Winner

Last edited by ArtySmokesPS; Thu May 09, 2013 at 09:48 AM..
Fri May 10, 2013, 07:04 PM
TrumpinJoe's Avatar
Since: Jun 2010
Posts: 4,557
Unless you want to study statistics all you need to know about variance is:

Variance is a measure of how far a set of numbers is spread out describing how far the numbers lie from the mean (expected value).

What's important is accepting that it is a fact of life and mostly outside of our control. I say "mostly" because our playing style is a factor in variance.

But higher variance is not always a bad thing. A overly tight player will typically have lower variance that someone more active. But a higher variance style, if not taken to extreme, can push their win rate substantially higher. An aggressive table, while having a giving you higher variance while you're there, is usually better for your bankroll, in the long term, than a passive one.

A few overly aggressive players at your table is fortuitous. A table full of them is truly a feast or famine situation.

Life presents us with many risk/reward decisions. Once again poker imitates life.

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