## Monday, May 28, 2007

### Confusion over Variance

Variance as it relates to poker is difficult to understand, both because the element of luck is hard to quantify and the mathematical function for variance doesn't provide many answers.

What does variance mean exactly?

In my mind, the term variance is used in poker to describe the amount of luck in any given game -- not the amount of swings. So when you say a game is high variance, that means the game's results are more likely to be determined by the cards that are dealt than by players' decisions.

Here are some definitions of variance:

1. Variance is the statistical measure of dispersion, or just how widely your results will be distributed. When variance is high enough, a small advantage may be of no use during your lifetime. When variance is low enough, a small sample will be much more likely to reflect your real advantage (or disadvantage). In other words, variance describes just how long the long haul is. In poker terms, high variance means that a small number of hands will not be very representative of your long-term expectation.
--Seriouspoker.com

2. The distribution of your results over a a set of hands or sessions, or the swings in a positive or negative direction of cash flow.
--Mike Caro University.

3. If $\mu = \operatorname{E}(X)"> is the expected value (mean) of the random variable X, then the variance is$\ This definition and equation is meaningless to me, but I like weird-looking variables.
--Wikipedia

As a poker player, I want to know which games maximize my skill edge over my opposition.

I asked the question, "what type of game has 'more' variance between no limit, limit and tournament hold 'em?" in the 2+2 Beginners forum. The responses to that thread, Variance: NL vs. Limit vs. MTT, back up my beliefs.

I only got three responses, but they were in agreement. Multi-table tournament hold 'em seems to have the highest variance, followed by limit hold 'em and no limit hold 'em.

While no limit seems to be "high variance" because you may have to put your entire stack at risk at any time, in reality the ups and downs aren't too extreme. No limit provides the best opportunity to get the most money in with the best odds. It's the game that will separate a fish from his money the quickest. It has fewer suckouts than limit or MTTs.

For a closer look at how to attempt a poker calculation of your variance, I found this article titled, "How much bankroll do you need?" in a search.

I also enjoyed a Mike Caro article published in Bluff magazine a few months ago, in which he argued that your luck may not even out in the long run, contrary to popular belief. Check it out here: "The importance of luck in poker."

Chad Carpenter (Yahoo IM: carchd) said...

As a strictly MTT player for the most part I will agree that it has the highest level of variance over other forms of poker. You make very good points about something I already thought to be true anyway.

Miami Don said...

Great post. I've had many discussions about the luck factor and I think poker, as in life, some people are luckier than others.

I don't think we see enough hands in a lifetime to truly have the numbers balance out. Thankfully skill is also a determining factor and IMO skill overcomes luck in the long haul.

See you in Vegas.

Grinder said...

I wonder where Short Handed Hol'm falls in that mix!