I ran across this statement the other day that I want to share: Variance is so fundamentally present in poker that it is entirely possible that you will never win another hand in your life. Isn't that reassuring?  I have not yet met anyone on that sort of bad streak, but I have been wondering to what degree such a thing could possibly occur. I mean, the odds are so infinitesimally small that it would ever happen to you or I that it's almost worthy of being called impossible. But impossible it is not. In fact, it is entirely possible that it will happen to everyone of us, just not in this Universe.

One of the first theories that tried to deal with the quantum nature of certain fundamental behaviors in this world was the "many worlds" interpretation of reality in which there are posited to be many Universes parralell to each other forming a multi-verse containing all possible variations of every event that has ever occured since time first started ticking, so to speak. A version of you and I would be in each one for our time lines. To go a bit further there may even be more than that; possibly many (an infinity of?) Multi-verses unrelated that form something called a Superverse. Well, in this Superverse, somewhere, there are poker players who will not ever win a single hand in their lifetimes. I'm sure it is quite an exclusive club. There should probably be some sort of futility bonus for these guys, don't you think? Here's hoping this futility is not going to befall you or I in this lifetime until such a bonus is put in place at PS (minimum number of required hands, to be certain). But would it really matter if we had to wait to be on our death bed to collect? I guess not.

As it were we only really know that we are here now and that we feel we have some sort of control over our destiny. The proof of this statement is that we study to get better at poker. There is an expectation that we are going to be dealt cards that we can win with if we make intelligent choices. It's smart to do so, because chances are very good we will in time be put in those situations.

If you' ve given much thought to what variance is and have read about it you' ve seen it described as a measure of the spread of data points in a set of data. Mathematically speaking it's the square of the standard deviation in a set, which is a measure related to the differences between data points and the mean (the average).

Basically, anything that can be measured for a population can have a standard deviation calculated for the set of data points and also a variance. When the variance is low (near zero) the data is very narrowly spread around the average.

When you think about poker and everything you can measure there are many instances when you can refer to variance. This measure can be related to a starting hand frequency, i.e. If you are wondering about AA (that has an expectation of coming in at a certain frequency) you could define a population of events and compare the frequency achieved in the set of data points for that population. This could mean possibly having 100 points of data refering to 100 sessions of poker which would have their own frequency of AA calculated . There would be a variance around the average and also one around the expected value (which the average approaches when the population goes to infinity).

So, imagine calculating this with only two sessions. You may not have received AA in them or you may have received it, say, 6 times. The frequency calculated for the first would be zero and for the second it would be (6/number hands played). It would yield an average of  (frequency for Session 1+ frequency for Session 2)/2. You could compare that against the expected frequency which is defined by statistical outcome (1/221). There is nothing that stops you from using a low number of sessions of, say, one hand either. We would expect to see greater variance in the numbers when the number of sessions and/or hands in a session is that small because you' re going to get 0 or 1 as the frequency for every point (the maximum spread).

We often hear stuff like: "variance killed me" or "that's variance for you" when someone loses a hand in a situation where the expected long term result is that he should only lose 2% of the time. In truth you may well be experiencing reasonable variance (for you carreer) when that happens and not be aware of it. The sample number is so small as to not even give us enough information about how things are going for you beyond now. Because it is a single hand the frequency count will either be 1 or 0 again (absolutely normal). In that regard, if you told me you lost to such and such a hand and were likely to have won that 98 times out of 100 you are applying the wrong type of comparison. There were only two possible results and one of them happened; therefore, nothing special happened. I could sound very insensitive if I said that, but it has much to do with perceptions.

If it happened that something like this happened to you twice in two hands and you were still interested in having me console you I would still tell you that it's not that special yet. Sure your variance is maxed out now, but it's such a small sample. Variance can be really huge in small samples. Having large variance in small samples is not rare! Get over it!!! What would it take then? Well it takes a lot of hands before we get a real picture and I declare you the unluckiest person in this Universe. It is why we are often told to not make any great conclusions from, let's say, less than 100 000 hands. In the short term, yes, you appear to be unfortunate, but how about if was to tell you it would never happen to you again? Wouldn't that be wonderful! You could be the luckiest guy in this Universe and not know it yet. So, don't beat yourself up yet, please.

When we focus on results we are almost always speaking about recent ones that reflect small recent samples. Our results can therefore be all over the map and not really say much. What' s interesting is that we can have really long stretches of low variance (the expected happens often) which are beneficial to us and long stretches of high variance that aren't. For certain extremely rare events it would take a really long time for things to average out. Winng a million dollar "spin and go" would be one of them. It is why I started my blog a few days ago with a discussion of the likelihood of winning large MTT freerolls. Those are very high variance events because your statistical chances of winning are pretty low to begin with. All your skill would have to overcome that. Each and every hand you play will come with its own associated result with large variance and there will be many of those. If the unexpected happens to you in one of them, I'm not that surprised---it can.

The more I think about it the more I tend to not be surprised when strange things occur. Rare things happen all the time somehwere. A rare event must have its moment. In fact, if you posted the last 9 handed hand you played with all your opponents cards and the complete board and I asked you to calculate what the odds were of that happening you might come back to me saying: There's no way that hand should have happened--the game must be rigged! Ah yes, it is quite funny how certain things look strange after we have seen them happen and look back at them. Talk about a confirmation bias. Statistics can lead us to all sorts of weird thinking when we interpret them the wrong way.

Happy poker and may you have good short term variance (I think),


PS, if you enjoy reading my thoughts in this blog please let me know because I'm not so sure it's well placed here when I compare to what others do. I looked at the guidelines, and I think I am ok.