In my last blog entry I wrote about some of my thoughts related to variance and what it could possibly mean to be unlucky in poker. In the commenting I expressed to have harbored an interest in seating algorithms and was asked about that. I don't think I could have done justice to it by replying in the comments; therefore, I'll deal with that here and allow you to look at my thoughts.

About two years or so ago I started to question what exactly was behind the seating decision making at the poker site I was playing at (not PS at the time). What led me to become curious was the effort I had made to understand different aspects of variance in large MTTs.  Specifically, I had done some calculations that were breaking down different scenarios and examing them for their potential for injecting more or less variance into the mix. How is that possible you say? Let me give an example. Let's say you go all-in on the first hand and procede to triple up.  The table may (emphasis on may) be disolved and the players reseated. What is the criteria used to "balance" the new tables? That all gets decided by a seating alorigthm, as far as I can tell. If you have ever payed much attention to how a game develops you will probably have noticed that over time larger stacks find themselves aggregated together to a certain degree. You may even have experienced being reseated at a table during the early stages with, let's say, three of the top ten stacks in the tournament when you have yet to even win a single chip. Something  has brought you there, and that something has also brought large stacks together. Why should I be concerned at all about it? It turns out that it has a really deep and profound effect on how many hands you might have to play to reach the lofty heights required to win.  If you win early and often it is in your interest to be doing so against stacks equal to you. If you had initially trippled up and were not reseated (as it can happen) you are going to be, dare I say, wasting any great opportunities you are given then pecking away at small stacks. Someone else may doubling through a stack equal to his bloated stack at the same time with a similar opportunity. What does that have to do with variance? Let's have a look at that.

If you read my last blog entry you saw me mention that anything that can be measured for a population can have standard deviation and variance measured. Every hand you play has a certain expectation to win or lose that rides around a very long term average; it has it's own variance. If we were always playing races that were coin tosses we would have a 0.50 long term expected win rate each time. After two tries it would be 0.25, after three it would be 0.125. The more hands we have to play to double up, say, once. The more our overall expected win rate will be eroded, and the variance about that will tend to shrink as we play more hands (a more certain expected death). Players who double up efficiently are not immune to this effect, but they are always going to be better off doing it in less hands. The speed at which you climb also give you some pretty great edges in poker: fold equity and the ability to scavange on the bodies of those who are wasting away due to time/blind/ante pressures.

So, let me introduce a new measure to you: the frequency of favorable seating arrangement. That measure has variance just like anything else you can measure. Try as you may, though, it is not something that you can really affect--a proprietary algorithm is doing some calculations and deciding that for you.

What had initially got me wondering was a game in which I had been seated with 8 other players who were sitting out. I had a small stack at the time, and so did all the others. The blinds were small and every hand meant I collected the blinds with certainty. Great, right? No, not so much. It lasted quite a while. As I was collecting these small blinds I was watching the chip leaders race ahead, leaving me itching for a chance to get some action. Eventually, I was reseated with others who were actually playing. It turned out I was seated with three of the top ten stacks in the tournament and mostly larger stacks than mine. I had to then play hands in which the bets where more reflective of the stack sizes than the blinds/antes. In this case I had experienced two different aspects of the variance around the seating arrangement variable.

I remember summoning up a live customer support agent to ask about it. "How is the reseating done" I asked. The assistant didn't quite understand my question because she replied: "it is all random". I quickly shot back: "it can't be, because your site mentions that there is a "balancing" of the tables occuring. "I assure you that it is all done randomly and that no one is punishing you" was the reply I got. At this point I was quite peeved because I was not implying that anything nefarious was going on that was unjust. I simply wanted to know a bit about the decision making process. I then described what had happened to me and certain observations about how it was very unlikely that there would be tables with mostly chip leaders and tables with just bottom feeders if it was all random. It didn't seem to register with the person and I was forced to conclude by saying she had been a great help to me, because it was going nowhere.

The existence of seating algorithms is not a great revelation. It isn't a way to cheat, per se, but I do see in it how easily one could favor someone if ever one wanted to weigh things with some variable of their liking. What my point has always been is that the existence of seating algorithms injects a important layer of variance into the equation. If you accept that skill and starting hand frequency are two important factors, I submit that seating arrangement is also. The bigger the tournament the more it factors in because many will be favorably seated. You will have to overcome that with skill and other factors if you are not.

That in a nutshell are my thoughts about it. I have never been able to find any site that would discuss this or describe how seating is done to attain the desired "balance".

Thanks to Ovalman for reminding me of it.