A Slave to Variance

I’m back from BARGE, so it’s time for me to fill in a few of the blanks.

So, my last post was a bit cryptic, but the first response is the exact response. Under typical conditions, there is usually a cost to acquire information. In poker, betting patterns are one of the primary conduits of information. The more actions in a typical betting pattern, the more information. For example, a check-raise always carries more information than a check. The crux of the information problem is that when the price of the information is too great you should generally eschew paying for it. This is a bit of inversion of the “Why raise?” question posed by others. Often times you’ll hear players saying that they are raising for information, or raising to “find out where they are at.” In general, most players take this tack far too often.

Both Daniel and David brought this up.

This isn’t so much as a result, or some novel theory. It’s more a recasting of action motivation. Aggression is good because it allows you to get money into the pot, especially if you have the best hand. Passivity is good because it allows you to be less confident about the strength of your opponents hand, and thus promote the relative strength of your own hand.

Of course, the difficulty comes in determining when you should switch from betting to calling. In limit poker, this turns out to be fairly easy to solve for most heads up confrontations.

I’ve been doing all sorts of vacation type activities for a while now, and won’t be back to “work” till the end of August.

For those of you who want something interesting to think about, here is a concept which might seem paradoxical.

Poker is a game of information, usually the more information you have the better. But there are a lot of situations where you are given a choice about how much information you’d like, and it is often better to choose less information. What are some of those situations? What does that suggest about in game tactics?

In The Theory of Poker, David Sklansky introduces his “Fundamental Theorem of Poker”:

Every time you play a hand differently from the way you would have played it if you could see all your opponents cards, they gain; and every time you play your hand the same way you would have played it if you could see all thier cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.The primary problem with this formulation of poker strategy is that it requires you to step outside the game. Specifially, it measures the appropriate response in terms of parameters which are not available during the game. Once you know what hand your opponent holds, it’s not poker anymore. It might be an interesting game, but by removing the element of the unknown, you’ve removed an essential aspect of poker.

You know, it seems like every month someone is exposed for crossing some sort of line in a poker game and getting into trouble. People have had money confiscated from accounts, and been banned from sites. The most distrubing thing isn’t that this is going on though. It’s the fact that a lot of people, even those who aren’t being caught, don’t think it’s a big deal. That’s just the weird world of poker. It lives in it’s own little grey world, filled with grey people, doing grey things all the time.

Because of this, there is often no consensus on where a line should be drawn. For example, it’s been ruled that playing multiple seats in the same tournament is not ok. But, if you and your friends each individually enter a tournament, but play out of the same bankroll, that is ok. The distinction is subtle, and at a practical level is close to meaningless. Assuming all play is “honest” what is the difference between ten people each entering the same tournament ten times, and those people each entering ten different tournaments and sharing the results? This sort of stuff has been going on forever. Men ‘The Master’ has made a fortune out of doing this, yet he and his horses are still allowed to play at any tournament that they like.

So when it comes to the new breed of players getting caught red handed, I can certainly understand how they slipped down that slope. There are just so many examples of poker biggest and brightest — from authors to champions to internet pros — bending, twisting, and cajoling the rules to suit their own personal needs and desires that it almost seems like it’s part of the game. That doesn’t make it all right though.

The problem is that without clear rules and guidelines, players looking for an edge will do everything they can in order to make it as large as possible. This takes all kinds of forms, from coffeehousing to shorting chips, from active collusion to shared bankrolls. What is fair and what is not when it comes to poker? It’s a hard question to answer, and it’s one that a lot of smart people have come to very different conclusions about.

When I first started playing poker, I worried a lot about the rake. The available games were expensive, with 10% up to $5 being a common riverboat rake. One of the first things I did when I had enough data was to do a very remedial rake analysis. I took logged hands from play on IRC, and estimated the cost of the rake based on what would have been taken if there had been a rake. I varied the percentage and the cap. [I just love the old school SGI/Motif window decorations.]

The basic results of that chart indicate that a 5% rake is much worse than a 10% rake. As a result, I made it a point to never play in games that had a 10% rake, no matter how low the cap was. And that was that. Only recently, with the proliferation of rake-back, and other bonuses for online poker have I come back to consider the rake. I used my new simulator to construct a table which looked kind of like something you might find online. I made the players bit loose, and a bit passive, but otherwise good. Of course, the sharks had to be better than the fish to get a clear picture of win rates.

I ran the same exact simulation for 30,000 hands, and varied only the limits at which the players played. The first simulation had no rake, and all the others had a rake of 5% to a max of $3. The rake was taken out in $1 increments at every $20. So a pot which was in the range [$40,$60) would have a $2 rake applied to it. A pot which was $60 or larger would have $3 taken for rake. The results were dramatic.

By the end of 30K hands, the expert player was winning at a rate of 4.77 bb/100 in the unraked game. When the expert was playing in a raked 2/4 game, his earn rate dropped down to 1.05 bb/100. The rake is taking over three-quarters of his winnings. In fact, players don’t begin to escape the gravitational pull of the rake until 5/10.

This goes a long way towards explaining why higher limit games are sometimes easier to beat than lower limit games. Consider how much you have to beat the players for to make the same earn rate. At 2/4, you need to beat the players for about 4.72 bb/100 to take home 1 bb/100. At 15/30, you only need to beat the plays for 2.25 bb/100 to take home 1 bb/100 after the rake. Your edge over the field can be cut in half, and you’ll still acrue big bets at the same rate.