High Variance Poker vs. Low Variance Poker

I was commenting on something over on the Full Tilt message boards the other day and I started me thinking about the concept of variance. First off, wild, loose, aggressive games are beatable. Almost by definition, if you play an optimal strategy you can win. In fact, because your opponents are making so many more mistakes, your win rate should be even higher than the norm against more predictable opponents.

We all know the coin flip probability problem. If I offer you a chance to flip a coin and agree to pay you $2 every time you win and you only pay me $1 when I win, only a fool would pass up such an opportunity. But what if we up the stakes a bit? Let’s flip a coin but you pay me every single dime to your name when I win and I pay you twice your net worth if you win. Unless I’m willing to extend you a line of credit on your losing flips, you can only afford to lose once. Do you take the same bet? The coin flip odds are the same and you’re being offered the same odds on your money so if you were a fool to pass it up at $1/$2 stakes, aren’t you a similar fool for passing it up at these bet amounts?

Obviously I don’t agree that those are two similar situations. In one, you’re out a trivial amount of money and in the other you’re playing with your entire net worth. If you lose in the first, maybe you don’t order cheese on your burger tonight. If you lose the second, you don’t eat at all.

So, getting back to poker, what if you had the chance to play in one of two poker games? In the first, it was loose and aggressive with lots of wild and unpredictable opponents who played poorly. In the second, you had somewhat better players than the first table but they still made a fair number of mistakes even though they played fairly tight, predictable poker. In the first game you might expect to average 2BB/100 or more while in the second game you might average 1BB/100. Which game would you rather play in? Before you answer, let me offer that in the first game, you can expect swings of 80BB either up or down and in the second game your swings would be more in the 40BB range.

Now, if you’re a $30/$60 player slumming it at the $2/$4 tables, the 80BB swings might seem like chump change to you so you would prefer the game with the highest expected win rate. But if you’re a $2/$4 player who is trying to work his/her way up the limits, an 80BB downswing might be a devastating blow to your bankroll.

Since we know that many people play differently when they are out of their comfort level or when the stakes are too high, as someone moving up in limits, does it make more sense to take the steady, low-variance games or the high-variance games? Mentally, I’ve been exploring the idea that it might be better to play against better opponents if your goal is to move up in limits. Here’s the reasoning I’ve been exploring:

First, you’ll find yourself tilting less and playing more correct poker if you’re playing within your comfort zone. In theory, we should all play our “A Game” regardless of the circumstances, but that becomes harder and harder to do as your losses mount. Even pros are susceptible to playing less than optimal poker under these circumstances so expecting an amateur to have the maturity to rise above it seems about as reasonable as expecting a heroin junkie to be able to quit smack simply by not doing it any more.

Second, it has the potential to keep people focused on the right aspects of their game. Poker is a game that often rewards poor play and punishes correct play. It seems to follow that the higher the variance, the more likely poor play will be masked and correct play will look foolish. As you move up in limits, your opponents make fewer and fewer mistakes. I’ll admit that at $5/$10 or $10/$20 those mistakes might seem as bad as some of those you’ve seen at the $1/$2 tables but overall, the quality of play goes up. While it’s common to crush a smaller stakes game for 2 or 3 BB/100, at the higher limits ($50/$100 - $200/$400), even expert players can expect win rates as low as 0.5BB/100. It would seem to follow that those things as fundamental as making correct value bets on the river can be the difference between being a breakeven player and being a winning player.

My speculation is that because of the higher variance and higher win rates of looser, aggressive games, many players don’t master some of these finer elements. These players move up so quickly and on a path that is so forgiving as long as they are marginally better than their opponents that when they finally get to a level that has skilled opponents, they think they can win just by tightening up their game. Many players plateau. They just get to a level where they seem stuck and they can’t move up in limits any higher.

That leads into my third reason. Players who come up in tougher games with lower win rates play many more hands in order to move up to the next level. Let’s just follow a $1/$2 beginning player up the ranks:

Player A starts off with a $600 bankroll and starts playing slightly tougher games at a 1BB/100 win rate. Player B starts off with the same $600 bankroll but players at looser, more aggressive games. To move from $1/$2 to $2/$4 both need a bankroll of $1200. Player A will play 30,000 hands before moving up ($2 x 30,000/100 = $600) and player B moves up after 15,000 ($4 x 15,000/100). To move from $2/$4 to $3/$6 both need a $1800 bankroll and Player A will play 15,000 hands at $2/$4 while Player B plays 7500. Even if we stop right here, you can see that Player A has played 45,000 hands while Player B has only played 22,500.

Now, part of my hypothesis is that Player B might plateau at $30/$60. He can make good money at that level (.5BB/100) but other than finding an uber-soft $50/$100, he gets a good whacking when he tries to move up due to the leaks in his game. Player A, on the other hand, is playing $100/$200 and winning 0.5BB/100. His game is still improving and he often takes shots at the $150/$300 when he can find a good game. Over time, Player A will have lifetime earnings far greater than Player B if they play a similar number of hands due to Player A playing at higher limits. And the only way he got to that level was by staying focused on mastering the game rather than trying to attain the highest BB/100.

So, am I trying to say that playing in tougher games is better than playing against loose, aggressive games? No. I’m simply presenting a different way of looking at things. Some of my reason for asking the question had to do with a truism in the investment world which is that while the stock market (in aggregate) tends to go up 8% - 10% a year (given a large enough sample period), the vast majority of investors don’t enjoy 8% - 10% gains. Dr. Marin Zweig theorized it was because the natural tendency of investors is to exit the market at bottoms and enter at tops. He created a series of funds designed to minimize volatility so that investors wouldn’t feel the need to jump in and out of the market. His thinking was that, over time, investors who stayed in his fund due to the lower volatility would actually experience higher returns than those who jumped in and out of funds (or individual stocks) trying to chase the market.

How this applies to poker is that if you reduced the variance, perhaps you can produce better overall results by producing a more skilled player. If you change the focus from BB/100 to attaining mastery, you change many of the fundamental obstacles to becoming a long-term winning player.

So, with all of that said (and there was a lot said), I don’t propose the above as the answer. For every argument I come up supporting this theory I come up with a counter-example that makes the case for playing in games with the highest BB/100. I simply was batting this idea around in my head for a few days and thought I would get it out there on digital paper to see how it looked. I invite people to trash it. I invite people to support it. My own conclusion is that the biggest factor is likely to be one’s own comfort level. Some people have no problem taking an 80BB swing while others start playing scared which only aggravates the problem.

Personally, I think I gain something from playing both types of games. Playing online poker on auto-pilot has its appeal (mostly money) while I profit enormously in the knowledge department playing in HDouble’s weekly games against other poker bloggers. When I first started playing online poker, I played mostly on Paradise which is like a rock garden. When I moved up in limits to a point where the game selection on Paradise became almost nil, I switched to Party and got creamed. I was, IMHO, a far better player than the fish who were taking my money but it took me a relatively long time to adjust to this Wild, Wild West style of poker. I’ve probably made a lot more money playing in those loose, aggressive PartyPoker games than I would have ever made on Paradise but I can’t help but wonder if my game wouldn’t be different playing against a different type of opponent.