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.

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12 comments

  1. Grand article Bill.Ive always noticed that it takes a special breed of player to play his/her normal NL game when the stakes are raised.I firmly believe this differentiates between long term winners and losers.

  2. just came across this site and thought you might enjoy this…

    http://en.wikipedia.org/wiki/St._Petersburg_paradox

    It’s a variation of the high-stakes coin toss dilemma that i first read about in an undergraduate math textbook, and it goes sort of like this:

    I toss a coin until it comes up tails. If n is the number of times I tossed the coin, I pay you 2^n dollars. We repeat as often as you would like. How much are you willing to pay to play?

    The expectation value of this game is infinite! In other words, you should be happily willing to pay $100 billion per tossing session. But the variance of a $100 billion St. Petersburg game would be so ludicrously large that the world would almost certainly run out of cash before anybody won.

    Mathematically, poker games against stupid-aggressive opponents are a lot like a real-life St. Petersburg paradox: extremely profitable, but with terrifying bankroll swings. (and if you really want practice at wild poker, try the NL play-money tables!)

  3. wow great poker theory there. I really think that it is true about if you play at a game over your head you will play fundamentally worse poker. I usually play 1/2 but when I am in 2/4 I play terrible because I am too focused on how low my stack is getting in one hand. So I tend to fold hands I would have never folded in 1/2. I also think that it depends on the poker room. Some rooms having players that are sitting fucks other’s are there to take your money…

  4. I certainly agree with the comfort zone theory. I still cringe at the weak-tightness of my play in a $300 satellite, and that after super-satting my way in for about $30. I was hugely conscious of the amount, relative to my bankroll and the effects lasted on into “normal” size events for some time after.

    I think there’s also mileage, from the improvement perspective, in sampling games at equivalent stakes in various environments. FOr me that means bouncing around Party, Stars, Full Tilt (of course) and Paradise with occasional visits to Bodog for spice. The list changes from time to time as the mood takes me. I’m also convinced that learning to cope with other games and betting structures helps to develop overall poker “sense” to more general situational play.

  5. HDouble,

    Interesting take, especially #2 which I would agree with. On #1 though, I see it a little differently. If you’re playing a typical Party game of $5/$10 full with at least one raise pre-flop and 5 or 6 to the flop on every hand, that’s a very, very different game than even $5/$10 6 max where it’s likely to be heads-up or three handed to the flop. So, in essence, it sounds like playing an aggressive 6 max game would do more to prepare you for higher limits than would playing in loose, aggressive full table at the same limit.

    And, if I’m reading you correctly, what we’re really talking about here is the change in hand strengths. K9o is a good hand heads-up. It’s a crap hand in a loose, aggressive game with a raise in front of you. 76s is a great hand in a loose aggressive game where you can get the odds to draw to your straight or flush. Heads up, it loses a lot of value.

  6. Good post, I like hearing theories about how players get better. However, I’m going to disagree on two points:

    1. As you move up in limits, the games get much looser and more aggressive on the individual level. Meaning, there is much raising with hands like K9o, but usually the pot ends up heads up on the flop. I think that learning how to play against loose aggressive players is one of the most important skills to learn in low limit poker.

    2. “Now, part of my hypothesis is that Player B might plateau at $30/$60.” The most successful player will move up in limits as fast as he possibly can (with some constraints thrown in here)– I believe that the most successful players are driven by their competitive instincts, and don’t concern themselves with win rates– only the question if the bankroll to play in the bigger game.

    Also, I believe the jump from 30-60 to the bigger games is a tough one, but a players chance of successfully making the leap has little to do with their previous experience. The game is so different that non technical skills become far more important.

  7. EasyCure,

    Well, I know that Full Tilt had that reputation for some time. Though, the site has been growing so quickly that the games have softened a bit. I think each site has their own reputation for their games. For instance, the low limit games on Site A might be tougher than on Site B but site B’s middle-limit games might be tougher than Site A’s.

    Bill

  8. I played in a PLO8 game last night that was devoid of the usual 1/2 buy-in fish that swim in. Needless to say I didn’t turn down my usual aggressiveness at these games and lost most of my stack because I never gave credit to the players having the hands they represented.

    It was a good lesson, and I will probably profit more from the lesson far more then the chips I bled off last night.

  9. Really good post, but I have a follow up question. Everybody debates where the the worst players play (with Party being high on the list of fish), but where do the “best” players play? Stars? I don’t know.

    Also, is it possible for a site to somehow attract only “better” players so their site isn’t riddled with fish? It would be nice to have people respect a re-raise once in a while, but is it realistic to avoid the schools of fish just to play with “better” players to improve your game?

  10. Great Post Bill

    HH Mark has often maintained that he prefers the tougher games (plays at paradise) because his goal is to improve and learn, not just make the most BB/100 hands.

    I agree and like what you said about playing in both the fishy and tough games. Part of being a good player is recognizing the type of game you are in and adapting. While it is still hard to find a tougher game at .5/1 through to 2/4 it occasionally does happen. I was playing last night on party at a full table and 8 out of ten of us had a VPIP of 20% or lower and the Pre/post flop AF was high. Very unusual for party but still fun to play. even at the same stakes you need to be able to recognize a tougher table and play accordingly.

  11. Bill, I agree with a lot of what you say. Let’s take it one step further and into a tournament scenario. Pros with much higher bankrolls who play dozens of tourneys a year have no second thoughts about taking that 65/35 edge for all their chips.

    Amateurs whose tourney entry fee represents 50% of their year’s winnings will hesitate to take those edges because this will be the only tourney they play.

    It’s all about sample size and the ability to withstand swings such that the law of large numbers begins to hold true.

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