Skill Levels in Poker

In chess, there is a rating system that is able to predict performance based on the gap in ratings between two players. If I recall, an 800 point gap would predict a 99% chance of the stronger player winning the game. Someone with an 800 rating would rate as a very weak club player (in practice I think nearly all club players will have over a 1000 rating), but someone that might still think they were the stuff in maybe a junior high or high school setting (they would be relentlessly crushing the opposition they ran into, perhaps having a nearly 99% win rate over some opponents that others might regard as skilled).

Against this hypothetical player, a solid club player with a 1600 rating would be able to win 99%. Against this solid club player, a strong master with a 2400 rating (probably aspiring to international master status), would win 99% of his games. Against this strong master, the strongest players in the world, with ratings perhaps in the 3000 range, would win well over 90% of their games.

If we think of every 400 points as being a very clearly different level of skill, in chess you might argue that there are at least 8 clear levels of player skill. If 200 points is a clear enough boundary, then perhaps 15 levels.

In go, a rank beginner at 40 kyu can be given a gigantic 9 stone handicap (and could win vastly more than 99% in an even game) by a 31 kyu player. A 22 kyu player could give that player a 9 stone handicap. A 13 kyu player could give that player a 9 stone handicap. A 4 kyu player would be even odds with a 9 stone handicap against that player, and a 6 dan amateur could give that player a 9 stone handicap. 1 dan pro can then give the 6 dan amateur a sizeable handicap (not 9 stones… and I forget the exact amount), and then the increases are smaller up to 9 dan pro.

I’d speculate that each 2 levels here is at least a 200 point chess rating gap, but even being very conservative and saying 4 levels, that creates roughly 15 distinct skill levels (and I’d really say it is well over 30). I suspect a 4 dan gap, even at the professional grade, will usually equate to nearly a 99% win rate in an even game.

I suspect most people would imagine there is far less skill involved in poker than in both of these games. I would contend that poker actually has more distinct levels of skill than chess, and is perhaps in a league similar to go.

But how do we compare? There is obviously no gap in skill that allows one player to win 99% of the hands that they play. But I think a single hand is more like a single move in chess or go, and that it is a long session, of hundreds and hundreds of hands, that is the more natural point of comparison with “a game of chess”, or “a game of go”. I think there are at least a few perspectives that can be illuminating.

First, there is a question of how much knowledge or brain power does a given level of skill require. For both chess and go, each of these levels is generally associated with an exponential increase in knowledge about the game. I’d guess in chess that a 200 point increase in rating probably correlates to twice as much literature digested (or twice as much of some other form of acquiring knowledge, pattern recognition, and/or computational ability). Similarly, go professionals will typically spend well over 40 hours a week working on their game, often beginning this well before they are 10 years old, and continuing as long as they strive to maintain a professional standing. And this is often above and beyond time actually spent playing go.

Poker of 40 years ago did not require this level of attention to theory. The best players would spend long hours thinking about the game, but there simply was not a deep library of theory about poker that someone would need tens or hundreds of thousands of hours to digest. That has changed over the last 20 year, and especially over the last 10, and the study of optimal poker has become increasingly deep. Many books by professional players don’t reflect this, but there are bad books published on chess or go, also (and some of these are not really bad as books, but just very light on advanced theory… a bibliography or a beginner’s book can still be good reading). I’d still say that both chess and go have much deeper libraries of literature, but it takes time to wright books, and both chess and go have been at it for over 1,000 years.

The second approach involves trying to think of what constitutes a clear level of skill in poker, and I think that something as straight forward as stakes illustrate this. I’ve played every level on this site from 1/2 to 100k/200k regularly (and recently), and have tracked my performance. It is obvious that at each level, my average win rate, measured in big blinds won per 100 hands (with samples of at least 3,000 hands at every level) decreases, showing that on average, as stakes go up, players at each level are distinctly stronger on average. I suspect the size of this skill gap from say, 1/2 to 2/4, is smaller than a 200 point gap in chess, or a 2 kyu gap in go, but still easy to detect, with very noticeable differences in play. On this site, for no-limit holdem cash games, we have 18 different blind levels, ranging from 1/2 at the lowest, to 500k/1m at the highest. Cutting that in half gives 9 levels (though we see very little activity on this site at the highest two levels). Further, it is not like the highest two levels on this site probably have the strongest players in the world… if anything, these in general are our strongest amateurs, perhaps equivalent to the 4 to 7 dan amateurs in go, with pro 1 dan still being a meaningful step up.

Now, I’ll admit that poker as a whole draws a less intellectually elite crowd, and that means you have a lot of “club” poker players that with an equivalent chess rating would probably be rated wellllllllll below 1000. You just don’t have this body of players in chess and go that just want to gamble, or think that by knowing how a knight moves, they can now expect to win any game against a grandmaster. It’s like many poker players, if they were chess players, think it is enough to know how the pawns move, without even learning the way the other pieces move. So somehow people are happy playing poker with a level of skill that would be frustrating in these games where you get more immediate feedback about how bad you really are.

Finally, I think it is meaningful to ask if we have a measurable way of rating poker players that is more objective and logical like the rating systems used in chess and go. The objective of poker is to win money (or chips if you prefer, on a play money site). Those that achieve this more regularly are stronger.

In the past, in live play, these win rates were hidden, and it was more difficult to tell objectively who was crushing games. But with the advent of online sites, we also soon saw the advent of databases tracking results, and of course Replay poker actively displays bank roll. Now some players put more of their bank roll at risk, and so will shoot up and down the ranks more rapidly, but for players that play exclusively on one level (tables of the same stakes) for and extended period of time (preferably 10,000 hands or more), big blinds won per 100 hands played becomes a very objective way to compare two players and say who is stronger (or at least better at extracting chips in that environment), and could probably be used as the foundation for an objective, mathematical rating system.

OK… I’ve just kind of typed this out in a stream of thought. I certainly don’t think this suffices as convincing evidence that there are more skill levels in poker than chess, or even as many. But I believe there are, and that becoming one of the strongest players in the world at poker today is every bit as hard as becoming one of the top chess grandmasters in the world, and further has a much larger pool of people competing (which also impacts the bell curve distribution of strengths, and the size of the gap between the weakest and the strongest).

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I’m not sure what, if anything, you are asking, but I enjoy answering unasked questions, and have a solid record of being wrong, so…

Both chess and Go are perfect information games, poker is not. The proper application of theory to practice is much more clear cut in a game of perfect information.

Luck doesn’t play a part in either chess or Go, but does in poker. Yes, over a large enough sample size, the luck factor should be minimized, but never eliminated.

BBs/100 hands doesn’t feel like it would work that well for tournament players. What about SnGs? What if someone plays MTTs, SnGs, and ring?

I guess what I’m trying to say is that there might not be good way to quantify a player’s actual skill level across all formats.

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I concur with everything you said, BRAVO , Master of Wisdom .

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For whatever it’s worth, my opinion is that poker is vastly more complex than either Go or Chess, not simply for the reason SPG points at (information) but also because poker isn’t a single, unchanging game. It’s a whole universe of games with various formats, different betting structures, and different rules. Even the rankings change–got a Wheel? That’s a high only in some games; your 6-4 is all the same suit? That’s a flush, friend, and the game is KC Lowball, so the best hand is 7-5-4-3-2 of two or more suits. You’ve got a five-card hold? Now you can draw to it replacing up to five cards! Some games even have wild cards. Now, what? Think you’ve got all that covered? Now, try stripping the deck, eliminating all the cards below the 6. How does that work, eh?

The comparison isn’t even close. Most serious poker players specialize in a few games they understand and enjoy. Games that are “in fashion” today may well be ignored as “old hat” by tomorrow afternoon. In living memory, 7-stud accounted for more than 60% of all casino poker games; now, it’s about 15% of tables in casinos–and a lot of the smaller card rooms don’t spread it at all. Other than in California, virtually no one spreads Draw Poker anymore–and, for nearly a century, that was the only legal form of the game in that state. Some of this is merely changing fashions, but some is because players’ desires and preferences change, too.

Now, add in the element of money to be won or lost. Bankroll management alone can make or break a player–we see this every day, don’t we? There are serious players who absolutely master the cards–but never get control of their own money and end up broke, anyway. We see this daily!

So, I say there is no comparison to poker except, perhaps, war–and I’d prefer not to have to play that game.

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BBs/100 hands doesn’t feel like it would work that well for tournament players. What about SnGs? What if someone plays MTTs, SnGs, and ring?

Hmmm… I was thinking specifically of cash games, and tournaments of various kinds do feel quite different, and I haven’t given that much thought. BB/100 hands still feels like a good starting place for objectively measuring performance, but with the rising blinds, tournament play is fundamentally more volatile.

More often than not, the answers can be found in the wisdom of Caddyshack:

“Judge Smails: Ty, what did you shoot today?
Ty: Oh judge, I don’t keep score.
Judge Smails: Then how do you measure yourself with other golfers?
Ty: By height.”

There are many ways to measure skill levels in poker and all of them have limitations. As SPG noted above, this is a game of incomplete information and has an element of luck baked into it. If you are beating your games consistently, chances are you are a better player than your competitors. If you aren’t, then they are probably better than you are. Over time, the people who have beaten every game they have played in, find themselves playing each other. See who is beating those games and that’s the best in the world, IMO.

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This is interesting to think about. Since poker is the most complex game mentioned but also has the lowest skill requirement to participate, the distribution should be heavily weighted towards the bottom. Someone can begin playing poker and enjoying it after a 5 minute YouTube video. Not the case with chess or Go. Observation supports this as less than 10% of all poker players are actually winning in the longer term.

There are several sites that aggregate tournament results and give rankings. I think its based loosely on the way golf rankings are calculated - finishing results weighted by time (more recent weighted higher). Not a perfect system for sure but there is general agreement in who is at the top across several sites.

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Since poker is the most complex game mentioned but also has the lowest skill requirement to participate, the distribution should be heavily weighted towards the bottom. Someone can begin playing poker and enjoying it after a 5 minute YouTube video. Not the case with chess or Go. Observation supports this as less than 10% of all poker players are actually winning in the longer term.

While of course the strongest players will tend to win a disproportionate amount, driving down the number of winning players, especially when skill levels are skewed to the low end, I suspect that the rake is the largest factor driving the 10% figure. If there was no rake (or other form of “tax” to cover the business costs of providing a place to play), then even if 85% of the players were in the lowest tier or two of skill, I think you’d still tend toward a much higher percentage of winning players, especially given the separation of skill layers that having tables with different blind settings leads to.

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I’d argue that there really is some luck involved in both chess and go, though it is certainly much less prominent than in poker. But consider the following:

  • who gets black or white; in chess, you have a huge disadvantage with black, and in go, while it is quite a bit more balanced, black seems to probably have some advantage
  • which player wakes up in the morning with a mild fever, or some other ailment that impacts their ability to focus maximum brain power over what can often be a 5 or 6 hour session in chess, or a 12 hour session or more in go
  • opening choices often interact with your opponents competence in unpredictable ways; clearly players try to make advantageous choices here, but often your knowledge of your opponent is limited to an extent that this is a kind of roll of the dice
  • some days we just play better than others; you can probably attribute some of this to things like exercising more consistently, getting better nutrition and what not, but there is still a largely unpredictable variation from day to day
  • you can’t really see all the way to the end of either game most of the time (especially in go), and typically have many spots where you have multiple choices that are very close; which you pick to journey down, while certainly something that is impacted by skill, is also a reflection often of playing style, and yes, luck

a lot of words for a river winning joke site. this isnt really poker…

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Well, here’s a real world example to consider…

In televised high stakes cash games, Phil Hellmuth is down almost $300k overall. Should we conclude from this that he is unskilled?

And, no offense intended, but your attempt to put luck into chess and go are a little weak. One would have to squint to call the things you listed luck, and even then they don’t usually have a huge influence on the game.

Bobby Fischer once said, “I don’t believe in psychology. I believe in good moves.,” and I think that sums it up nicely.

There ARE skill levels in poker, but they are wicked hard to measure objectively.

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Oh, some other thoughts on factors that could drive the percentage of winning players down:

  • cash sites will have stronger fields that play money sites, driving edges down relative to the loss imposed by the rake
  • people in poker often probably illustrate the Peter principle: climbing in stakes until they reach a level where they are no longer winning players

LOL, truly spoken like someone who has only learned how a few of the pieces move.

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Is someone winning 30 BB/100 at 5/10 more skilled than someone winning 10 BB/100 at 5k/10k?

I like ROI as a metric for tournament performance because it is buyin independent. Could this (basically risk/reward) be used in rings too?

Is someone winning 30 BB/100 at 5/10 more skilled than someone winning 10 BB/100 at 5k/10k?

I’m not sure what the balancing point will be, and I expect it will also be site dependent. But I think if we had some sites that set up some kind of rating system based on win rate, with enough data it wouldn’t be too hard to calibrate that also, thanks to how players move up and down levels, and see their win rate change as a result.

For myself, from the Comparing Simple Strategies thread test runs, here’s how my average win rate changed at different levels. Note also that I was probably picking more complex, effective strategies for the higher levels, on the whole (though these numbers do still kind of run counter to some of my prior arguments, but variance is real, and there is still an overall trend down):

  • 1/2 (2,000 hand sample): 539 BB/100
  • 2/4 (2,000 hand sample): 222 BB/100
  • 5/10 (2,000): 230 BB/100
  • 10/20 (2,000): 210 BB/100
  • 25/50 (2,000): 289 BB/100
  • 50/100 (2,000): 160 BB/100
  • 100/200 (3,000): 77 BB/100
  • 200/400 (2,000): 40 BB/100
  • 500/1k (2,000): 131 BB/100
  • 1k/2k (2,000): 25 BB/100
  • 2k/4k (2,000): 20 BB/100
  • 5k/10k (2,000): 87 BB/100
  • 10k/20k (2,000): -6 BB/100
  • 20k/40k (2,000): 43 BB/100
  • 50k/100k (3,000): 49 BB/100
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I think this proves the flaw in using BB/100 to rate skill. Did you get progressively less skilled as you employed better strategies and moved up in stakes?

From a relative perspective, probably yes, but not in any absolute sense.

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I think the numbers did not help me make a strong argument, or the fact that I was probably “releasing” more of my skill as I played at higher stakes, but the samples are a bit small, and so you’d expect a degree of bumpiness, and the overall trend does show it got harder to win as much at higher stakes.

Note that from the beginning I defined the BB/100 metric as a way of measuring skill within a single blind environment. There would also need to be a scaling factor to extend beyond that, and you’d need some metrics to figure out the right scaling factor (and could test the effectiveness of that as players naturally moved up and down).

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Oh sorry, I missed that. Your OP had so many wurds for a lucky river joke site!

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There was a discussion about this a while ago - talking about the theoretical maximum bb/100 to be exploited at any given stakes. That maximum should decrease as skill levels increase. If skill levels and stakes are positively correlated (no matter how loosely), then the maximum possible winrates also decrease as you move up in stakes.

While no one has perfected a skill rating system for cash games, there are general guidelines to let you know how you are doing relative to the population. For example, the top winners at 25nl are probably taking 25-30bb/100 off the table. At 500nl, that number goes down to 4-5bb/100.

I suppose if we had all the data from all the hands played at each stake, we could find out the maximum bb/100 available to be exploited from the population? Then, you could rate players by what % of that they captured.

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At some point, we would have to define “skill.”

Knowing to mitigate the effect of variance through bankroll management is a skill.

Selecting a table where your edge is higher than the rake is a skill.

For that matter, selecting the stakes you can consistently beat is a skill.

Being well rested and free from distractions (mental focus) is a skill.

There are many factors that go above and beyond theoretical knowledge and its application. There’s no easy way to fully define skill, so there can be no simple way to define it.

Yeah yeah, don’t throw away the good because it’s not perfect. I get that, but I’m an engineer and hate spending time developing a metric that is unreliable and inaccurate. “Close enough” doesn’t work in my world.

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