[Apreche]

This article is correct, mathematically, from what I can tell. However, the author seems to not understand the meaning of skill.

Apparently to the author a skilled player is one who knows and plays all the odds correctly whereas an unskilled player plays randomly, or sub-optimally. If all players are equally knowledgeable of all the probabilities involved, then the game is a game of luck.

A true game of skill is one in which there is no luck factor. No matter the relative skills of the players, the most skilled player will win. For example, boxing is a game of skill. Poker is not. Two grand masters of poker playing against each other, the result will be determined by the cards. They might as well play Candy Land instead.

[tansey]

I agree that the paper makes some naive assumptions. However, you seem to be equating poker to chess, which is a common but erroneous analogy.

Poker is a MUCH tougher game (dozens of orders of magnitude, depending on the variant) than chess. We have no idea how close to optimal any human is at the game. Similarly, computer opponents can only play well in very limited settings like heads-up, fixed-limit Hold'em, where the game tree is a reasonable size.

Also, it depends on the period of time that you're looking at. If two people play a single hand, it's almost entirely luck. However, as the paper argues (though again in a simplistic way), as the number of iterations increases, the CLT comes into play and skill wins out.

This is true, even for "grand masters" in poker. Tom Dwan has an open challenge to play him in 50,000 hands online. If his opponent is ahead after 50,000 hands, he will pay them an additional $1M. He's not doing this because he loves to gamble. He's doing it because he knows 50K hands are a sufficient sample size to significantly reduce the luck factor.

Do you think a game like backgammon is also luck?

[ThomPete]

It is much more so than chess.

[aquateen]

I am not sure how you quantify toughness, but this is the worst use of "orders of magnitude" I've ever seen.

More so, since I have spent a nontrivial percentage of my life playing both games.

[tansey]

Size and complexity of the search space (i.e., the game tree). The tree is several orders of magnitude larger for poker than for chess.

I've spent a non-trivial percentage of my life both playing and researching AI for poker. See http://poker.cs.ualberta.ca/publications/billings.phd.pdf for an initial discussion on the differences between the 2 games' search trees. He notes that for 2-player, limit hold-em, the game tree consists of 1,179,000,604,565,715,751 nodes. The tree expands exponentially as you add players and different betting sizes. For no-limit and other real-valued variants like pot-limit, the game has an effectively infinite search space.

[aquateen]

If I recall, there are more possible chess games than atoms in the universe. So even if you were to quantify toughness as number of possible decisions, it would still be completely off. However, in both those games, a lot of the plays would be ridiculous.

It's easier to try and measure toughness by the time/effort it takes to be competent or the best. In this case I would say chess is hands down much tougher.

[tansey]

Sure, the number of possible moves is huge in both games. However, it's more about the number of relevant moves at a given game state. Alpha-beta algorithms for chess can do a much more thorough search than their poker-specific extensions and related methods like MCMC.

I suppose if you're measuring difficulty of a game as how difficult it is for a human player to beat the current masters, then that seems a little unfair. Poker has been around for less than 200 years and the current variants are less than 100 years old. Chess has been around since the late 1400s according to the Wikipedia article. There has been a lot more research and time spent on chess, and the community is consequently much more mature and skilled.

[aquateen]

To clarify, before you were comparing a tree of every possible move in a chess game against the decisions in a poker game?

That has to be a joke to compare the games that way. Even here you mention number of relevant moves at a given game state. I have to be misunderstanding that. Bet/check/fold vs say half dozen candidate moves?

I've been assuming difficulty for a human the whole time, to attain any level of skill. Since the chess community/theory is more established, it's going to be a more difficult game.

[mistermann]

Also, don't forget that when you're playing chess, you can see your opponents pieces on the board.

[yurisagalov]

That's not exactly correct. Poker is a game of probabilities, which means that it has built in varience, which people call "luck". In a game of poker where two "grand masters of poker" play againt each other in a vacuum (i.e. one tournament, or one hand, or whatever you want), the result may be determined by the cards alone. HOWEVER, as is the nature of varience and probability, given a sufficiently large sample of hands/tournaments/sessions, the better player WILL converge to be a winner. The margin by which he is a winner will be determined by his skill.

Prior to focusing primarily on startups and entrepreneurship, I spent a lot of time playing a lot of online poker. I've put in close to a million hands over a few years at the micro/small stakes, and I've seen bad beats, I've had bad beats, I've put on bad beats, which can all be attributed to "luck", and the swings of the day can be attributed to luck, but over the entire life time of my game, you can certainly see gradual improvement that can be attributed to skill.

When we look at televised tournament poker (not shows like Poker After Dark / High Stakes Poker, where the players need only to have the sufficient buy in and/or be invited to participate), it is not particularly surprising to see the same "grandmasters" (or pros, or whatever oyu want to call them) appear over and over again. Yes, they don't win every tournament, or every hand, or every session, but in the long term, they do win (assuming they don't start playing poorly).

[ThomPete]

Wouldn't that would mean an accumulation of grand masters that would then by an large win all tournaments in the long run. Is that in fact what is happening?

Gus isn't winning every tournament. That might be due to the fact of other better players entering the game. But if your theory is correct wouldn't it mean that the more you play the better you become?

It would seem to me that a game where so much information is hidden from you and that information was randomly distributed luck is a bigger part than skill.

[yurisagalov]

Phil Hellmuth has 11 WSOP bracelets and 75 "in the money" (ITM) finishes

Doyle Brunson and Johnny Chan have 10 bracelets as well as 33 and 42 ITM finishes, respectively

Erik Seidel has 8 bracelets and 57 ITM finishes

Phil Ivey has 7 (two of which he got last year, and he final tabled at the main event as well) and 36 ITM finishes.

Daniel Negranau has 4, and 42 ITM finishes

and this is just in the WSOP. I'll leave the WPT tournaments to you to look up :-)

I don't know what's going on with Gus, I don't really follow poker much anymore, but I know he's still a formidable player, even if he's not winning as much as he used to. That being said, Gus isn't someone I'd consider a "grandmaster"

Playing alone does not make you better unless you strive to improve (this, at a high level means, learning. playing != learning in the game of poker. playing is definitely crucial, but you really need to review and study the hands and the players post mortem. This is very similar to chess, imo.)

The younger players coming in (i.e. Tom Dwan) have the stamina and energy to put in _serious_ hours that allow them to improve and adapt much quicker and faster than older players, it's just the nature of the beast.

[tptacek]

There is luck involved in boxing. There is much less luck involved in boxing than there is in poker, because poker is a game that is about managing risk and uncertainty.

Chess and Go may be "pure skill" games, but there are very few popular games, sports, and practices that are similarly pure, and so the notion of how valuable or important "skill" versus "luck" is becomes murky.

[michael_dorfman]

They might as well be playing Candyland? Not really.

The luck of the cards tends to even out over time-- this is why tournaments consist of a large number of hands.

I'm not sure of the specific numbers with Poker, but an expert Cribbage player tends to win about 55% of the time.

[aquateen]

Just because there is an element of chance doesn't mean it's not a "true" game of skill. Sites like pokertableratings.com and sharkscope.com keep track of cash and tournament winnings, and maybe 100k hands gives a good sample that overcomes variance.

Poker's become much tougher the last five years or so. Quite a few of the top players formerly played Starcraft, MvC2, Warcraft, backgammon, Magic the Gathering, chess, etc. at the highest levels.

That mentality does make the games profitable though.

[dazzawazza]

I think you are forgetting the element of psychology that enters in to poker.

While it's true that all the top players understand the odds equally well there are some players that are still considered better poker players as their ability to read other players is better tuned. That's the skill element.

[ThomPete]

Exactly. Chess is another example.

[tspiteri]

There is a good article about luck in chess here: http://www.chessninja.com/migonchess/migonchess005.htm

To quote a bit:

There is no "chance" on the chessboard, the pieces don't move by themselves. ... However, "extraordinarily improbable" things happen all the time.