Thinking of skill in a different way

[Daisydog]

Assume the following:
1. There exists a game of pure skill
2. Two people play this game and one is more skilled at the game than the other.

Will the more skilled player always win? I say no because I think there is a distinction between a player's overall skill level and how skillfully the person plays for one particular game.

When we say someone is more skilled, we don't mean the person always plays with more skill, we mean that on average the person plays with more skill. If skill levels are close, then one player might play with more skill 51% of the time. If one player is much more skilled than the other, he might play with more skill 90% of the time.

I guess I'm viewing a person's skill level as the mean of a distribution and how skillfully the person plays for one game as a sample from the distribution. The variance of the distribution would be a measure of the consistency with which the person plays.

If we think about a person's skill as the mean of a distribution then we are able to say that in a game of pure skill, the more skilled player will not always win.

Does this make sense?

[soko]

If luck is not involved in the game at all, there will be absolutely no variance and therefore the better player will always win.

[MaxWeiss]

If there was a game of PURE skill, then the skilled player would have to always win. If you have a group of people with different amounts of skill you could say one was more skilled than another, but in a head up match, there is the skilled one and there is the unskilled one who will always lose.

Ideas like this happen IMHO because of a misunderstanding of the terms skill and luck. There is skill involved in any game. Skill is the ability to gather and utilize useful information. Luck is the fact that you will never have all the information necessary (except in your game) and because of that, the outcome is not 100% certain. I don't think there is a game out there that is pure 100% skill.

[arahant]

I guess you define skill rather oddly then.
When a lower rated chess player beats a higher, where is the luck?
The OP said something so obvious i was going to mock him for it, then the first two responses are both disagreement...

[soon2bepro]

[ QUOTE ]
Does this make sense?

[/ QUOTE ]

It does make sense, but you have to consider outside luck. For example, in chess, there is no luck INSIDE the game, but there is a lot of luck from outside.

One has a hangover from last night. One has a cold today. One is thinking about the beautiful girl he's starting to date. Also, the game itself relies on knowledge. If a player is more experienced at playing one opening than the other, and the other chooses this opening (not knowing this, obviously), then he may very well lose that game.

Etc, etc.

[madnak]

[ QUOTE ]
I guess you define skill rather oddly then.
When a lower rated chess player beats a higher, where is the luck?
The OP said something so obvious i was going to mock him for it, then the first two responses are both disagreement...

[/ QUOTE ]

A failed gambit. The worse player didn't sleep well that morning. There are a wide variety of ways luck can affect it.

Do you believe that if two chess players face off, the same one will always win? (Let's assume no change in skill.) I think that's a ridiculous idea.

[Daisydog]

[ QUOTE ]
[ QUOTE ]
I guess you define skill rather oddly then.
When a lower rated chess player beats a higher, where is the luck?
The OP said something so obvious i was going to mock him for it, then the first two responses are both disagreement...

[/ QUOTE ]

A failed gambit. The worse player didn't sleep well that morning. There are a wide variety of ways luck can affect it.

Do you believe that if two chess players face off, the same one will always win? (Let's assume no change in skill.) I think that's a ridiculous idea.

[/ QUOTE ]

The same player will not always win. However, I believe that in a game of pure skill it is not luck that causes this to happen. There is no random element in chess. Maybe the more skilled player loses because he makes an uncharacteristically bad move. Is that luck? No, I think it is that the player didn't play with as much skill for that particular game. My whole point is that if someone's skill level is X, they sometimes play at a slightly higher level and sometimes at a slightly lower level, but on average they play with a skill level of X. Therefore, even in a game of pure skill, the more skilled player can still lose.

[madnak]

This strikes me as semantics. I would say that yes, if I get a bad headache during a chess game, that's bad luck for me. Of course, you can also say that the headache is diminishing my level of skill. The point for the purposes of this discussion is still the same - the more skilled (at the time, not on average) player will always win against the less skilled (at the time, not on average) player in a game of pure skill.

Which I don't think chess is. What about a failed gambit? It may be the correct play based on all the information a player has, but due to unknowns about the psychology of the other player may have negative results. Also, what about a poor player who blunders into a good move by accident? This is frequently how games are won by very casual chess players, "oh wow, look at that - I got you in checkmate!"

[keith123]

there are no pure skill games, including chess.

[Magic_Man]

[ QUOTE ]
I guess you define skill rather oddly then.
When a lower rated chess player beats a higher, where is the luck?

[/ QUOTE ]

Some people already addressed the issues of sleep, sickness, distractedness, etc. But there is another important issue here - the reliability of chess ratings. Your rating changes when you win/lose/draw against another opponent. If a lower-ranked player beats a higher-ranked player, it may be because neither of them has played enough games to know what their "true" ranking is. In fact, there will never be a way to know. Every time you play a match, you are focusing and trying to learn more about the game, so arguably, every time (or nearly every time) you play, your skill level increases. If we had two players who had some sort of learning disability imposed on them so that their skill could not increase, AND they had also all played against a million opponents (who had also each played against a million opponents so that their rankings were correct), then we could probably go by their rankings to determine who would win 99.99% of the time, assuming that they were equally rested, in good health, and not distracted.

~MagicMan

[arahant]

[ QUOTE ]
[ QUOTE ]
I guess you define skill rather oddly then.
When a lower rated chess player beats a higher, where is the luck?
The OP said something so obvious i was going to mock him for it, then the first two responses are both disagreement...

[/ QUOTE ]

A failed gambit. The worse player didn't sleep well that morning. There are a wide variety of ways luck can affect it.

Do you believe that if two chess players face off, the same one will always win? (Let's assume no change in skill.) I think that's a ridiculous idea.

[/ QUOTE ]

I don't get your response. Both I and the OP specifically said that we feel the lower rated player has a chance of winning.

[arahant]

[ QUOTE ]
there are no pure skill games, including chess.

[/ QUOTE ]
We have language for a reason, you know. Obviously, 'luck' and 'skill' have no objective meaning in a deterministic universe. For the purposes of discussion though, I think it is safe to consider chess a game of skill.

I like how every thread now is a semantic debate...bunch of dual philosophy/linguistics majors here...

[keith123]

we are considering variance to be luck, right? the weaker the players involved in a game like chess, the more variance we can expect, right? like two brothers that get a chess set for Christmas and learn all the rules of the game. most of the time each brother will win some games. the same is true for shooting free throws. or anything else. over the long haul, the best player will end up winning more though, even at a relatively low level of skill.

we can call games of skill games that can have a controlled outcome, where chess and free throw shooting etc can fit, but poker never will.

[Daisydog]

[ QUOTE ]
we are considering variance to be luck, right?

[/ QUOTE ]

I'm not. I'm saying in a game like poker, luck (or the randomness of the cards) certainly causes variance. But there is an additional source of variance that exists in poker as well as games of pure skill. If someone loses a game because he makes bad decisions, that is not luck. Highly skilled players can make bad decisions (e.g., Mike Matasow). Most of the time they make very few bad decisions but occasionally they do. That causes variance. The most highly skilled players are those that make the highest percentage of good decisions, but they don't always make good decisions. That's why a less skilled player can win against a more skilled player in a game of pure skill. Over many games the less skilled player will not win, but occasionally he will win one game.

[jogsxyz]

[ QUOTE ]
there are no pure skill games, including chess.

[/ QUOTE ]

What about tic-tac-toe? You against a five-year old.

[jogsxyz]

[ QUOTE ]
we are considering variance to be luck, right? .


[/ QUOTE ]

That's the way I see it. For limit poker luck is your standard deviation in bb/100 hands. Skill is your winrate in bb/100.

[bigpooch]

CHESS
------

Let's assume for the sake of argument that this is one of
the games of pure skill. If there are two players playing
and human A is stronger (or more skillful) than human B and
not only do A and B agree that is the case, but the FIDE
rating of A is greater than that for B (let's say it's at
least 100 rating points) and that the almost unanimous
consensus of the chess fraternity would also agree that A is
stronger than B.

Let's say A plays B in a tournament. Will A ALWAYS win?
Obviously, if A's FIDE rating is 2500 and B's rating is
2400, any knowledgeable chess player would say no. This
would especially be the case if A had the Black pieces
because of the inherent practical advantage that any
reasonably competent player (such as B) has with the White
pieces.

Not only that, but suppose A and B were playing in a Swiss
tournament (there aren't many rounds and the field has a
few hundred players) where the monetary prizes are very
"top-heavy" in that A could not afford to have many draws in
order to win a decent prize. Player A, even though he has
the Black pieces, may take a risk and play a dubious line,
hoping that Player B is on unfamiliar turf and make some
errors that give A some practical winning chances. This
happens sometimes in these tournaments: an acquaintance of
mine has mentioned "rolling the dice" but obviously, things
sometimes turn out very badly and A sometimes ends up losing
the game!

Also, a chess player's skill is measured by an Elo rating
which is a way of measuring success versus humans (in rated
tournaments) that are prone to make mistakes. Success is
not simply finding the best moves or making less errors in
chess, but exploiting weaknesses in the opposition and this
can take many forms; here are just a few:

a) Does the opponent have an exploitable flaw in his
opening repertoire? Serious chess professionals will know
their opponent's tournament games during the last year if
they are diligent enough to bring a laptop armed with
chessbase or a rich database of games.

b) Is the opponent uncomfortable with certain types of
positions? If there is a great disparity in the frequency
of mistakes, it's clear to steer the game into lines where
the opponent is more likely to make a fatal error. A strong
IM or GM can simply look through several of his opponent's
games on his database to get an idea of what kind of player
his opponent is and make a fairly accurate assessment.

c) Is the opponent is good physical shape? If he had very
long games in the last two rounds, it pays to drag the game
into a long positional struggle with the goal of reaching a
very prolonged endgame and this is especially important if
the opponent does not play sudden-death time controls as
well as his FIDE rating may indicate.

Also, since a player's strength is not just the "error rate"
but also how well he uses an "exploitative strategy", it's
subject to some variability. Also, some players have been
notorious in the "variance" of their playing strength: some
may play like a GM in one game and a "patzer" the very next
game! On the other hand, there are players that prefer to
steer the game into quiet lines and endgames, so they tend
to have a disproportionate number of drawn games and their
strength seems to be fairly stable from game to game. It
does make some sense if FIDE were also to have another
number to describe this "variance".


OTHER GAMES
--------------

I would think that the most skillful games, not in any
particular order, that require knowledge, analysis and
positional or strategic understanding to excel are:

Go (this is considered by some to be the most skillful)
Bridge (especially team IMPs)
Backgammon (especially matches)
Poker (especially deep NLHE cash games)

[madnak]

[ QUOTE ]
[ QUOTE ]
there are no pure skill games, including chess.

[/ QUOTE ]

What about tic-tac-toe? You against a five-year old.

[/ QUOTE ]

What about two five-year-olds?

In order for a game to be pure skill, there has to be no luck involved even when it's a couple of monkeys playing. It's impossible, because a monkey might just make the right move by mistake. That possibility means that no game can ever be pure skill.

Also, plenty of 5-year-olds rock the tic-tac-toe.

[Daisydog]

[ QUOTE ]
[ QUOTE ]
we are considering variance to be luck, right? .


[/ QUOTE ]

That's the way I see it. For limit poker luck is your standard deviation in bb/100 hands. Skill is your winrate in bb/100.

[/ QUOTE ]

In poker, do you ever have times when you are making more poor decisions than normal? If yes, then at least part of your standard deviation is not due to luck. I agree that in the long run your win rate is determined by skill.

[hmkpoker]

I agree. A game can only be pure skill if the player has both perfect information, AND the ability to predict every possible outcome. For this to be the case, a game would have to be very simple, and even then someone just making guesses is still playing a luck game. Educated partial information guesses occur frequently in chess (mostly during mid-game). The information may be perfect, but there's no way someone can account for all possible situations until late game (at which point luck becomes irrelevent, and the game, for all practical purposes, has been resolved.)

[51cards]

[ QUOTE ]
there are no pure skill games, including chess.

[/ QUOTE ]

Since your gunna claim a universal nagative here, do you actually have a proof? A good definition would be a start.

[51cards]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
there are no pure skill games, including chess.

[/ QUOTE ]

What about tic-tac-toe? You against a five-year old.

[/ QUOTE ]

What about two five-year-olds?

In order for a game to be pure skill, there has to be no luck involved even when it's a couple of monkeys playing. It's impossible, because a monkey might just make the right move by mistake. That possibility means that no game can ever be pure skill.

Also, plenty of 5-year-olds rock the tic-tac-toe.

[/ QUOTE ]

Ok, what about a game where the number of possible moves is the cardinality of the reals, and the number of moves that lead to a win or a possible win are finite?