Here is from the English translation:

“After examining different possibilities, I am proposing a division into four main rubrics, depending on whether, in the games under consideration, the role of competition, change, simulation, or vertigo is dominant.”

So here he phrases it as a question of each rubric being “dominant”.

This is utterly fascinating. Jesper, I know you like blaming Caillois (as you did with the rules and fiction thing in Half-Real), but he never posits that skill and chance are mutually exclusive – quite the contrary, in fact, as he could be submitted as proof that poker is a game of skill more than chance. I just happen to have the original french text at hand since my students had to read it this week. I am not using quotation marks since I am translating on the fly, but this is all taken from his description of alea:
Some pure examples of this category would be dice, roulette, heads or tails, baccara, lottery, etc. The player is entirely passive, and does not deploy his qualities or dispositions, the resources of his motor/reflex/coordination skills (“adresse”), his muscles, or his intelligence.

He does say that alea relies on a player-attitude exactly at the opposite of that which agôn expects, but then goes on to give examples of games where agon and alea are found together:
Agon is a taking in charge of personal responsibility, alea is a suspension of will, an abandoning to fate. Some games such as dominoes, “le jacquet” (whatever that is), most card games, combine agon and alea: randomness decides on the distribution of the cards in hands, and each player then exploits, to the best of their abilities, that which blind fate has given them. In a game such as Bridge, it is knowledge and reasoning that constitute the player’s defense and allow him to make the best out of the cards he received: in a game along the lines of poker, it is more qualities of psychological penetration (mind-reading) and character. (the poker-face and physical composition, I assume. the exact nature of the skills required by poker is of course debatable, but that’s not the main point here.)

The balance between chance and skill can be better explained if we continue a few lines down the text, with:
alea’s function is not to reward the most intelligent players, but in the contrary to abolish natural or acquired superiorities of individuals in order to put them all on an absolute equal foot in front of the blind verdict of chance.

Given this definition of chance and skill, I would definitely say that poker belongs more to skill than chance (but then it looks to be common sense around these blogging parts). For all the probabilities and statistics involved in getting a good hand, when one takes a step back from the mathematical microscope and looks at the overall unfolding of a whole game, ultimately it is the player’s decision to raise or match his opponents’ bets and his ability to recognize when it is a good opportunity and when the risk is worth it that determines his “chances”. (pun not intended, but now that I see it I kinda like it.)

A game without skill is LCR (http://www.boardgamegeek.com/game/3522)
A game without chance is anything with perfect information (chess, draughts, most modern abstracts).

is this a “definition of game vs play” issue?

I would have said skill and chance are directly related, in a non-linear way.

@Petri: I’ve visited Finland a couple of times and noticed sometimes there are little casino tables in the corners of bars, tended by a croupier. How does that work? Are fruit/slot machines not popular? Can you play any game? I think I just noticed people playing pontoon/blackjack.

But that’s not what I wanted to say. I just wanted to point out Richard Garfield’s Getting Lucky article in Game Developer Nov 06. It really lays it out why poker is a game of skill and luck and I think they should have used that article as evidence in court :)

So, yes Poker involves both skill and chance, as loads of cards games, but games solely based on chance or skill does exists, and I think that explains why he separated agon from alea.

By-the-way, don’t you think that the two others categories of Caillois, namely ilynx (vertigo) and mimicry, are related to skill and not to chance ?

I mean, the ilynx behavior implies oneself to test its own limits, so are related to his skills.
And a “well-played” mimicry require the player to skillfully reproduce or imitate some social role.