[nnoobi]

I think an additional factor to consider in addition to Luck\Skill is Open\Closed.

Chess is a completely Open game. All information about the current state of the game is available. The only luck present is the player starting order.

Yahtzee is another open game. Random chance is present on every turn.

Most other games have varying degrees of closed-ness. In poker the player's hole cards are the closed items; common cards, up cards, betting actions and the like are the open items.

Closed games are often confused as lucky games by people who do not understand the skill involved. However, the real impact of closed-ness is to lengthen the period of time necessary for skill to overcome luck.

In order for the skill of the player to become the determining factor of a game that has both closed-ness and random elements, many games must be played.

Ranking Luck/Skill and Closed/Open on scales of 0-10 for a single game/round we have:
Chess (10,10)
Yahtzee (3,10)
Bridge (6,6)
NL Poker (4,3)
Limit Poker (5,4)

The Luck/Skill ratings for poker games seem pretty low. That's a result of the random events that make up a single hand of poker.

If the game was a 10 hour contest, then these games would look like this:
Chess (10,10)
Yahtzee (7,10)
Bridge (9,7)
NL Poker (8,5)
Limit Poker (8,5)

Basically, skill values increase as random events balance out and openness increases as you learn about your opponents.

I think bridge has skill determine the outcome of the event more often. This is not a commentary on the skill of bridge vs. the skill of poker but more of a result of the skill necessary to utilize the open-ness of the game in the later stages of the hand.