In most countries the regulations of gaming depend on the fact that the outcome of a game is predominantly influenced by skill or chance. In the past several proposals were given to measure skill in games (predominance test or predominant test)., 
In a paper, which I published in 2017 in a German legal journal , and in an appended chapter of the 7th German edition of my book "Glück, Logik und Bluff"  I presented an overview of laws, judgments, legal and mathematical literature on this topic. Some of these documents are dealing with proposals of a skill factor, which can partly interpreted as probability that a game is determined by skill. Of course, for most games this factor isn't really a probability in a strict mathematical sense. Anyhow, it is possible to compare the success of low skill players and high skill players based on the relative frequencies of their success in a sequence of games.
The legal interpretation of the word skill is depending on jurisdiction. It may differ from state to state. But mathematics is an universal science. It is restricted to logical implications and helps to analyze reasoning. But there isn't any skill game in a mathematical sense, because a jurisdiction defines the context of playing the game and the meaning of a word does not matter in mathematics (David Hilbert explained axioms of geometry with the following words: "one must always be able to say, instead of 'points, straight lines, and planes', 'tables, chairs, and beer mugs'."). For example German jurisdiction requires to look for skill levels reachable by an average player.
In the mentioned papers I examined several simple games as case studies and benchmarks using insights based on game theory and statistics (two of these games are illustrated in the diagram below). As conclusion I presented a sufficient condition for a predominance of skill in a game.
In a first step the criterion is limited to the simple case of a symmetric two person game with only two outcomes +1 and -1. Such a game is predominantly skill influenced if the following sufficient condition is fulfilled: You can find two persons who a are both relevant in the legal sense (depending on the jurisdiction, which means for example in Germany that they are average players) where the better player has a probability of more than 0.75 to win a game. In this case the probability for an outcome decided by chance cannot be greater than 0.5, because each game which is decided by chance is won with probability 0.5 of each player.
The main idea of this sufficient criterion is very basic: The symmetry of the game can only strongly disrupted in average by the influence of the players. Similar considerations were alraedy made in the past, but it seems that there were some minor gaps in the argumentation concerning the restriction to symmetric games respective to the sufficient character of the criteria., 
I presented similar criteria for other games, too: non symmetric games, games with several amounts of outcomes and games with more than two players. In the case of a tournament I computed the minimal number of games which is sufficient for a predominance of skill. An application to the game of poker is possible, but only based on complete rules including a fixed poker variant like Texas Hold'em, limits, number of players and tournament rules.
The diagram shows two symmetric two-person games, which are equivalent in the sense of their game-theoretical minimax analysis:
Each of these two games starts with two random moves depending on a fixed probability p. Depending on the results of these two moves the game terminates or continues by playing subgame of pure skill: a chess endgame king-rook-king (left game), respective a match of Go with komi 6½ (right game, a draw is not possible).
In the case of p = 0 both games are equal. The game is a pure game of chance.
In the case of p = 1 both games are consisting of a random decision of colors followed by a pure game of skill.
Most interesting is the case p = ½: The left game will be won by the player moving the white pieces. Therefore each player will win in 50 % of the plays, like in a symmetric pure game of chance. In the right game a player with more experience will win 75 % of the plays in average. In the case of p > ½ the game is predominated by skill.
Some important judgments concerning skill and chance in games: