Wednesday, September 19, 2012

20 thoughts on skill vs. chance in poker, part 13: On control and equal challenges

<-- Part 12: Why not sports betting and investing?

One common approach to considering the nature of the role of chance in a game is to focus on the degree to which the players and their actions or decisions exhibit control over the outcome. Certainly, in a game with close to no intrinsic random elements such as chess, ignoring the coinflip to start the game, the actions of the players will be essentially the only factor which controls the outcome, whereas in games of pure chance such as roulette, the player clearly has no control at all over the outcome. When considering whether or not market-based activities such as sports betting or investing might be games of skill, this approach would focus on the fact that the player cannot influence the result of the bet, so it draws a distinction between betting on an external event and playing a game like poker, as we have in the previous thought.

The Pennsylvania Supreme Court once used this approach to rule on the predominance of chance in a house game called "Electro-Sport", apparently some bastardized non-poker derivative of poker. Thankfully, the court recognized this key difference between video poker and poker. This ruling was cited in Pennsylvania V Dent as follows:
While appellee has demonstrated that some skill is involved in the playing of Electro-Sport, we believe that the element of chance predominates and the outcome is largely determined by chance. While skill, in the form of knowledge of probabilities, can improve a player’s chances of winning and can maximize the size of the winnings, chance ultimately determines the outcome because chance determines the cards dealt and the cards from which one can draw — in short, a large random element is always present. That the skill involved in Electro-Sport is not the same skill which can indeed determine the outcome in a game of poker between human players can be appreciated when it is realized that holding, folding, bluffing and raising have no role to play in Electro-Sport poker. Skill can improve the outcome in Electro-Sport; it cannot determine it.

There is a danger in this sort of approach when it comes to poker with the distinction between "improving an outcome" and "determining an outcome". If the "outcome" in poker were considered to be which player wins a single hand, then this creates a focus on who wins at showdown rather than on how many chips are won or lost in each pot, which will be treated in more detail in a future thought. Still, I can think of no games of skill that don't involve the players having significant control over the outcome, though often the player will not have full control, as in poker. It's pretty good as a rule of thumb. Every strategy game where the strategies have a nontrivial impact are games where players have some degree of control over the outcome; players choose strategies, and strategies contribute to outcomes in games of skill. What I feel this approach does best is to cleanly separate strategy games from advantage gambling without strategic interaction (e.g. market-based activities, video poker such as this Electro-Sport), and it does so in an intuitive way. Without the strategic interaction of a multiplayer game, there is generally no means for a player to control the outcome in a one-player game.

A related but different approach to predominance focuses on the nature of the role of skill in a game by focusing on whether players of a game are always presented with "equal challenge" as in whether or not the particular game positions and strategic opportunities available to one player during a game will always be available to the other players as well. This was famously captured in a North Carolina Court of Appeals ruling, also cited in Pennsylvania V Dent:
[W]hile all games have elements of chance, games which can be determined by superior skill are not games of chance. For example, bowling, chess, and billiards are games of skill because skill determines the outcome. The game itself is static and the only factor separating the players is their relative skill levels. In short, the instrumentality for victory is in each player’s hands and his fortunes will be determined by how skillfully he use (sic) that instrumentality. Poker, however, presents players with different hands, making the players unequal in the same game and subject to defeat at the turn of a card. Although skills such as knowledge of human psychology, bluffing, and the ability to analyze odds make it more likely for skilled players to defeat novices, novices may yet prevail with a simple run of luck. No amount of skill can change a deuce into an ace. Thus, the instrumentality for victory is not entirely in the player’s hand. In State v. Taylor, our Supreme Court noted this distinction. 111 N.C. 680, 16 S.E. 168 (1892).
Ah, yes, no amount of skill can change a deuce into an ace. Indeed, this approach to predominance turns out well for mostly-deterministic games of skill (modulo coinflips) but not for many other games of skill such as poker, bridge, backgammon, or Scrabble. (Also note that this ruling, like many others, treats "game of skill" as "game involving skills".)

The premise here is shaky. While the possibility of players being presented with unequal challenges does necessarily imply the presence of chance in a game, it has no bearing on the depth of skill in a game. Really, this approach presupposes that a fair card game where each of the players have the same probabilities of getting dealt each possible hand is an "unequal challenge" as soon as the players are dealt different hands. Competitive games with intrinsic and overt random elements, such as poker, bridge, backgammon, and Scrabble, are still symmetric games as long as the probabilities are fair, even if players end up getting given different cards each time they play. The focus should be on the structural symmetry, rather than on the presence of random components.

Overall, the presence of equal challenge doesn't seem to correlate very well with the influence of either skill or chance in a game. Rando chess, with any probability of reversal, does happen to present its players with an equal challenge, but can be modified to reach any desired point in the fallacious skill-chance continuum. More importantly, duplicate poker, as we'll discuss soon, is a poker variant that manages to present its players with more of an equal challenge but does not necessarily eliminate (or even reduce!) the role of chance in the game. All that this approach captures is that the game contains a nonzero element of chance, but, despite this fact being overlooked by the ruling, this is true even for almost-fully-deterministic games such as chess and billiards, where the random selection of the turn order does indeed present the players with an unequal challenge.

Of these two approaches, both are fairly narrow. As the treatment of the many thoughts in this essay have shown, there is much more relevant detail and nuance to the relationship between skill and chance in games than can be captured by a single argument alone. That being said, as far as simple arguments go, the idea of control is a reasonably good measure of the presence of skill in a game, though it doesn't measure chance well. On the other hand, the idea of equal challenge must necessarily discriminate against games whose random components generate a variety of gameplay, despite this being a common component of many high-skill games.

Part 14: Does rate of showdown matter? -->

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1 comment:

  1. Hey man keep up the good work. I'm enjoying the blog!

    David @Transformpoker


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