Monday, September 17, 2012

20 thoughts on skill vs. chance in poker, part 11: Why not blackjack or other casino games?

<-- Part 10: Games of skill vs. "involving skills"

We've generally restricted our focus so far to symmetric, closed, competitive strategy games (orthogames). Traditional casino gambling almost exclusively consists of one-player "games" played against the house, structurally dissimilar from poker and from all other traditional games of skill. To me, the presence of strategic interaction is the essence of skill when it comes to non-physical games, which is why I feel that the categorical divide between one-player and multiplayer games should be central to the approach of classifying games. However, there are some subtleties to the dividing line between house games and competitive games that are worth considering further before we assume them all away.

The argument that I find to best illustrate the ideal legal distinction between house games and poker was stated well in the law review article Video Poker and the Skill Versus Chance Debate. Unfortunately, the article does not seem to be freely available anymore, but I had noted its summary of its main idea:
In order to be profitable to the casinos, these games [video poker] must be based on chance. If skilled gamblers could win regularly, the casinos (or bar or restaurant owners) would begin to lose money, and the machines would soon be removed from the gambling floor.
This is a sensible approach to the definitions of skill, chance, and predominance; any 1-player gamble played against the house that a for-profit corporate entity offers openly must be a game of chance, because, in theory, it wouldn't make sense for a game freely and openly offered by a business to be a game of skill, as adverse selection and a rational customer base would ensure that the profitable customers would bankrupt the company. Games of skill could only exist between two or more players competing in a symmetric game, where perhaps a company could take a fee for facilitating the game.

This definition is clearly an easy fit for most -EV casino games, all of which are more or less identical to a series of simple bets on random events. If the player inputs in a game such as (most) video poker or craps only serve to change what type and degree of fixed-odds -EV bet is made, then the "game" is essentially a slot machine variant with a few different levers to pull. It is less obvious that this definition applies to blackjack and other games that can, under some conditions, be +EV for the player, but I believe that a careful analysis shows no meaningful theoretical distinctions between blackjack and strictly -EV house games.

It is first worth acknowledging that blackjack exists as somewhat of a special case, an anomaly, a market inefficiency, a triumph or travesty (depending on your perspective) of human irrationality and behavioral tendencies. The casinos make enough profit off of suboptimal play in blackjack that they make the most money by continuing to offer the game and spending resources to identify and block people who play correctly. The fact that the average person knows that blackjack can be beaten presumably drives a lot of traffic to that game. But even blackjack being a potentially beatable game doesn't make it a game of skill.

The expected value (EV) of the player in a house game is essentially just a cost of playing that the casino sets. Any casino game could have its odds or payoffs shifted so that it had zero EV for the player, with the casino instead charging some sort of external fee or rake, and the game itself, in terms of its mechanics and decisions, would be the same. Even if the casino chose to set the payoffs and fees so that the player had a positive EV on something like a slot machine, perhaps as a promotion, there is no sense in which the playing of the slot machine has had any skill or strategy injected into it. Identifying the profitability of the promotion would be a skill involved in being successful at making money at casino games, but this skill is external to the game itself and, for the reasons I've argued in the last thought, not of any particular bearing on the fundamental nature of the game.

It is potentially worthy of note that, despite being stylized to resemble a game played against a human dealer, blackjack is still a one-player game. The house is not a player in the sense of game theory, since it has no ability to make decisions and instead follows a pre-specified strategy. The optimization problem posed to the player of blackjack is one of decision theory, not game theory.

There are some potentially-interesting implications of this perspective. A symmetric, competitive two-player variant of blackjack could be created where players compete against each other instead of playing against the house. The players might alternate positions with each other and each follow the same set of rules (note that traditional blackjack is not actually symmetric since the dealer cannot split or double down), and this adaptation of blackjack would make it into a game in the same family as poker, though it may not have much of a depth of skill. Similarly, a symmetric, competitive, multiplayer game could be made into a one-player game played against a casino by offering electronic or dealer-operated instances of it in which the house played the role of one of the players with a fixed strategy, much like the heads-up limit holdem machines introduced onto casino floors in Vegas.

The key distinction here is that a "player" adhering to a fixed strategy is not a player at all in the sense of game theory. When one knows with certainty that one's opponent will adhere to a certain strategy, there is no room for strategic interaction. Note that this is different than situations in simple games where each player would likely know the opponent's strategy or at least what the opponent should be doing, such as when two experts play a heads-up No Limit Holdem endgame with 5bb effective stacks. Each will almost certainly closely approximate the known Nash equilibrium of this subgame. However, whether it be as a mistake or as an attempt to exploit perceived weaknesses in his opponent, each player could change their strategy if they wanted to. The opportunity for strategic deviation does exist. In contrast, in something like blackjack, the house's decisions are fixed by definition of the rules of the game. Sure, a trivial game such as 5bb heads-up No Limit Holdem will not have much of a depth of skill, but its structure as a game where each party has strategic choices keeps it distinct from casino gambling, even though the outcomes will closely resemble coinflips as they will in any low-skill game.

This highlights some issues with what many have adopted as a quick and easy approach to predominance. This common but imperfect approach classifies any game in which a player can sometimes have a positive EV as a game of skill and a game in which a player can only have a zero or negative EV as a game of chance. There's a good intuitive appeal here, but this would classify some clear pure-chance activities as games of skill under conditions, perhaps promotional, where the payouts or odds were shifted to favor the player, completely independently of the depth of skill or strategy within the activity. More troubling would be that a game such as poker could be classified as a game of chance if the rake were too high, an idea which will be treated further in a later part of this essay. Categorizing games purely on their EV under various conditions may be of practical financial importance to a player trying to earn a living by playing a game, but does not necessarily measure any structural presence of skill in the games. It's possible to be a professional gambler by making a living from exploiting profitable casino game opportunities, and doing this does involve skill, but this is not the same as being a professional player of poker or any other symmetric, competitive game.

Logically, there one direction of the relationship between EV and the existence of skill in a game that holds up in some cases. If we assume that we're only looking at symmetric games, symmetry being key here, then the existence of a +EV player/strategy for any given game under some conditions indicates that there must be some component of skill in the game, i.e. that nontrivial strategies exist and impact the game outcome. However, the converse is not true; it is not the case that the lack of existence of +EV players/strategies imply that there is no skill in the game. A clear game of skill such as chess could fail to demonstrate +EV players if the rake taken on the game was too high or, alternatively, if the observed population was all of expert players of similar ability. The argument which focuses only on EV is essentially an outcome-based approach to predominance and thus has shortcomings in each of the ways we've explored already.

In terms of actual legal interpretations of predominance, unfortunately, most of the time, house games and multiplayer strategy games are lumped in together and treated as a homogeneous group. Another part of the mostly-wonderful the DiCristina ruling that disappointed me was a very succinct dismissal of the possibility of treating one-player "games" separately from multiplayer games, though I acknowledge that the historical precedent probably does work this way:
2. Gambling Not Limited to House-Banked Games
There is no evidence in the record that Congress considered whether a game was housebanked was a relevant characteristic in determining whether it constituted gambling under the IGBA. Neither dictionary nor common law definitions of gambling distinguish between games based on that factor. Nor does any federal gambling statute other than the IGRA rely on whether a game is house-banked to define its scope.
Certainly, we must keep in mind that both some legal systems and some of the general public will refuse to appreciate the relevance of the categorical distinction between multiplayer strategy games and simple gambling. So, if we are in a situation where we must consider both types of games together, we can't classify the relative influence of skill and chance in a game by EV alone, as that might be affected by the particular nature of an operator's chosen fee structure or the population of opponents under observation.

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

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