<-- Part 14: Does rate of showdown matter?
Most of our analysis so far has treated poker on its fundamental merits, ignoring or dismissing its social association with casino gambling. Whatever poker actually has in common with casino games is largely historical and incidental rather than being due to the inherent similarities with those games, whereas poker is fundamentally of the same structure as games which are almost universally seen as predominantly skill. Nonetheless, this association with gambling easily persists due to some salient similarities between poker and casino games, the most potentially-convincing trap being that the "house always wins" is also true in poker due to rake. If we accept that most real-world poker is raked, does this make poker meaningfully similar to house games?
Let's take a look at how the rake in poker can make poker resemble a casino game from some perspectives. Indeed, a raked poker game is no longer zero-sum but negative-sum, therefore the average player will lose. The house will take some portion of every "bet" in both poker and in casino games, be it from a fee such as a rake or from a built-in edge (which could be reframed as a rake on an otherwise payout-shifted zero-sum version of a one-player casino game). It's possible that a certain poker game could have so high of a rake that no player could have a positive expected value. If so, the player payoffs in this highly-raked poker game could resemble those of a casino game such as craps or video poker; players who make more proper decisions will lose less on average, but will still lose. Alternatively, the odds in casino games with player inputs could be shifted so that the best players do win on average, as is the case with blackjack. So why doesn't a rake "make poker into a casino game"?
Well, this has mostly been answered in part 11 during our discussion of why expected value doesn't dictate whether or not a game is a game of skill. As discussed there, while it's true that winning players can only exist in raked poker when the rake is not set to be exceedingly high, the lack of existence of winning players in a symmetric game does not necessarily imply anything about the nature of the underlying game. Just as shifting the player payoffs of a slot machine due to a promotion doesn't add any skill or reduce any chance in the play of that slot machine, adding a rake doesn't reduce any skill or increase any chance in poker.
For completeness, there are a few other reasons why rake specifically is not a component of the fundamental structure of a game.
The fact that the house makes money by offering poker does not make it any different than any other business. Of course a casino acting as a third-party operator for a competitive, symmetric game like poker will charge a fee to operate the game, just as a theater will take in money from everyone who sees a movie and just as the grocery will be making a profit from the sale of a gallon of milk. This is certainly the case for a commercial organizer of any game of any type.
The government's expert witness in the DiCristina case took a perspective which also implicitly involved rake, basing his arguments upon the perspective that, if poker were a game of skill, more of its players should be long-term winners. Games of skill don't need to have a certain percentage of players that win. This approach's focus on how many players end up making money also conflates the amount of skill in a game with the number of players participating in it. As the ruling pointed out, a large, multiplayer tournament in any game will have few winners and many losers.
If the rake imposed by a third-party operator were to be a factor in the classification of games, then this would apply equally to any game, regardless of the degree of chance present. A for-money chess, backgammon, bridge, or Scrabble tournament would cease to be predominantly skill when the tournament organizer takes out a fee of almost the entire prize pool. This rule would effectively create caps on rakes that would be dynamic and based on the player populations, rather than on the inherent structure of the game in question. Practical consistency would be difficult, as players might face variable external costs relating to the playing of the game, such as the costs of materials necessary to play (as in golf or in trading card games) or the costs of transportation for the players to reach the venue. It is a farce to try to build a world in which fees charged to run a game should legitimately affect the legal classification of the game.
The motivation that would presumably underlie such a classification would be concern over players going broke. Perhaps society would want to restrict the opportunities for players to lose money at games. Mathematically, however, in terms of the long-term probability of going broke, there is no difference between a negative expected value game and a zero expected value game. In each case, the probability of losing any finite bankroll over an infinite time horizon is 1. Since there can be no symmetric game where all players have positive expected value, this would logically lead to all symmetric games for money being prohibited or being treated similarly to casino games. Even without this fact, the divergence between player skill levels at any game is enough to create negative expected value situations for the weaker players. A generalized strategy game of any skill and chance structure could reproduce the player win probabilities of any given poker game if the set of players' strategies were chosen to be appropriately divergent. If we're searching for a sensible distinction between games of skill and games of chance, this doesn't get us there.
From a social, regulatory, or practical standpoint, rake cannot be seen as intrinsic to poker. While economic policies of price controls on certain goods and services may be useful in various contexts, they do not change the underlying nature of the activity. Similarly, macro-poker skills such as bankroll management and table selection are not direct evidence of skill in poker, though such concepts couldn't exist in a symmetric game with no skill. External or market forces do not have any bearing on the roles of skill and chance in a game.
Part 16: Does duplicate poker have higher skill relative to chance? -->
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