<-- Part 4: What if an outcome-based approach specifies observing "average" players?
David Sklansky has popularized an argument for poker being a game of skill based on the fact that a player can deliberately lose at poker, but cannot deliberately guarantee a loss at roulette, craps, slot machines, lotteries, etc. The argument does concisely draw a clear distinction between multiplayer strategy games like poker and noninteractive casino gambling, and for that it is valuable when dealing with the general public, but can this argument hold any robust role in a formal classification of games?
This argument is very narrow and fragile, as it would no longer apply if the casino games added a "you lose" button as an option during play. The argument groups blackjack into the skilled category, perhaps intentionally, but the fact that one can hit until they bust at blackjack merely a particularity of the rules; a blackjack variant that prohibited hitting on 18+ would be a very similar game. One might also observe that some games, such as roulette and lotteries, do allow a guaranteed loss if a player places multiple bets to cover all numbers. Interestingly, this approach deems rock-paper-scissors to be a game of chance since no move will lead to a guaranteed loss. Overall, the argument blurs the line between symmetric multiplayer games and noncompetitive house games, which seems especially unnecessary given the limited scope of what is actually demonstrated. All that it shows is that the game has strategic inputs which can affect outcomes. I don't think this argument is good for much more than being an effective soundbite to an audience that will not be receptive to longer arguments.
To attempt to tie this idea into a formal approach to predominance, one could imagine a study that measures the performance of novice or expert human (or computer) players relative to the performance of an algorithm designed to make extremely poor moves, as one such study, On a Relative Measure of Skill for Games with Chance Elements, has done in an effort to quantify the range of possible payout outcomes for poker and for casino games. For any type of poker, the outperformance should be sizable and converge quickly, especially in variants of poker such as NL where the deliberately bad player could bet most of its stack and then fold. Alternatively, rather than a worst-possible player, a randomly-moving player could be used, choosing equally among all possible moves at all times, as at least one real scientific study has done. Here, too, the humans win rather handily, leading to a conclusion that poker must be predominantly skill since the player decisions affect the outcome so dramatically in the extreme cases. These are effectively outcome-based approaches that specify measuring play between a competent player and an incompetent player.
Theoretical consistency would lead this rule to make some strange classifications. We can build hybrid games that effectively have "you lose" buttons without doing so blatantly. For example, consider tic-tac-toe, a game of skill under this approach, and roulette, a game of chance. Then a new game, Tic-Crap-Toe, could be defined as first playing a round of tic-tac-toe and, if the instance of tic-tac-toe ends in a draw, move onward to craps to determine the winner of the overall game. So if a player wins in the tic-tac-toe, the overall game is over, and the chance-only game only happens when the tic-tac-toe game is drawn. Since tic-tac-toe can be deliberately lost, such an approach would classify the Tic-Crap-Toe amalgam to be a game of skill, no matter what the underlying Game Y is. In practice, of course, tic-tac-toe should almost always end in a draw, even among the population that would be attracted to Tic-Crap-Toe, so this is just a fancy way of embedding a game of chance into a shell of a simple strategy game.
Even without resorting to pointless stitching together of games, really, this approach would end up classifying every symmetric multiplayer game that I can think of as predominantly skill, as almost all games do contain sufficiently-terrible strategies. A game having a clearly bad strategy doesn't say anything about the rest of its strategic lines or their complexity. The worst strategy path doesn't reveal anything about the rest of the strategic paths, so these approaches cannot accurately measure the depth of skill in a game. Under this approach, if a "you lose" button was attached onto any game, these measures would say that more skill has been added to the game, but the only skill that has been expanded is the skill of knowing that, hey, you probably just shouldn't ever push this button. That's some sort of skill, sure, but only in a very limited, impractical sense.
The poor performance of a worst-possible player only shows that a nonzero amount of skill exists in a game, and that's the limit of this type of approach.
Part 6: An impractical dependence on game duration -->
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