Saturday, September 8, 2012

20 thoughts on skill vs. chance in poker, part 4: What if an outcome-based approach specifies observing "average" players?

<-- Part 3: Outcome-based approaches fail on populations of similarly-skilled players

While we have seen that an outcome-based approach based on empirical data will vary depending on the player population being observed, a possible means of rectifying this is to fix as constant the levels of skill or experience that observed players should have. According to the recent study "Is Poker a Game of Skill or Chance? A Quasi-Experimental Study" by Meyer, Meduna, Brosowski, and Hayer (and, oh, don't worry, we will most certainly be getting to this study in more depth later), German law apparently does exactly this. A game is deemed to be gambling in Germany by a predominance test based on the "skills and experience of the average player" versus that of an expert, where the average player is "defined as an individual who is generally interested in playing the game, has learned the fundamental rules and has had some practice playing". David Sklansky also muses on this sort of approach here, noting that an outcome-based approach which compares the winrate of an expert against that of the comparable lossrate of an amateur (rather than against a baseline of zero) will yield faster convergence, i.e. fewer hours played before the expected value of winnings will exceed the standard deviation by any desired amount.

Both of these approaches to defining the average player depend, quietly but importantly, upon self-selection. Somebody who is interested in playing poker or actively plays poker has chosen to do so, potentially because they are at least moderately skilled at it relative to some peer group. Depending on the marketing of poker or the overall popularity of the game, the skill level of such a player could vary tremendously both over time and over different geographical locations and markets.

Some might argue that the "average" poker player would be an infrequent, casual player who rarely puts much thought into strategy, is drawn to the game for social or risk-seeking reasons, and plays fairly badly. I would generally disagree with this characterization, but if you looked at a median taken over every human who has ever played a hand of poker, perhaps it's close to this. For the sake of this consideration, let's assume this is true. What would it mean if a large presence of casual players like this were enough to nudge poker over the line into being predominantly chance under a given approach to predominance? This would mean that, if poker had been less popular or marketed in a less-appealing way to casino gamblers, then the remaining more serious players might have been able to enjoy a classification as a game of predominantly skill, if not for the horde of terrible players that the game happened to attract. What if this group of casual poker players were to all quit poker and take up another game with a significant chance element, such as backgammon? Would the predominance classification of every game jump back and forth alongside the whims of the casual-gaming masses?

This highlights the more practical concern that the skill level of the average self-selected player in poker or in any game varies considerably over time. In the height of the first US poker boom, the average self-selected online player was incredibly weaker than the average online player is today. If poker were to become less popular with casual players, then only the strong, serious players would remain, and they will have become the new "average" player. As time goes on and the surviving poker players improve their skills, the $1/$2 NL cash game could cross over from predominantly skill to predominantly chance under any particular outcome-based approach to predominance, which brings along with it to all of the paradoxes and issues from part 3. A measure of predominance should be representative of the game itself, static and not varying its classifications over time.

An alternative approach might be to define an average player as an adult of average intelligence without any prior experience playing the game. Run down the rules of the game, maybe even give them an hour of basic strategy advice, and see how they do against the experts, as at least one study has done. This is a more consistent approach, but even this will vary over time if the overall intelligence level of society increases. For example, in a parallel universe where humanity is much worse at strategic thinking and logic, tic-tac-toe might be too difficult of a game for the average person to master. Only the top intellects in this society, perhaps trained in the game since birth, could hope to become tic-tac-toe grandmasters. Maybe the human minds in this society are skewed towards being good at playing as "O", but fail to play properly as "X", so that the outcome of the game between most players is mostly determined by the coinflip to determine turn order. Is tic-tac-toe a game of predominantly chance in this parallel universe? If so, does it cease to be so if some profound event increases the strategic intelligence of everybody to our real-world level? Yes, this is highly hypothetical, and this effect should be fairly negligible in practice, but it is still theoretically troubling.

The questions I have posed here are, to me, philosophical questions with no clear answer. There are reasonable arguments as to why a refined average-player approach, despite a dynamic dependence on humanity's intelligence, could have practical merit in a society which wishes to permit for-money strategic competition while prohibiting pure gambling. If so, however, these issues should be acknowledged... and it'll be interesting to see just how big of any future poker booms might be.

Part 5: On intentionally losing -->

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