Tuesday, September 25, 2012

20 thoughts on skill vs. chance in poker, part 16: Does duplicate poker have higher skill relative to chance?

<-- Part 15: Does rake matter?

Duplicate poker is a poker variant which attempts to reduce the impact on game outcomes of the intrinsic randomness from the shuffle of the cards. The general principle is that two poker games take place on two separate tables, with the order of the shuffled cards controlled to be the same at both tables for each hand. The payoffs to each player, rather than being the standard number of chips won or lost in that hand, are based on a function of the difference between the net chip performance between that player and his or her duplicate at the duplicated table. In this sense, some of the salient chance features are mitigated by playing duplicate poker instead of regular poker. A player dealt a good starting hand isn't automatically being given a profitable opportunity, as he must outperform a duplicate player who has also been dealt the same hand. In the sense that regular poker "is skill in the long run" once the randomness of the cards has evened out, duplicate poker attempts to speed up this timescale by keeping the hands even throughout any interval of play. It's ok that "no amount of skill can change a deuce into an ace", as this will impact both of the paired players.

While duplicate poker has never gathered much popularity, its cause has been taken up by various companies over the years. The eponymous DuplicatePoker launched the first real-money online duplicate poker room several years ago, closing its doors and disappearing in 2008 without much public statement. More recently, SkillBet has launched a variant of duplicate poker in which there is only one human player at each table with the rest of the players being bots, which removes the possibility of particularly-exploitive collusion between conspiring players sitting at different seats that duplicate poker would provide. Perhaps most relevant is that the International Federation of Poker, an organization seeking to spread awareness of poker as a mind sport, has adopted a duplicate poker format for a major tournament it held last year in London.

In all three of these cases, the parties involved have marketed their ideas using claims that duplicate poker "has more skill" than regular poker, or, in some cases, asserting that it "is all skill" and has no chance elements at all. There's a strong intuitive appeal here, but are these claims accurate?

At this point in the essay, we quickly recognize the idea that duplicate poker has more skill than regular poker to be nonsense. Removing chance from a game is not the same as adding skill to a game. The depth of strategy in most duplicate poker games should be roughly the same as regular poker. A duplicate poker cash game with a typical payoff function on the differential between player performances would have the nice property of the correct EV-maximizing strategies being the same as they would be for a regular poker cash game, as every incremental chip won or lost contributes equally to the players' payoffs. Duplicate poker tournaments, however, will necessarily involve different considerations for any payoff function due to the nonlinearity of chip values, which will lead to different strategies than both cash game poker and traditional tournament poker. The scoring system for the IFP's London tournament and for SkillBet's tournament games, essentially rewarding only the players who get the highest scores at their tables, would induce players who are behind in the standings to take increasingly large risks as the end of the tournament period nears — and to hope their opponents were not making the same plays, which would eliminate the possibility of earning or losing any points in that hand. These strategies will not necessarily be more or less intricate in their strategic depth than the strategies for corresponding cash game, just different, perhaps in the same way that a regular poker cash game and a regular poker tournament have different strategic considerations due to nonlinear chip values.

If moving to duplicate poker has any impact on the relative influence of skill and chance in poker, it would certainly be to reduce the chance in the game, but even that is not formally clear. The rules of the duplicate variant do certainly eliminate the role of chance in the random deal of the cards, but that is only one source of randomness in poker. Randomness in poker also comes from the unknown or simultaneous strategic choices of one's opponent, as discussed in part 2 of this essay. When it comes to that source of chance, not only does duplicate poker not reduce it, but it actually increases it. The outcome of a hand or game will depend not only on the traditional strategic interplay between a player and his opponents at the same table, but also on the strategies of his duplicate, and the sensitivity of the outcome to this additional source of randomness can be immense. For example, if a good player is in the fortunate position of playing a duplicate poker cash game against a very poor partner (opponent) at the duplicated table, the good player might properly fold a speculative, slightly -EV hand, but when his duplicate decides to play it, the good player will often get a large positive or negative swing depending on whether or not his duplicate hits his draw. In a situation where folding and calling might be close in expected value, regular poker would let the player choose to fold and take no further risks in the hand, but this situation in duplicate poker is precisely the situation most likely to lead the two paired players to make different choices and lead to a large payoff or loss. It is totally plausible that a player's outcomes in duplicate poker could have higher variance than that of regular poker. Even if we don't focus on the spread of a player's outcome distributions, the duplicate poker variant certainly introduces an additional source of randomness to the game while it eliminates the salient source of the shuffle of the cards. It's not clear that one outweighs the other.

A similar take on duplicate poker by Nick Jones at Pokerfuse drew parallels between this fallacy of duplicate poker and the incompleteness of Sklansky's Fundamental Theorem of Poker. In the sense of my own generalizations to the Fundamental Theorem of Poker, duplicate poker could only hope to mitigate some of the randomness that lies between Level 0 and Level 3, leaving all of the strategywise uncertainty untouched (and adding the very impactful extra source of strategywise uncertainty from the duplicate player).

For duplicate poker to truly have no chance elements at all, as some of its proponents have claimed, is to accept that the object of a poker game is to predict what cards will fall, that an expert poker player will have the prescience to know to properly continue with a speculative hand only when it will end up hitting its draw. In reality, poker accepts that future random events are unpredictable and instead has the objective of maximizing expected value over these future uncertain events, and there is plenty of uncertainty remaining in duplicate poker.

On the whole, from any measure of the relative influence of skill and chance in games, it's not clear that duplicate poker is any further along the theoretical scale of predominance than regular poker is.

While it has never become popular or had many strong endorsers, thus suggesting that it's not a particularly good variant of poker, duplicate poker is a bona fide variant of poker. The game is still poker, it's just poker under a perturbation to the payoffs and strategies that I (and presumably others) feel is an unnecessary departure from the purity of the game.

The salient randomness is convincing, though. Among other implications, duplicate poker does gives each of its players much more of an "equal challenge" than regular poker. So, while I wouldn't discourage entrepreneurs and poker enthusiasts from trying to pass off duplicate poker in a region or social context which discriminates against regular poker for various informal reasons relating to salient randomness, please don't claim that duplicating out the shuffle of the cards makes the game all skill. Just focus on the honest fact that the impact on the outcomes of the random deal of the cards is mitigated and that the remaining uncertainty in the game is more obviously similar to that of other games commonly accepted as skill.

Part 17: Why does poker need randomness? -->

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