Dr. Richard Garfield, legendary game designer and creator of Magic: the Gathering, brings an incisive perspective and unique experience to questions of theory in and around games. He recently gave a lecture which was an excellent, compact tour through several of his key ideas on luck in games.
The lecture is geared towards an audience of players/designers of both casual and competitive games, but the ideas in the first 15 minutes of the video are extremely relevant to the questions of the role of skill and chance in poker. (The rest of the lecture is a worthwhile watch for anyone interested in games other than poker or in game design, for sure.)
Seriously, I want you to watch this if you haven't already. Watching this one 15-minute video will be much less effort than reading the rest of this blog series and will likely communicate ideas much better. It will give you some interesting thought experiments to ponder while laying a solid foundation for some of the rest of my thoughts. So, go watch it.
In order of their presentation, here are the most interesting concepts Garfield discusses:
- Garfield defines an orthogame as a finite, multiplayer game which results in the players being ranked (i.e. deems a winner). In the context of his game design lecture, this is to draw a distinction between competitive multiplayer games and solitary or noncompetitive pursuits such as 1-player video games and Dungeons & Dragons. In our context, however, this classification separates poker from all other traditional forms of gambling, both 1-player casino gambles and open-ended, non-game, market-based gambling such as sports betting and stock trading. Poker is the only orthogame among activities commonly treated as a game of predominantly chance or as gambling. This is an extremely fundamental distinction, and that it is so relevant to the design of games suggests that it should also be relevant to the social and legal treatment of games. I typically reserve the term "game" to refer only to proper games in the sense of game theory, which is synonymous with orthogame. I will generally use this convention throughout.
- The toy game example of rando chess is an elegant means of constructing a game with customizable levels of chance. Garfield uses it here to illustrate how skill and chance are not opposites. Rando chess is exactly the same as chess, except that, after play has finished, the winner is reversed with probability 1/6. Rando chess, with any probability (<0.5) of reversal, would universally be agreed upon to involve more chance than chess, but would involve the exact same strategic considerations as regular chess and hence the exact same amount of skill. Every skill and every strategic concept in chess applies equally to rando chess, and, perhaps modulo tilt control, the best chess players in the world will also be the best rando chess players in the world... it just might take a longer period of play to determine this ranking. If, somehow, chess could only be played as rando chess, what would society think of it? What probability of reversal would make rando chess a game where neither skill nor chance predominates over the other?
- Garfield discusses overt randomness, the randomness caused by explicit random elements inherent to a game such as dice, shuffled cards, or random number generators. While many laymen assume that overt randomness is the only possible source of randomness in games, almost all games include non-overt randomness as an incidental consequence of their structure — and non-overt randomness can contribute significantly to the role that chance plays in a game. Obvious examples of non-overt randomness include factors in physical sports such as irregularities in turf and the impact of wind. In strategy games, the broadest and most important source of non-overt randomness is that arising from uncertainty over one's opponent's strategic choices. Rock-paper-scissors illustrates this best; the game has no overt randomness, but since the moves are simultaneous and subject to the unpredictable decisions of the opponent, one can never know with certainty which move is correct to throw. Furthermore, even in games with sequential actions and perfect information, strategic uncertainty still contributes to non-overt randomness. Consider a chess-like game in which one can choose between two strategies, one of which will perform better if the opponent's strategy (in the general sense of specifying all moves in all situations) for the game will cause him to respond a certain way, but will perform worse if the opponent plans a different strategic reaction. When you don't know what your opponent's strategy will be, that creates randomness even in deterministic games. This sort of strategic uncertainty is highly present in poker; the random shuffle of the cards is not the only source of uncertainty in poker.
- Garfield’s “pi game” (for a given large N, try and guess the Nth digit of pi, whoever is right wins) example is a great demonstration of a totally deterministic game which is guaranteed to have chance-driven outcomes. This serves as another illustration of how uncertainty and chance are present even in games which would be commonly seen as mostly or purely skill. Whenever a game demands an amount of physical or mental effort which is impossible for a human to execute perfectly every time, uncertainty will be present in the results.
- A novice will have a positive, nonzero probability of beating a grandmaster at chess by making all moves randomly. This will be true in any symmetric strategy game, for any strategy probability distribution which includes all possible moves. A common and salient aspect of poker is that a weaker player will beat a stronger player reasonably often on any given day, but this is true of all sequential strategy games, at least very slightly. Where would one deem the threshold of predominance when taking such an approach?
Garfield brings it all together with a convincing, practical definition of luck: uncertainty in outcome. Whenever no human could possibly know with certainty the outcome of an event, then chance or randomness must be playing a role in the outcome of that event.
Even in a game of ostensibly pure skill like chess, the limitations of human ability and the entropy of human cognition will ensure that the outcome of a single game could go either way, as long as one player does not too badly outmatch the other. On the other hand, it may be reasonable to know with certainty the outcome of a game of tic-tac-toe when it is played between two intelligent people. Despite tic-tac-toe and chess each being deterministic, turn-based strategy games, it might be reasonable to say that chess has luck where tic-tac-toe does not, which is how games of chess between the same players rarely play out the same way every time. So every strategy game which is difficult enough to be attractive for intelligent people to play has at least some amount of chance, in this sense.
While poker is intuitively and emotionally seen as a game with a high chance component, this intuition comes almost exclusively from the salient randomness in the game generated by the shuffle of the cards. For sure, poker has much more salience in its random elements than most other competitive strategy games. However, Garfield's ideas illustrate all of the more subtle, non-overt ways that games can have uncertainty in the outcome, which should lead anybody to second-guess a superficial assessment of poker as predominantly chance solely because of suckouts. Counterintuitively, it's possible that perhaps the shuffle of the cards isn't even the largest source of randomness at work in poker. It is certainly not the only source, and the other sources are common to all games, including those that are generally never considered to be games of chance.
Part 3: Outcome-based approaches fail on populations of similarly-skilled players -->
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