# On the (pseudo?)-paradox of “fair” games.

### Fair Games and 50% Win Chances

I’ll take it as an assumption in the rest of this article that a fair game is one where each player has a 50% chance of winning. We also sometimes call such a situation a “good match” or say that the game will be good if we believe such a state of affairs prevails. We also tend to view negatively the opposite condition, wherein one player has a huge advantage over the other and hence where we expect the probability of that player losing is very low (implying the probability of the other player losing is very high).

These considerations aren’t limited to two player competitive games.  If we are playing a single player, digital or otherwise interactive game, we call that game “fair” when we have about a 50% chance of winning. We would call a game where our chance of winning is ~1% unfair or badly designed, and where our chance of winning is ~99% boring or badly designed.

At first glance this seems to imply a contradictory attitude, one illustrated by recalling that we also call a coin flip “fair” if there is a 50% chance of the coin landing on either face. If the purpose of a game is to determine which player is the better player, how can it be that we seem to also want the outcome of the game to be as random as possible (such that for good matches, each player has a 50% chance of winning). It would appear that good games have random outcomes and that seems to contradict their apparent purpose in measuring how well a player plays.

(NB. The account is a little harder to render in the case of single player interactive systems. However, it seems paradoxical that a player would engage with a system with the intent of winning when the outcome could equivalently be determined by the toss of a coin).

### Resolution

I don’t think this is a genuine paradox, of course: when we say a game is fair, what we are saying is that the outcome isn’t random, but that it depends, sensitively, on which player makes the better sequence of moves in response to the other player. Why sensitively? Well, when two players are closely matched the the outcome of the game, if the win probability for either player is 50%, should depend very sensitively on how well each player actually plays. In particular, close matches come down to one or two critical mistakes or strokes of brilliance to tip the scales in one direction.

(This is particularly true because of another property of games (approximate reversibility) which I believe games must also have, but which I don’t discuss here.)

So it isn’t really surprising that we can resolve this merely apparent contradiction about games. But the resolution points us towards another important argument:

Because the outcome of a good game should depend sensitively on the moves of the player, the randomness present in a good game should be minimal or not present at all. Why? Because if the outcome of a game depends sensitively on the moves the player makes, then it also must necessarily depend sensitively on random influences on the game state. Why? For outcomes to depend sensitively on a move implies that each move a player makes is carefully tuned for the game state, which they have correctly appreciated in order to make the right move. But if the game state changes randomly, then a good move might be turned into a bad move by a random change in the game state.

(It is possible to imagine random changes to the game state which don’t change the quality of moves. But if this is the case, then these changes to the game state are _extraneous_ to playing the game and may as well be removed).

### Conclusion

To restate the argument:

1. we believe games should be fair, which is to say that a given player should have a 50% change of winning
2. this is because we want games to be sensitive tests of the quality of play of the given player, where the outcome depends sensitively on moves. We don’t want the game itself to be actually be random in the sense that the outcome is extraneous to the game itself.
3. Random elements (which are necessarily extraneous to the game in their origin) reduce the sensitivity of the win condition on the specific moves made by a player
4. Hence, good games should have minimal random elements.

This argument puts game designers in a difficult position. For designers of multiplayer games, they must make sure that the game’s rules don’t advantage particular players or add the appropriate handicap if they do. This turns out to be difficult. In Chess, for instance, white has a slight win chance, although the precise probability is unknown. Typically, for a new game without a long history of play, it will be very hard to determine whether such a bias exists and what size it might be.

With the rise of computers and single player strategy games a different set of design concerns manifests. The temptation in single player game design is to use random elements to provide variety for a gameplay system which may not have the strategic depth furnished by the presence of a second rational player. It is hard to imagine a deterministic single player game with the same initial conditions each play that can stand up to repeated play.

I think the way forward here is to randomize the initial conditions of any such game subject to the constraint that a given initial condition preserves the win 50% rate (perhaps based on artificial intelligence play or some other way of characterizing win chance) and then to make play from that point forward completely deterministic.

# Yawning

The baby was fussy all morning, and when he finally went to sleep, in the crook of his mother’s arm, after nursing we were scared to leave him alone in case the silence woke him up. I made carbonara downstairs, ate, and then went to lie beside him reading while Shelley took her portion.

As I re-positioned my leg, my knee popped loudly, startling the baby. He stretched his arms above his head and pawed at his face with the backs of his hands. These gestures were familiar to me from my own body. I had seen, too, him sneeze or yawn. I imagined for a moment, that I had given these things to him, but that transposition made a deeper truth clear.

My cat, who slept above us, on a table over the bed we had arranged on the floor, stretched and yawned. He sneezes. When we turn the lights on at night to change Felix’s diaper, he sprawls onto his stomach and covers his eyes with his paws, sulkily. These gestures, taught to us by no one, inherent in us, which you could have observed in my child minutes after he was born, belong to an unimaginably ancient process of which we are merely brief manifestations.

Human beings tie themselves into knots or grind themselves to featureless lumps, struggling to connect with something vast and ancient. We don’t stop to think that each time we yawn we are in contact with something profound and atavistic, something older than history, bigger than the merely human.

# The Ethics of Game Design

In the next week or so, I’ll be on the Dinofarm Games Community Podcast talking about the ethics of game design. My baby is just one week old, though! So I might not have been as coherent there as I wanted to be. As such, I thought I’d collect a few notes here while they were still in my head.

As a preamble: there are lots of ethical implications of games that I don’t discuss here. Particularly social ones: since games often depict social and cultural situations (like novels, plays or television shows) similar ethical concerns operate for games as for those artifacts. Here I’m specifically interested in those special ethical questions associated with games as interactive systems.

The question I’m interested in is: “What are the ethical obligations of a game designer, particularly to the player?” In a way, this is an old question in a new disguise, recognizable as such since the answer tends to dichotomize in a familiar way: is the game designer supposed to give the player what they want or is she supposed to give the player that which is good for them?

Let’s eliminate some low hanging fruit: if we design a game which is addictive, in the literal sense, I think most people will agree that we’ve committed an ethical lapse. There are a few folks out there with unusual or extreme moral views who would argue that even a game with bona fide addictive qualities isn’t morally problematic, but to them I simply say we’re operating with a different set of assumptions. However, the following analysis should hopefully illuminate exactly why we consider addictive games problematic as well as outline a few other areas where games ethical impact is important.

I think the most obvious place to start with this kind of analysis is to ask whether games are leisure activity, recreation or whether they provide a practical value. By leisure activity I mean any activity which we perform purely for pleasure, by recreation, I mean an activity that is performed without an immediate practical goal but which somehow improves or restores our capacity to act on practical goals, and by practical value, I mean something which immediately provides for a concrete requirement of living.

Its a little unclear where games fall into this rubric. It is easiest to imagine that games are purely leisure activities. This fits the blurb provided by the wikipedia article and also dovetails, broadly, with my understanding of games in public rhetoric. Categorizing games as purely leisure activities seems to justify a non-philosophical attitude about them: what is the point of worrying about the implications of that which is, at a fundamental level, merely a toy¹?

Point number one is that even toys, which have no practical purpose but to provide fun, are subject to some broad ethical constraints. It isn’t implausible to imagine that we could implant an electrode directly into a person’s brain such that the application of a small current to that electrode would produce, without any intervening activity, the sensation of fun. We could then give the person a button connected to that electrode and allow them to push it. This is technically an interactive system, perhaps even a highly degenerate game. It is certainly providing the player with the experience of fun, directly. However, its likely that a person so equipped would forego important practical tasks in favor of directly stimulating the experience of fun. If we gradually add elements between button presses and the reward or between the electrodes and the reward circuitry, we can gradually transform this game into any interactive system we could imagine. Clearly, at some point, the game might lose its property that it overwhelms the player’s desire to perform practical tasks. That line is the line between ethical and non-ethical game design.

In other words, game designers subscribing to the leisure theory of games are still obligated, perhaps counter-intuitively, to make their games sufficiently unfun that they don’t interfere with the player’s practical goals.

We have two interpretations of game value: the recreational and the practical interpretations.

Of these, the idea of the game as recreation may be closest to what is often discussed on the Dinofarm Discord channel. Its also frequently the narrative used to justify non-practical games. You’ve likely heard or even used the argument that digital games can improve hand-eye coordination or problem solving skills. This interpretation rests on their existing an operational analogy between the skills required to play a game and those required to perform practical tasks. There is a lot of literature on whether such a link exists and what form or forms it takes.

If no such link exists we can rubbish this entire interpretation of games, so its more interesting to imagine the opposite (as it least seems to sometimes be the case). When a link exists the value proposition for a game is: this game provides, as a side effect of play, a practical benefit. Why the phrase “as a side effect of play?” Because, if the purpose of the game is to provide the practical benefit, then we must always compare our game against some practical activity which might provide more of that same benefit than an equivalent effort directed towards non-game activity.

To choose a particularly morally dubious example, we might find that playing Doom improves firing range scores for soldiers. But shouldn’t we compare that to time spent simply practicing on the firing range? Without some further argumentative viscera, this line of thinking seems to lead directly to the conclusion that if games are recreation, we might always or nearly always find some non-game activity which provides a better “bang” for our buck.

Elaborating on this line of argument reveals what the shape of the missing viscera might be. Why is it plausible that we could find some non-game activity that works as well or better than any given game at meeting a practical end? Because games must devote some of their time and structure to fun and, as such, seem to be less dense in their ability to meet a concrete practical goal. In Doom, for instance, there are a variety of mechanics in the game which make it an exciting experience which don’t have anything to do with the target fixation behavior we are using to justify our game.

But we can make an argument of the following form: a purely practical activity which results the improvement of a skill requires an amount of effort. That effort might be eased by sweetening the activity with some fun elements, converting it to a game, allowing less effort for a similar gain of skill.

On this interpretation the ethical obligation of the game designer is to ensure that whatever skill they purport to hone with their game is developed for less effort than the direct approach. If they fail to meet this criteria, then they fail to provide the justification for their game.

The final interpretation we need to consider is that games themselves provide a direct, practical, benefit. I think this is a degenerate version of the above interpretation. It turns out to be difficult to find examples of this kind of game, but they do exist. Consider Fold.it, a game where player activity helps resolve otherwise computationally expensive protein folding calculations.

In this kind of game the developer has a few ethical obligations. The first is to make sure that the fun the game provides is sufficient compensation for the work the player has done or to otherwise make sure the player’s play is given with informed consent. For instance, if we design a game that gives player’s fun to solve traveling salespeople problems which, for some reason, we are given a cash reward for solving, a good argument can be made that, unless the game is exceptionally fun, we’re exploiting our player base. If the game were really so fun as to justify playing on its own terms, why wouldn’t we simply be playing it ourselves?

Game designers of this sort also need to make sure that there isn’t a more efficient means to the practical end. Since the whole purpose of the game is to reach a particular end, if we discover a more efficient way to get there, the game is no longer useful.

I think there is probably much more to say on this subject but I had a baby a week ago and three hours of sleep last night, so I think I will float this out there in hopes of spurring some discussion.

#### The Dinofarm Community Interpretation

At the end of the podcast we decided on a very specific definition of games (from an ethical standpoint). We (myself and users Hopenager and Redless) decided games could  be described as a kind of leisure whose purpose is to produce the feeling of pleasure associated with learning. Since this is a leisure interpretation, we aren’t concerned directly with practical value, which I think is square with the way we typically think of games. However, as a leisure interpretation we need a theory of how games operate in the context of the player’s larger goals.

Let’s sketch one. What circumstances transpire in a person’s life where they have the desire for the pleasure associated with learning but are unable to pursue that desire in productive terms? One possibility is fatigue: after working on productive activities, a person might have an excess of interest in the experience of learning but a deficit of energy to pursue those productive activities. In that situation, a game can satisfy the specific desire with a lower investment of energy (which could mean here literal energy or just lower stress levels – games, since they aren’t practical, are typically less stressful than similar real world situations).

Once the game is completed, the desire ought to be satisfied but not stimulated, allowing the player to rest and then pursue practical goals again.

Again, there are probably other possible ways of situation ethical games in this interpretation, but I think this is a compelling one: games should satisfy, but not stimulate, the desire to learn, and only in those situations where that desire might not be more productively used, as is in the case of mental exhaustion or the need to avoid stress.

Games shouldn’t have a “loop” which intends to capture the player’s attention permanently. Indeed, I think ethical games should be designed to give up the attention of the player fairly easily, so they don’t distract from practical goals.

And them’s my thoughts on the ethics of game design.

¹: Note that there is a loose correspondence between our rubric and The Forms. Toys, roughly, seem to be objects of leisure, puzzles and contests are arguably recreation, and games are, potentially, at least, objects of real practical value. Maybe this is the interpretation of games is the one underlying “gamification” enthusiasts.