Rules.of.Play.Game.Design.Fundamentals [Electronic resources] نسخه متنی

Breakdowns in Uncertainty

Luck is very much fate's last hope. It is the play of the last chance. It is the play of everyman.. . . In this sense it is useful to think of games of chance not only as models of the irrevocability of fate but also as fate fantasized. —Brian Sutton-Smith, The Ambiguity of Play

That ends our brief introductory investigation into the classical operations of probability. But before departing from this subject altogether, we would like to discuss a few ways that probability fails to operate in exactly the way that we think it should. As the "feeling of randomness" we discussed earlier demonstrates, the actual operation of probability does not always match up with the way that players experience or interpret it. For the design of meaningful play, understanding the player's point of view is paramount. The next few sections touch on three problematic contexts for probability: randomness on a computer, strategic manipulation of chance processes, and commonly held fallacies about uncertainty.

Breakdown 1: Computer Randomness

If you are designing digital games, it is important to have a sense of how computer programs generate random numbers. Digital games make extensive use of random algorithms, whether to determine which player goes first, to generate the background texture of a game level, or to randomize the behavior of an in-game agent. Ironically, computers cannot produce random numbers. They can execute algorithms that result in random-seeming results, but they are not capable of producing pure randomness. Why is this so? John Casti offers an explanation:

Back in the early days of computers, one of the more popular methods of generating a sequence of random numbers was to employ the following scheme:

Given a starting number between 0 and 1, we can use the proce-dure—often termed the logistic rule—to generate a sequence of numbers that to all appearance is completely random. For example, in such a sequence each of the ten digits 0 through 9 appears with equal frequency and the statistical correlation between groups of digits is zero. Note, however, that the members of this sequence are specified in a completely deterministic way by the starting number. So the sequence is certainly not random in the everyday sense of being unpredictable; once we know the starting number and the rule for calculating an element of the sequence from its predecessor, we can predict with complete confidence what every element in the sequence will be.[8]

Although Casti uses a historical example, the ways that computer programs generate random numbers today are not fundamentally different. Computers can never compute purely random numbers, because the numbers they provide are always the result of algorithms. A computer program can "flip a coin" internally to determine whether a computer-controlled character will turn left or right with equal probability, but the program is iterating a deterministic formula that only superficially resembles the operation of a random coin flip. The generation of random numbers is a well-heeled problem in computer science. We won't go into detail about it here, except to point out that it remains a challenging dilemma. Still, for most game design purposes, the randomness that computers can generate is sufficiently random.

Usually, an intimate understanding of how computers compute random numbers is not part of what a game designer needs to know. But you should never forget that random functions are not infallible. Eric was once working on a game prototype about swarming microbe-like creatures in a fluid environment (the game was never published). The microbes would grow, give birth, and die, flocking together to seek out food in their environment. Although they exhibited complex behavior, it was more or less clear why the microbes were doing what they were doing. However, one aspect of the game was puzzling. The microbes always tended to seek out the upper left corner of their 2D environment. The designers first thought they had stumbled upon a genuinely emergent behavioral pattern, but couldn't for the life of them figure out what was causing it. Did it have to do with the way the food multiplied? Or the way a player was handling the mouse? At the same time, the inevitable and universal drift of the microbes was ruining the game play by making the overall behavior too predictable.

Eventually, they discovered that the emergent behavior was coming from an error in a randomizing function. Each timed step, a microbe would move in one of sixteen directions. Even though they could sense their immediate surroundings and moved accordingly (towards food and away from danger), the program always weighted their decision with a random input. The problem was that because of a programming oversight, the program began counting in the upper left corner, and then counted that corner again at the end, giving the randomizer twice as much chance of picking the upper left than any other position. Even though the degree of additional chance this error added was very small, because of the complexity of the system, the emergent effects were quite strong. Once the randomizer was fixed, the corner drift ceased. The lesson? Even if you are not a computer programmer, understand how randomness operates in your game's program.

Breakdown 2: Strategizing Chance

The second example of the unexpected nature of chance is when the use of chance becomes strategic, when players manipulate uncertainty itself during a game. Will your players really take randomness at face value, or will they scheme to turn chance into strategy? In "Strategies in Counting Out," an essay in The Study of Games, folklorist Kenneth Goldstein looks at the ways that children aged four to fourteen in northwest Philadelphia in 1967 secretly and expertly manipulated the operation of chance. His study focuses on "counting-out," operations such as "eenie-meenie-miney-moe" that kids use to determine who will be "It" in a traditional neighborhood game like Kick the Can.

Counting Out is not usually considered a game: it is a procedure that helps determine roles in a future game. However, by our definition, we can consider it as a simple game of chance. In Counting Out, a player appoints himself or herself the counter; the goal of the game is to avoid being selected as "It."The quantifiable outcome requires that one player is selected as the loser. The premise of counting-out procedures is that they are patterns of counting that randomly select a player. This is, in fact, the way that the children in the study described the act of counting-out to Goldstein when he interviewed them. However, his essay's conclusion is that despite the fact that the children described Counting Out as a purely chance operation, they used complex and subtle strategic methods to achieve the results they desired.

Following are the six general methods of manipulation that Goldstein observed in use. Many of them represent techniques that would require sophisticated mathematical skills to operate in a group with changing numbers of participants.[9]

Specific Rhyme Repertory: This straightforward strategy requires the counter to select a rhyme of a specific length that will achieve the desired result.

Extension of Rhyme: The counting-out rhymes are modular and extendable, and if the rhyme is about to end on someone that the counter does not want to be selected, the counter can spontaneously add an additional phrase or rhyme of the proper length to achieve a different result.

Skipping Regular Counts: The counter simply skips himself or herself when going around the circle, if the counter is about to be selected. Although this was the most popular technique employed, it was also the most obvious, and the one most frowned upon.

Stopping or Continuing: Because most rhymes do not specify whether the selected player is "It" or whether the selected player is "counted out" and is safe from becoming "It," the counter can decide the significance of the selection after the first player has been picked.

Changing Positions: This mathematically intensive strategy entails the counter subtly switching to a new spot in the circle in order to be selected as the next player counted "out."

Respite by Calling Out: In this blatant strategy of avoidance, a player will simply call "safe" or "free" and be exempt from counting in the current round. The groups that allowed this technique did place restrictions on it, such as having only one player be able to call "safe" per counting round.

The paradox of Counting Out is that even though players describe it as a game of chance, it is a game with a rich strategic component, in which experienced players can achieve the results they desire. The point of this example, as with the operation of chance in software, is to demonstrate that sometimes the differences between randomness and non-randomness are more subtle than they appear. When you are designing a game, pay close attention to the procedures used to determine randomness and make sure that they operate in the manner that you intend. Of course, the bigger issues to which this example points is that when you design a game, that game is always going to be used in a particular context by particular players. In our schemas on Breaking the Rules and Games as Social Play, and in many of the chapters within the primary schema CULTURE, we explore in more detail some of the experiential and contextual issues raised by this complex example.

Breakdown 3: Probability Fallacies

A third example regarding the problems of probability does not concern computer software or strategy and chance, but the ways that players conceptualize and understand randomness itself. You may have created a game that contains very specific kinds of probabilities, and you may even communicate these to players. But this in no way means that your players will accurately understand the way that chance operates in your game.

Game players will rarely have the same grasp of the random functions of your game system that you do. Game players and the public tend to suffer from a number of fallacies and misunderstandings when it comes to the operations of chance. The following list is a paraphrased sampling from Epstein's longer list of fallacies in The Theory of Gambling and Statistical Logic. [10]

• 
  

  Overvaluing the long shot. Game players have a tendency to overvalue "long-shot" bets that have a low probability of achieving a high gain,in contrast to "safe" bets that have a higher probability of achieving a low gain.



• 
  

  The tendency to think of successive chance events as additive. For example, the chance of rolling a 1 on one die is 1/6 or 16.67 per-cent.The chance of rolling a 1 with two dice is not 2/6 or 33.33 percent, as you might think at first glance. As we know from probability theory, the chances are 11/36 or 30.56 percent. This difference might seem small in this example, but with successive iterations, the differences between the actual probability and the presumed one can be quite large.



• 
  

  The Monte Carlo Syndrome. This refers to the tendency to think that after a run of failures, a success is likely, and vice versa. In other words, if the Roulette wheel has just landed on a black number, it is not more likely that the next number will be red.



• 
  

  Overemphasis on good outcomes. Given a very unlikely negative outcome and a very unlikely positive outcome, people tend to overemphasize the good one. Epstein uses the example of winning the lottery and being killed in a car accident in the next year. Both have about the same chance of occurring (1 in 10,000), even though most believe that the lottery win is more likely.



• 
  

  Lightning striking twice. Related to the previous fallacy, people tend to believe that highly unlikely negative events will not repeat themselves (such as getting struck twice by lighting), but that highly unlikely positive events will happen again (such as winning the top jackpot on a slot machine). In fact, the chance of a random event occurring is not related to the frequency of past occurrences.



• 
  

  Luck. From a purely mathematical point of view, there is no such thing as luck. People aren't lucky, dice aren't lucky, charms aren't lucky, calendar dates aren't lucky. However, widespread belief in luck persists, even among experienced game players.

Each of these fallacies has important implications for game design. For example, think about the long shot fallacy. If your game allows players a choice between a long shot and safe bet, you should expect most players to take the long shot and balance your formal system accordingly. Overemphasis on good outcomes and the lightning striking twice fallacies can help keep players optimistic in a game with a large chance element. Even if a player has seen a lot of bad luck, these fallacies keep hope for a turnaround alive.

The larger lesson is that when you design a game with a random element, it is important to understand not just the probabilistic mechanisms of chance, but also the way that players will interpret or misinterpret these mechanisms. All three "breakdowns" of chance highlight common pitfalls to avoid in game design. On the other hand, any of these hiccups in the strictly formal operation of chance could be used positively, as the starting point for a game design:

• 
  

  It may be true that a computer cannot generate true randomness. Why not make a digital game in which the operation of randomness is intentionally out of balance? Perhaps what seems to be a randomly generated string of numbers is really a secret code that needs to be deciphered. Or in certain locations of the game-world, the player can shift the operation of chance to his or her advantage.



• 
  

  It may be true that chance operations become strategic elements in the hands of competitive players. You might design a game in which players can legally construct or modify the "random" component of a game, such as spending game money to affect the outcome of a die roll or giving players the ability to strategically stack a deck of cards.



• 
  

  It may be true that players suffer from probability fallacies. Design a game around one of them. Build a game around luck, in which players pick lucky and unlucky numbers for themselves, rolling dice and trying to avoid unlucky numbers and score the lucky ones.

Any "rule" of game design that you might think of can be broken, and as we will discover in Breaking the Rules, broken design rules can often lead to innovative game design ideas.

[8]John L. Casti, Complexification: Explaining a Paradoxical World Through the Science of Surprise (New York: HarperCollins, 1994), p. 93.

[9]Kenneth Goldstein, "Strategies in Counting Out" In The Study of Games, edited by Elliott Avedon and Brian Sutton-Smith (New York: John Wiley & Sons, 1971), p. 172–177.

[10]Epstein, The Theory of Gambling and Statistical Logic, p. 393–394.