SOREN JOHNSON
One of the most powerful tools a designer can use when developing games is probability, using random chance to determine the outcome of player actions or to build the environment in which play occurs. The use of luck, however, is not without its pitfalls, and designers should be aware of the tradeoffs involved—what chance can add to the experience and when it can be counterproductive.
Failing at Probability
One challenge with using randomness is that humans are notoriously poor at evaluating probability accurately. A common example is the gambler’s fallacy, which is the belief that odds even out over time. If the roulette wheel comes up black five times in a row, players often believe that the odds of it coming up black again are quite small, even though clearly the streak makes no difference whatsoever. Conversely, people also see streaks where none actually exist—the shooter with a “hot hand” in basketball, for example, is a myth. Studies show that, if anything, a successful shot actually predicts a subsequent miss.
Also, as designers of slot machines and massively multiplayer online games are quite aware, setting odds unevenly between each progressive reward level makes players think that the game is more generous than it really is. One commercial slot machine had its payout odds published by wizardofodds.com in 2008:
1:1 per 8 plays
2:1 per 600 plays
5:1 per 33 plays
20:1 per 2,320 plays
80:1 per 219 plays
150:1 per 6,241 plays
The 80:1 payoff is common enough to give players the thrill of beating the odds for a “big win” but still rare enough that the casino is at no risk of losing money. Furthermore, humans have a hard time estimating extreme odds—a 1 percent chance is anticipated too often, and 99 percent odds are considered to be as safe as 100 percent.
Leveling the Field
These difficulties in estimating odds accurately actually work in the favor of the game designer. Simple game-design systems, such as the dice-based resource-generation system in Settlers of Catan, can be tantalizingly difficult to master with a dash of probability.
In fact, luck makes a game more accessible because it shrinks the gap—whether in perception or in reality—between experts and novices. In a game with a strong luck element, beginners believe that no matter what, they have a chance to win. Few people would be willing to play a chess grand master, but playing a backgammon expert is much more appealing—a few lucky throws can give anyone a chance.
In the words of designer Dani Bunten, ‘‘Although most players hate the idea of random events that will destroy their nice safe predictable strategies, nothing keeps a game alive like a wrench in the works. Do not allow players to decide this issue. They don’t know it but we’re offering them an excuse for when they lose (‘It was that damn random event that did me in!’) and an opportunity to ‘beat the odds’ when they win.”
Thus luck serves as a social lubricant—the alcohol of gaming, so to speak—that increases the appeal of multiplayer gaming to audiences that would not normally be suited for cutthroat head-to-head competition.
Where Luck Fails
Nonetheless, randomness is not appropriate for all situations or even all games. The “nasty surprise” mechanic is never a good idea. If a crate provides ammo and other bonuses when opened but explodes 1 percent of the time, the player has no chance to learn the probabilities in a safe manner. If the explosion occurs early enough, the player may stop opening crates immediately. If it happens much later, the player may feel unprepared and cheated.
Also, when randomness becomes just noise, the luck simply detracts from the player’s understanding of the game. If a die roll is made every time a StarCraft Marine shoots at a target, the rate of fire simply appears uneven. Over time, the effect of luck on the game’s outcome is negligible, but the player has a harder time grasping how strong a Marine’s attack actually is with all the extra random noise.
Furthermore, luck can slow down a game unnecessarily. The board games History of the World and Small World have a similar conquest mechanic, except that the former uses dice and the latter does not (until the final attack). Making a die roll with each attack causes a History of the World turn to last at least three or four times as long as a turn in Small World. The reason is not just the logistical issues of rolling so many dice—knowing that the results of one’s decisions are completely predictable allows one to plan out all the steps at once without worrying about contingencies. Often, handling contingencies is a core part of the game design, but game speed is an important factor too, so designers should be sure that the tradeoff is worthwhile.
Finally, luck is inappropriate for calculations to determine victory. Unlucky rolls feel the fairest the longer players are given to react to them before the game’s end. Thus the earlier luck plays a role, the better for the perception of game balance. Many classic card games—pinochle, bridge, and hearts—follow a standard model of an initial random distribution of cards that establishes the game’s “terrain,” followed by a luck-free series of tricks that determines the winners and losers.
Probability Is Content
Indeed, the idea that randomness can provide an initial challenge to be overcome plays an important role in many classic games, from simple games such as Minesweeper to deeper ones such as NetHack and Age of Empires. At their core, solitaire and Diablo are not so different—both present a randomly generated environment that the player needs to navigate intelligently for success.
An interesting recent use of randomness is Spelunky, which is indie developer Derek Yu’s combination of the random level generation of NetHack with the game mechanics of 2-D platformers such as Lode Runner. The addictiveness of the game comes from the unlimited number of new caverns to explore, but frustration can emerge from the wild difficulty of certain unplanned combinations of monsters and tunnels.
In fact, pure randomness can be an untamed beast, creating game dynamics that throw an otherwise solid design out of balance. For example, Civilization III introduced the concept of strategic resources that were required to construct certain units—chariots need horses, tanks need oil, and so on. These resources were sprinkled randomly across the world, which inevitably led to large continents with only one cluster of iron controlled by a single artificial intelligence (AI) opponent. Complaints of being unable to field armies for lack of resources were common among the community.
For Civilization IV, the problem was solved by adding a minimum amount of space between certain important resources so that two sources of iron never could be within seven tiles of each other. The result was a still unpredictable arrangement of resources around the globe but without the clustering that could doom an unfortunate player. On the other hand, the game actively encouraged clustering for less important luxury resources—incense, gems, and spices—to promote interesting trade dynamics.
Showing the Odds
Ultimately, when considering the role of probability, designers need to ask themselves, “How is luck helping or hurting the game?” Is randomness keeping the players pleasantly off balance so that they can’t solve the game trivially? Or is it making the experience frustratingly unpredictable so that players are not invested in their decisions?
One factor that helps to ensure the former is making the probability as explicit as possible. The strategy game Armageddon Empires based combat on a few simple die rolls and then showed the dice directly onscreen. Allowing the players to peer into the game’s calculations increases their comfort level with the mechanics, which makes chance a tool for the player instead of a mystery.
Similarly, with Civilization IV, we introduced a help mode that showed the exact probability of success in combat, which drastically increased player satisfaction with the underlying mechanics. Because humans have such a hard time estimating probability accurately, helping them make a smart decision can improve the experience immensely.
Some deck-building card games, such as Magic: The Gathering or Dominion, put probability in the foreground by centering the game experience on the likelihood of drawing cards in the player’s carefully constructed deck. These games are won by players who understand the proper ratio of rares to commons, knowing that each card is drawn exactly once each time through the deck. This concept can be extended to other games of chance by providing, for example, a virtual “deck of dice” that ensures that the distribution of die rolls is exactly even.
Another interesting—and perhaps underused—idea from the distant past of gaming history is the element-of-chance game option from the turn-based strategy game Lords of Conquest. The three options available—low, medium, and high—determined whether luck was used only to break ties or to play a larger role in resolving combat. The appropriate role of chance in a game ultimately is a subjective question, and giving players the ability to adjust the knobs themselves can open up the game to a larger audience with a greater variety of tastes.