将随机性整合到《Pedit5》的设计中引起了一个有关计算机时代的古老问题：当我们放手，让一切听天由命时会怎样？但这也是游戏在各个世纪会以不同形式呈现出来的问题，并伴随着将自己的命运投掷在随机机制中的人类。20世纪基于骰子的桌面游戏，如Ludo和印度双骰游戏便可以追溯到1914年由德国人设计的《Mensch ?rgere Dich Nicht》。我们可以将其粗略地翻译为“喂，别生气”，即意味着游戏带有让人沮丧的随机性关卡。一款1965年的家庭类游戏《Trouble or Frustration!》也是完全依赖于运气元素。在这款游戏中，玩家必须滚动骰子并获得点数6才能出发。这些游戏都是受到印度双骰游戏所谓的“交叉和圆圈”家庭规则的影响。
英国建筑师兼作家Edward Falkener在其1892年出版的书籍《Games Ancient And Oriental And How To Play Them》中探索了16世纪的印度双骰游戏，根据报道，印度皇室会将活人当成棋子，并在一个巨大的棋盘上操纵着他们玩游戏。Falkener写道：“印度阿克巴皇帝和他的侍臣们会一起玩这种游戏；16个年轻的奴隶被命令穿上代表不同棋子的颜色的衣服，并根据骰子的滚动朝方形移动。”根据Falkener，玩家是用来自宝贝螺（一种海产软体动物）中的6个贝壳代表骰子。然后玩家会计算有多少贝壳是开放一面朝上。所以印度双骰游戏是最早基于随机掷骰子原理的游戏（人类是在20世纪20年代一个苏美尔人的坟墓中发现这一事实）—-这要追溯到公园前2600年，那时候他们还是使用四面体的骰子。
The Director只是关于支配《求生之路》中随机元素的算法集合的名字。它不带有任何感情或目标，但是玩家必须将The Director的想法当成一个实体，并如此进行讨论与思考。
在YouTube上名为《The Director Hates Us》的视频中，一名玩家描述了其最近的游戏体验。他说道，The Director会选择性地攻击自己与好友，并隐藏重要的健康包，直到他们来到关卡的最后环节。他在视频的描述中写道：“他会在采访车和急射机枪右边设置一个女巫。”
基本上人类总是希望能够看到代理和模式，即使现实中什么都没有。我们很容易想象到特性是如何在人类发展过程中保留下来。游戏《100 Rogues》的设计师，同时也是《Game Design Theory: A New Philosophy For Understanding Games》的作者Keith Burgun认为，当人们在玩游戏时，这种继承性便会表现出来。他说道，当孩子们在玩《Candyland》这样的桌面游戏时，他们便会相信在自己的骰子角色背后拥有一个代理。甚至当人们逐渐长大并开始清楚自己不能真正控制骰子这样的事物时，他们仍会将在大多数随机游戏中的成功归功于自己。
在Rusty Rutherford离开了原本的工作和自己所创造的先驱游戏后，18岁的Paul Resch来到了伊利诺伊大学的地下室。Resch沿着混凝土阶梯走下，走进一间泛着橙色灯光的房间，这是PLATO系统所发出的光线。一群学生集中在机器附近，正在使用这些机器去学习果蝇的杂交（生物课）。看来这是一项有关教育游戏的项目。
他自己的班级还未上课，但是Resch却非常想要试试这些先进的机器，所以他便假装自己也是一名生物学学生，偷偷地访问了一个终端。正是在那里，他发现了一个被遗弃的文件：Pedit5。Resch联系了一些好友，并在接下来几个月的时间里开始修改代码去完善它。Resch创造了基于网络的多人聊天系统，并将其整合到游戏中。他还添加了来自《龙与地下城》世界中的更多规则，他们甚至还想办法获得了Tactical Studies Rules（游戏邦注：TSR，《龙与地下城》在那时候的发行商）的使用许可。
欢迎来到本课程的第五堂课：关于游戏设计的基本介绍。在阅读本文前请确保你先了解教学大纲和课程信息。今天我们将讨论游戏设计中的机会和技能。本文是遵循我们的教科书《Challenges for Game Designers》的第五章和第八章。我的灵感同时还源自Schell的《The Art of Game Design》（第十章内容）以及Adams和Rollings 的《Fundamentals of Game Design》（第十一章内容）。
Jesse Schell在他的《Art of Game Design》中区分了3种主要的技能类型。需要注意的是许多游戏都需要混合这些不同的技能，而这些策略也只是提供了一个起点：
最后一种适用事后运气元素的情况就是非常短小的游戏。我喜欢《King of Tokyo》，尽管它完成是一场骰子游戏，含有大量事后运气元素。即使你真的只得到一些很糟糕的点数，这款游戏也不过10-15分钟，不会让你觉得浪费时间。而如果你在一个骰子上投入4个小时，那就真的太不值得了。
在桌游中，Stefan Feld可以说是事前运气的大师。他的许多游戏都包含此类限制你操作的运气机制。例如，在《The Castles of Burgundy》或者《Bora Bora》中，你掷骰子，并由这些骰子上的数字来决定你可以采取的行动。
在游戏设计中，我最喜欢的词汇便是随机化。如果能够正确使用，它可以极大地提升游戏的再玩性。诸如《幽浮》和《暗黑破坏神2》之类的经典游戏都绝妙地运用随机化来让玩家不断玩游戏。近期出现的独立游戏，比如《Dungeons of Dredmor》、《Din’s Curse》和《Space Pirates And Zombies》，这些都是可以用来阐述随机化利弊的绝妙例证。
高：包含以上两种程度，再加上世界的随机化。rogue-like游戏通常使用这个程度的随机化，但是这个类别并不局限于rogue-like题材游戏。《Space Pirates And Zombies》在游戏开始时允许玩家创造随机的宇宙。诸如《文明》之类的TBS游戏也允许玩家在随机化的世界或预设的地图条件中玩游戏。
当然，随机化也存在某些弊端。回到之前那个赌博机的比喻，虽然其奖励充满诱惑力，但是如果失败次数过多会让人们感到很沮丧。在游戏《Dungeons of Dredmor》中玩最高的难度时，因为敌人和装备出现的位置，我有90%的情况在跳下第一层楼之前就失败了。
我要提的首个随机化关卡的不良例证便是《Phantasy Star Online》。在这款游戏中，每个地下城的布局都是随机的，但是游戏中的每个世界都只有几个空间。这意味着每层或许有4个不同的空间模型，而这就是游戏的全部。关卡设计完全是自毁式的，让人感觉像是将各种元素拼凑起来。这也是我们在创造随机化关卡时需要避免的事情，游戏世界的设置需要某种程度的凝聚力。《Dungeons of Dredmor》的首款零售版本有展示房间样式的地图，这从某种程度上降低了游戏的质量。
要创造出能够发挥作用的随机化系统，就必须将其构建在线性的层次之上。这意味着，对于每个随机化元素而言，都必须有某些担保的东西。比如在《Dungeons of Dredmor》中，虽然游戏世界每次都具有随机化特点，但是每层的敌人样式基本都受到限制。你永远都不会在第1层碰到本该在第5层看到的敌人，反之亦然。
Games of chance: what does randomness bring to videogames?
By Edge Staff
In the autumn of 1975, Reginald ‘Rusty’ Rutherford watched a monster – his monster – wander around a computer screen at random. The orange glow of the vector monitor displayed a map, a tiny hero with a sword, and contextual information rendered in the solemn style of Dungeons & Dragons. This is Pedit5, the earliest known roleplaying game on a computer.
Rutherford was a programmer working on the University Of Illinois’ Programmed Logic for Automated Teaching Operations (PLATO) computer system. The hardware, built in the ’60s, was among the first networked computer systems to be used for educational purposes. In the ’70s, decades before the Internet came into being, PLATO could connect to around 150 locations worldwide, and it was regularly being expanded to new ones. Space on the system was limited, but Rutherford’s group had access to two unused files, which were labelled ‘Pedit4’ and ‘Pedit5’.
Disregarding the rules against such things, Rutherford took Pedit5 and began working to develop a game based loosely on Dungeons & Dragons. Pedit4, meanwhile, became an instruction manual for his new game. Rutherford was attempting to emulate an incredibly rich and intricate boardgame, but his program lacked complexity. Each dungeon contained one floor and about 50 static rooms. The creator puzzled over how to keep the experience from getting stale.
He found the solution within D&D’s rulebook: randomisation. If Rutherford allowed PLATO to make its own decisions about where to place the monsters and treasure, the number of potential level layouts would skyrocket, and the game had a much better chance of holding players’ interest. Rutherford worked on Pedit5 until late ’75, but soon after moved on, leaving behind his job, the PLATO system, and the two secret files that would later become the foundation of an entire videogame genre.
The idea to incorporate randomness into Pedit5’s design brought an age-old question into the computer age: what is possible when we let go and leave things to chance? But this is a question games have been posing in various forms for centuries, with human beings throwing their fates into the hands of random mechanics. Dice-heavy 20th-century race boardgames such as Ludo and Parcheesi can trace their roots back to the 1914 German-designed Mensch ?rgere Dich Nicht. The title translates roughly to “Don’t be mad, man”, indicative of the game’s frustrating level of randomness. An irritating dependency on luck would also define the 1965 family game night atrocity called Trouble or Frustration!, depending on which side of the Atlantic you lived on. In it, players have to roll a six just to get on the board and play. These games fall into the jurisdiction of the so-called ‘cross and circle’ family, which most researchers believe originated with the Indian game of Pachisi.
In his 1892 book, Games Ancient And Oriental And How To Play Them, English architect and writer Edward Falkener traced Pachisi back to the 16th century, where royalty reportedly played on enormous boards with live human figures as pieces. “[Indian Emperor Akbar I] and his courtiers played this game; 16 young slaves from the harem wearing the players’ colours represented the pieces,” Falkener wrote, “and moved to the squares according to the throw of the dice.” According to Falkener, the game was played by throwing six shells from cowries, a type of marine mollusc, in lieu of dice. Players would then count how many shells landed open side up. And Pachisi is predated as the first game to leave an element of play up to random rolls of the dice (or a fishy equivalent) by The Royal Game Of Ur – discovered in a Sumerian tomb in the 1920s – which dates to 2600 BC and featured tetrahedral dice.
All these games, from The Royal Game Of Ur to Trouble, are really just more codified versions of a favourite BC pastime: casting lots. These were games of chance – simple systems built around a simple luck-based tool. Randomness has always been the easiest way to leave the outcome of a competition to the whim of God, instead of solely to skill.
But while today’s games – both board-based and digital – owe a debt to the history of early randomisation tools, it’s only in recent decades that we have begun to discover what randomness can achieve when we harness it in new ways.
‘Create New World’ says Minecraft’s rectangular button. Click it and an instant later you might find your nose pressed against a vine-covered tree trunk. Or perhaps you’re standing knee-deep in water. Maybe you’ll appear in a pumpkin patch, with a spotted cat lurking nearby. The possible scenarios are so numerous as to be effectively endless, generated by a fixed algorithm in combination with a random or player-given ‘seed’ sequence. Since each seed grows into a different world, few buttons can surprise and delight like the one in Mojang’s blockbuster hit.
Minecraft is about creating, living, and working resourcefully within a universe that has been instanced just for you. As a result, no GameFAQs walkthrough can tell players what’s around the corner in any particular cave, and YouTube tutorials won’t show you exactly where to find diamond ore. Since the advent of the Internet, videogames have been, as a rule, unable to hide secrets from their players. With its randomness, Minecraft spurns becoming solvable. You can learn how the game works at a basic level in minutes, but you have to play well to survive and thrive.
Like boardgames, videogames with lots of design randomness have traditionally been abstract. Think of Tetris with its ‘T’ and ‘L’ shapes, and that ever-elusive long block. Or consider Bejeweled, a game of raw systems built on the concept of matching like-coloured objects that fall from the heavens. But neither is truly random. Tetris, for example, generates randomly shuffled but discrete sets of all of its block types to ensure you never play a game that presents an endless procession of ‘Z’ blocks.
But games need not be abstract to benefit from leaving swathes of the experience up to chance. The Diablo series has progressively striven to randomise as much of its own content as possible, from loot drops to map layouts. And 2009’s Borderlands, with its purported 17.75 million guns, used a random item generation system as the crutch of its marketing campaign. Even popular mass-market series like Gears Of War are embracing randomness to alleviate repetition. Die and restart a level in Gears Of War: Judgment and its Smart Spawn system sends you a group of new, randomly selected enemies to fight.
The notion of semi-authored randomness is core to the genius of Spelunky, Derek Yu’s sublime merging of the platforming and roguelike genres. Like many games before it, Spelunky features randomly generated levels, in this case constructed from rooms made of randomly selected tiles from a fixed set. An algorithm then runs a set of checks and populates the level with monsters and obstacles, which are also subject to randomness, but balanced by intelligent rules. You play this setup just once. Either it kills you and you restart, or you succeed and move on to the game’s next world, which is built from a new set of level tiles and algorithms.
One of the most obvious benefits of this is that the game avoids becoming repetitive. Instead of falling back into a world you’ve partially conquered once, Spelunky’s levels ask you to overcome a new space that’s forged by the same consistent laws. It expects you to navigate the new landscape using what you’ve learned from previous runs.
Randomness allows players – and even creators – of games to be continually surprised by them. But is randomness in game design all about world and weapon generation? Is creating a game with endless content a goal worth pursuing? Yu doesn’t think so.
Needlessly padding out a game’s length using randomness, he says, can be “one of the worst things you can do unless you’re still introducing new things to the player and giving them a great experience”. To Yu, this means constantly observing and learning new things, being challenged, and “having your concept of the world expand”.
An extreme example of a not-fun implementation of a random system would be a slot machine. Pulling a lever and watching cherries and lemons spin teaches you nothing – the spinning is meaningless noise. Trying to understand and control it is a little like trying to divine a pattern in TV static, but that doesn’t prevent some people from becoming hopelessly addicted to the machines due to the rush of endorphins they can induce. Yu calls this handling of a system by the human brain “the inherent addictiveness of randomness”.
The human brain is wired to find patterns in noise, and so even when an implementation of randomness is just static, players will often interpret it as coming from an unseen controller.
Take Valve’s 2007 hit Left 4 Dead, which may have fixed, unchanging levels, but employs great degrees of randomness in other areas of its design. Vital resources such as health packs and weapons can be found in different quantities and locations on each playthrough. The game’s hordes of zombies are also placed at random, with huge waves bursting forth at times, all dictated by an underlying AI system called The Director.
The Director is really just a name given to a collection of algorithms that dictate the implementation of Left 4 Dead’s random elements. It has no emotions nor goals of its own, but players have latched on to the idea of The Director as an entity, and often discuss the game in terms of them versus it.
In a YouTube video titled The Director Hates Us, one player describes a recent gameplay experience. He says that The Director chose to attack him and his friends, and hid vital health pickups from them until a late part of the level. “He also threw a Witch right next to where the news van and minigun were,” he wrote in the video’s description.
Of course, the man behind the curtain is just a machine, but because the verdicts and outcomes delivered by it are unpredictable, players have anthropomorphised it. The Director – or the bits of code that compose him – assumes a living quality because unpredictability makes him seem human.
It is a basic human need to see agency and patterns even when there are none. It’s easy to imagine how that trait has remained an asset throughout the process of human evolution. Keith Burgun, designer of the game 100 Rogues and author of Game Design Theory: A New Philosophy For Understanding Games, argues that this inheritance reveals itself when people play games. When children play a boardgame like Candyland, he says, they believe that they have agency behind their dice roles. Even as people get older and begin to understand that they don’t have real control over things like dice, they continue to attribute successes in mostly random games to themselves.
“People stand up and celebrate when they roll a 20 in Dungeons & Dragons,” says Burgun. “They allow themselves to participate in this very human thing, this tendency to see agency where there isn’t any.” Burgun remains quiet for a moment, then observes in a manner and tone that is characteristic of him and his work: “This is also the origin of God.”
A few weeks after Rusty Rutherford left his job and his pioneering game behind him, the 18-year-old Paul Resch walked into the basement of a building on the University Of Illinois’ campus. Resch descended a flight of concrete stairs and entered a room lit by the neon-orange glow emitting from more than a dozen PLATO system displays. Groups of students huddled near the machines, using them to learn about the cross-breeding of fruit flies for a biology class. The program seemed to be some sort of educational game.
His own class wasn’t scheduled to begin yet, but Resch desperately wanted to toy with the highly advanced machines, so he pretended to be one of the biology students, stealing access to one of the terminals. It was here, through chance, that he discovered an abandoned file: Pedit5. Resch gathered some friends and over the course of the following months began modifying the code to improve it. Resch built networked multiplayer and a chat system into the game. He added more rules from the Dungeons & Dragons universe, and even retrieved proper permission to use them from Tactical Studies Rules (popularly known as TSR), D&D’s publisher at the time.
TSR’s response was mostly one of bewilderment. “They wrote back saying, ‘Sure, we don’t know what you’re talking about, but OK,’” Resch explains. More changes were made, and Resch decided that his game had evolved enough to warrant a new name. He titled his modified game Orthanc, naming it after Saurman’s tower from The Lord Of The Rings universe.
Eventually, Resch designed an algorithm that would automatically create random levels for Orthanc. Every six months in real time, the algorithm would run and Orthanc’s old world would disappear forever, replaced by a new, albeit temporary, one. A couple of weeks before the level-change event would occur, a message would display to PLATO users currently active in the game: “New levels are coming.” It was a friendly heads up, but also a warning – if users kept playing right up until the moment of the level-generation event, the entire world would vaporise around them, and a new one would materialise. It was more than likely that they’d then find themselves trapped by walls on all sides.
Resch – who is now 55 and has worked for companies including Atari, Apple, and Google – was developing features that we didn’t associate with videogames in the mid-’70s.
But why design a complex algorithm that only executes twice a year? Why not just design the levels yourself? Resch’s reasoning was both cogent and macabre: he knew he wouldn’t always be around to make new content. In a way, he was taking out an insurance policy in preparation for his own inevitable death.
Randomness in games has often been about replacing or simulating humans. Rutherford and Resch modified their games to become self-replenishing. The Smart Spawn system in Gears Of War: Judgment is a miniature designer included in the game who watches players and provides those who have to repeat a sequence with something new to play with.
Other videogames, such as Spelunky and Minecraft, make use of random systems not to pad out their length, but to allow for surprising situations to come about on their own. It’s a totally different application of randomness than when you roll a die and win based purely on luck in a game of Ludo or Parcheesi.
The surprise that comes when a game cooks up an amazing thing the designer didn’t think of is the sort of gift only videogames are capable of giving. So when choosing the random games we make or play, it seems wise to ask a simple question: do we want to be surprised, or do we simply want to feel lucky?
篇目2，Chance and Skill in Game Design
Welcome to the fifth week of class in the course: Basic Introduction to Game Design. Make sure to read the syllabus and course information before you continue. Today, we are going to discuss chance and skill in game design. This text follows closely from our textbook (Challenges for Game Designers, Chapter 5 and 8). I also take inspiration from Schell’s The Art of Game Design (Chapter 10, pp.150-170) and Adams’s and Rollings’s Fundamentals of Game Design (Chapter 11). However, this is the part when I break free.
Games, which feature meaningful decisions, do not always have to require or evoke skills from a player. Some games operate entirely by chance. Games that rely more heavily on chance than on skill are often found in the context of children’s games or gambling. Why does this difference matter? The player is going to play, play, play, play, play – are they not? Do not shake off the notion of chance too swiftly. Games of chance can be very engaging, because they can allow players of different skill sets to engage in a balanced competition. Games are for everyone; for people, who are used to rolling the dice and people, who like to feel the fear in their enemy’s eyes. Some people even think it is fun to lose and to pretend. However, games of luck in particular seem to feature more attainable goals and are winnable by more people.
On the other hand, games like Tic-Tac-Toe are entirely skill-based and can be mastered, once a player figures out a dominant strategy. See this example lecture for forming a Tic-Tac-Toe strategy via reasoning.
It might seem crazy what I am about to say, but there are several reasons for games to use chance as a game mechanic:
The game designer wants to prevent or delay the player from solving the game.
The game designer wants the gameplay to be balanced and competitive for all different kinds of players.
Chance can increase the variety of elements in your game system.
Chance can help you create dramatic moments in your game.
Chance can enhance the decision-making in your game.
On Game Balance
Adams and Rollings describe a balanced game as “fair to the player or players, [...] neither too easy nor too hard, and makes the skill of the player the most important factor in determining his success.” A game that is considered well-balanced, therefore, has the following characteristics:
The game provides meaningful choices. Several strategies can allow the player to win. There is no dominant winning strategy in the game.
Chance does not play a role so great that player skill is irrelevant. A player with more skill should be more successful than a poor player.
The game’s level of difficulty should be consistent. The players perceive the challenges in the game as not abrupt and within a reasonable range of their abilities.
In Player-vs-player games, the following characteristics also apply:
The players perceive the game as fair.
Any player, who falls behind early in the game, gets some opportunity to catch up before the end of the game.
The game seldom or never results in a stalemate if the players are of unequal ability.
Playtesting for luck and skill balance
When balancing games, an important factor to consider is the balance of skill and luck elements in the games. Some of the following are signs indicating that your skill/luck balance might be off:
Your players are bored. This is generally a sign of missing interesting decisions in the game and too many luck elements.
Your players are only bored when it is not their turn. Your game is likely lacking some strategic elements as none of the things players do during their turn seem to affect other players’ turns.
Your players do not become engaged in the game and are confused about what to do. This could be a sign of too many decisions or too much information to process for players.
One of your players beats all the other players by a wide margin. This could be an indicator that your game is heavily skill-based and one player has mastered this skill. To keep a game balanced for players with different skill levels, it is important to add some elements of luck to it.
Generally, adding “luck” to a game comes down to adding elements of randomness. In board games, this is often done through dice rolls or shuffling cards. If you find that you are using too many of these random elements, you can replace them by using distinct automated advances (e.g., moving a player token a distinct number of spaces during a turn) or by adding a player decision instead of the random element (e.g., players can choose from a given range of movement options). Player decisions are not just complex thinking decisions at all times, but can also be split-second dexterity-based decisions (twitch skills like hitting notes in Guitar Hero).
Our textbook (Challenges for Game Designers) distinguishes between three types of luck/skill games:
1.Games of chance. This can be either children’s games or gambling games. These games can often be enhanced by adding twitch and strategic elements to them. Often just the illusion of skill in those games is enough to make them more interesting.
2.Games of twitch skill. These are games that are focused on a challenge of dexterity. These games tend not to work too well with chance elements, but adding simple tactical options is quite common. Anything that keeps the flow of the game is a possible addition.
3.Games of strategic skill. These games can feel tense and slow, because they involve a lot of thinking. Adding twitch elements can be a welcome interruption of these long strategic sessions. Many long-winded RPGs feature little twitch mini games (such as lockpicking in Skyrim) to interrupt some of the longer stretches.
Types of Skills
Jesse Schell distinguishes between three main categories of skill in his Art of Game Design book. Keep in mind that many games require a blend of different skills, but these categories provide a starting point:
1.Physical skills: Skills like dexterity, coordination, strength, and physical endurance. These types of skills are most commonly found in sports games. However, some might argue that the correct keypress and controller sequences found in some esports would also fall into this category.
2.Mental skills: Skills like observation, memory, and puzzle solving. Often these relate to making interesting decisions in a game, as most interesting decisions are also tactical decisions.
3.Social skills: Skills like reading an opponent, tricking an opponent, and coordinating with teammates. These relate to a player’s ability to make friends and influence people in a game. They are often tied to a player’s communication skills. This is also commonly seen in team-based sports.
Schell also distinguishes between real skill, which means your actual skill as a human person in controlling the game in a certain way, and virtual skill, which relates to your in-game character’s skill at doing something. Real skills only improve when you work on them, while virtual skills can improve even when your real skill does not improve. In general, Schell suggests making a list of all skills in your game as an exercise to break down your game into skill components. Finding out what skills you require from your players will make you a better designer.
Chance can make games more fun, because it adds elements of uncertainty to it. Uncertainty equal surprises for players and humans do enjoy surprises. Chance is also related directly to probability in games, and Schell lists ten rules of probability with which game designers should be familiar:
1.Fractions are decimals are percents. Fractions, decimals, and percents essentially all work the same way and are essentially the same thing: 1/2 = 0.5 = 50%. As humans, we like to express probabilities in percentages.
2.Zero to one – and that’s it. This concerns, of course, probabilities, which all happen in the space between 0 and 1 (i.e., 100%). Chances like -10% or 110% do not exist when we speak about probabilities in games. If you are trying to calculate the probabilities of your dice rolls and they come up higher than 100, you know that you will need to run your calculation again.
3.”Looked for” divided by “possible outcomes” equals probability. Probability really means you take the number of times the outcome that you are looking for can (or has) come up and divide this by the number of possible outcomes (in the case that all outcomes are similarly likely) .
4.Enumerate. Let’s say that you are trying to find the outcomes that you are looking for and it is not as straightforward as the numbers on a D6; a good way of getting to your answer is just to list all the possible outcomes in your scenario. This helps you see patterns and combinations.
5.In certain cases, OR means ADD. When trying to determine the chances of x or y happening (like drawing certain cards from a deck) and these events are mutually exclusive, you can add the probabilities to get the overall probability of an OR event.
6.In certain cases, AND means MULTIPLY. When we are looking for the probability of two things happening simultaneously, we can multiply their probabilities. This only works if the two events are NOT mutually exclusive.
7.One minus “does” equals “doesn’t.” This quite logical as 1 represents a 100% chance of something happening. So, whenever you have calculated the probability of something occurring, you can subtract this number from 1 to find the probability of the opposite event occurring.
8.The sum of multiple linear random selections is NOT a linear random selection. By linear random selection, we are referring to a random event where all the outcomes have an equal chance of occurring. A die roll is a great example of this. Adding multiple die rolls does not mean that the possible outcomes have an equal chance of occurring. Rolling a die twice means that you have a higher chance of a seven occurring. The possible outcomes of this scenario follow a probability distribution curve (a normal distribution in this case), where the numbers in the middle (6,7,8) have a higher likelihood of coming up.
9.Roll the die. Schell distinguishes between theoretical probability and practical probability. Theoretical probability is what we have talked about so far. It is what is likely to happen in a general case. However, practical probability accounts for what has already happened. For this you would just roll a die over and over and record the number that you are getting and calculate your probability based on this. Ideally, this probability should approach the theoretical probability with a repeated number of trials. This is also known as the Monte Carlo method.
10.Geeks love showing off (Gombauld’s law). Schell basically recommends to find a math wiz friend, whenever you are facing a probability problem that you cannot solve on your own. This can also include posting math and probability related questions to mailing lists.
Some important things to remember about chance are (from Adams and Rollings):
Use chance sparingly.
Use chance in frequent challenges with small risks and rewards.
Allow the player to choose actions to use the odds to their advantage.
Allow the player to decide how much to risk.
篇目3，Randomness and Game Design
by Keith Burgun
For thousands of years, we’ve relied on randomness of various kinds to help our interactive systems work. While there will always be a place for randomness of all sorts in some kinds of interactive systems, I believe the current assumptions with regard to randomness in strategy games are largely wrong.
The major point I’d like to make is that noise injected between a player’s choice and the result (here referred to as output randomness) does not belong in a strategy game.
What is “randomness”?
For the purposes of this article, randomness refers to “information that enters the game state which is not supposed to ever be predictable.” The process by which random information is generated is designed to be something that humans can never figure out. Classic examples of random systems are rolling dice, shuffling cards, or random number generators.
Technically speaking, a die’s rolling pattern is not actually “random”. It’s simply responding to physics, and a computer could take information about how a die was thrown and predict the number that would come up. We use dice precisely because a human being can’t do that. In fact, when we incorporate dice into our game designs, we do it under the assumption that no human will ever be able – nor likely even try – to predict the outcome.
In fact, trying to actually predict how the die will roll, by perhaps carefully tossing it with a specific, intended trajectory, so that it rolls to a side you intend, would likely be called out as “cheating” by any observers. The whole idea with a die is that you’re not supposed to know. It is noise that must remain noise, forever.
Part of the reason for this is the fact that we’re actually dealing with two separate, closed systems in a game that contains randomness. A rolling die is a closed system of its own that really has nothing to do with the greater game system.
This is distinct from other kinds of “unpredictable” or “uncertain” events. In chess, for example, players have some limit to the number of turns they can look ahead. Beyond that point, the events that occur are indeed unpredictable for that player. However, players can and do learn to look further and further down the possibility tree as they get better at the game. Part of the skill of chess is being able to explore that ever-increasing possibility space and come out with more predictive ability.
So while chess does have unpredictability, it does not have randomness. All games must have some kind of unpredictability in order to function, but randomness isn’t the only way to achieve that. Chess’s source of unpredictability – a highly complex game state – is unlike a random source in that it can slowly be chipped away at and understood.
Types of Randomness
Randomness can be separated into two categories: input randomness, and output randomness.
Output randomness – when we think of randomness in games, we’re usually referring to this. Output randomness is noise injected between the player’s decision and the outcome. Examples would be the dice roll combat in Risk or Memoir ’44, or the random number generation combat in X-Com or FTL. I will refer to systems that do not have this type of randomness as “deterministic”.
Input randomness – this type of randomness informs the player before he makes his decision. Typical examples of input randomness would be map generation in Civilization or Rogue, or face-up tiles or cards in a worker placement game like Puerto Rico or Agricola. (People often use the term “procedural generation” to refer to this kind of randomness in digital games.) This article will not focus on this type of randomness, but it’s important to know the distinction.
Interestingly, while these two types are certainly distinct enough from each other to warrant the classifications, they do technically exist on a continuum. Without going into much detail on it, it should be noted that irresponsible use of input randomness – where the player has very little time to respond to the new information, or where the game generates problems of wildly varying difficulty match to match – cause similar problems as output randomness.
The Strategy Game Learning Engine
Strategy games are engines that allow us to understand them. We play a game, we win or lose, and we make connections. “Oh, I see!” we say as we figure out some element of how the system works. For evolutionary reasons, we find this process enriching and entertaining. This is the “essential fun” of strategy games (largely the premise of Raph Koster’s book, A Theory of Fun for Game Design).
Let’s break down the process further.
Informing the Player – The player takes a look at the game state, trying to figure out what move to make. He is informed by his “skill” database – the collective total observations about the system and how it works that he’s made up until now.
Deciding the Move – A move is chosen, and the action is taken. As a result, the game state is changed. Alternatively, this could be “deciding the strategy” – a series of moves that collectively adds up to a larger strategic gambit.
Feedback in Outcome – Over the course of the rest of the game, the system responds to this input. A series of events take place after that decision, including the final win/loss event; all of which serve as feedback for the player, highlighting some causal relationship between them. Feedback also comes following a strategy, or at the end of a game.
Recording Skill – The player observes and records this cause-effect relationship and records it to his database. The player can then use that skill to make moves in the future. (Notably, this moment is where the essential “fun” of strategy games comes from, but it of course relies on the rest of the machine to function.)
As a player plays a game, over many matches, he builds to this “skill folder” and becomes a stronger player. In a shallow game, there might not be very many of these moments, whereas a very deep game can continue delivering these moments for decades if not lifetimes. This is generally why it’s considered a good quality for games to be strategically “deep”.
How do we achieve that depth? Well, the first way, which all game designers already understand, is emergent complexity. In order to create complexity, we design our games so that they generate complex emerging situations throughout play. A bishop, knight and rook against three pawns and a queen is not inherently complex; there’s a very small amount of data there. However, unleash these two forces on each other on a chessboard, and the amount of possible situations that could emerge is huge.
The second method for achieving depth is, as far as I can tell, not understood by most designers today. This method involves being aware of complexity effectiveness: the amount of correlation between a state, and the history of past states.
A strategy game only has a finite number of states throughout a match. From what I can find, it seems that the average number of moves in a chess game is somewhere around 40, for example. A real-time game doesn’t have discrete “turns” per se, but there’s still a finite number of meaningful states, no matter how you divide it up.
If your game is a continuous series of events that lead causally from one to the other, then you are maximizing the amount of unique situations that can occur. I think this idea is counter-intuitive to many, who think that random events occurring somewhere in there must increase the amount of unique situations. However, the opposite is actually the case.
Having a system be entirely deterministic causes your emergent complexity to be maximally effective. This is because each emerging situation is given the maximum amount of contextual nuance by all of the events that came before and after it.
The pink egg here represents the current game state. In the deterministic game, it is getting pulled at by the events along the timeline of the match. In the random game, the timeline is severed and the current gamestate isn’t affected by as much.
In the deterministic game, the current game state has ties to every part of the entire timeline. Because of that, it is being pulled into a more complex and more unique shape. What this is illustrating is the way that context, when causally related, provides meaning to a game state.
Of course, even highly random games do have some deterministic elements that do provide some context to game states. For instance, in a game like Summoner Wars (a turn-based wargame involving dice roll combat), the health of your summoner and the positions of units are both relatively deterministic and do provide some context for game states.
However, the vast majority of contextual information in a game no longer has meaning. I attacked your unit, and I rolled the dice. It came up as a “miss”, and then next turn you killed that unit. That event – you killing my unit – is not really causally linked anymore to the actions I took beforehand. What happened was that I took an action, then something random happened, and then you took an action. The tie has been severed, and we can no longer use my move as contextual nuance for our current game state. Your game is now no longer “A, therefore B, therefore C”. Instead, it is now “A, then B, then C”.
The most significant bit of feedback is the goal-state. Once a match has ended, that win/loss condition sends a charge backwards through the course of events, revealing a positive or negative charge for every event that led to it. This move was somewhat good because it led to this, which led to that, which led to this, which led to that, which led to my win.
This is not to say that when a player wins, all his moves were good moves. However, it does provide an anchor point that informs every other move. Of course, moves are made in an attempt to get the player as close as possible to the win state. Once the match ends, we can now see how and why each of those moves was effective. (Because of this, players can get a lot of the same kind of fun out of watching a replay and analyzing it as they can from playing the game.)
Overall, after playing a deterministic game, a player is left looking at a coherent strategic picture that has been painted over the axis of time. Alternatively, the non-deterministic game could perhaps be considered more like a number of incomplete pictures. In this way, the deterministic game maximizes its complexity effectiveness, and the non-deterministic game does not. The non-deterministic game is adding complexity, whereas the deterministic game is multiplying it.
Output randomness does not increase the depth of a game. How could it? There is nothing to explore in a dice-roll. We all know that the odds are 1/6 for any face coming up. There is literally nothing else to know or explore.
What it actually does is obscure the outcome. You may have played perfectly, and still lost. The game has now sent you off on a wild goose chase, thinking about where you must have messed up, when in fact your play wasn’t the problem; dice rolls were.
Because of that wild goose chase, the game seems more complex than it is. The game provides unreliable feedback, and only after playing many, many games will it become clear which feedback you should ignore. Essentially, random games delay learning – the essential fun part of games – by injecting false signals into the engine. It’s a super-cheap way to create the appearance of depth, which is why it’s incredibly tempting for game designers.
Humans are pattern-seeking animals. We see figures in the clouds, we see images in the static, and we see conspiracy where there’s only coincidence. The reason is due to the fact that it’s evolutionarily favorable to think this way. The same quality that causes a person to think he saw a ghost in some rustling bushes is the quality that causes a person to think he saw a lion in some rustling bushes. And over time, those who thought they saw a lion were the ones who escaped when there actually was a lion. Those were the people who passed their genes along to us.
For this reason and others, we’re now both cursed and blessed with seeing patterns everywhere we look, and game designers have been exploiting this in us for as long as games have existed.
Gambling machines have always relied on psychological tricks to exploit us into playing them. In order for anyone to actually want to play something as vapid as slots or roulette, some degree of self-deception has to take place. On some level, the player has to feel like he is responsible if he wins. Otherwise, how can they be invested at all? From ancient religious superstition (the Gods are angry at me!) to their more modern counterparts, like “blowing on the dice”, kissing “lucky” items, or other self-deceptions such as the gambler’s fallacy, we find ways to attribute meaning to events that are actually pure noise.
Serious players of highly random strategy games tend to be skeptical that this same trick could be working on them when they play their Summoner Wars and their Hearthstones. But why? If players are able to perform this trick on themselves in a system that has no strategy at all, it seems very easy to believe that such tricks would work on a smaller percentage of the overall system. In fact, baking random elements into a strategy game makes it all the easier to conflate noise and strategy feedback, because some of what happens in the game really is strategic and deterministic!
In these games, there is the actual skill of the game, but then there is also an additional “phantom skill” amount, which makes the game seem vastly deeper than it is. In actuality, most players probably have the system close to solved somewhat quickly, and the randomness is the deciding factor.
I’ve been arguing this position for a few years now, and over time I’ve encountered a number of counter arguments that I’d like to address.
“Output randomness is just input randomness for the next turn.” – Game designer and blogger DanC of the Lost Garden has said this to me numerous times in response to my positions. Basically he’s arguing that there is no actual difference between output randomness and input randomness.
This position has two major flaws. One is that it seems unaware of the possibility of a larger strategic picture that could be providing tons of complexity effectiveness that otherwise you’re losing out on.
The other major flaw is that even if it’s actually input randomness for the next turn, that’s what I call “unfair input randomness”. It’s up so close in your face that you don’t have time to respond to it. You now have a significantly different game state than you did a second ago, and there’s no discernible reason for it. On some games, you might play optimally, but get put into this position and lose anyway. On other games, you don’t get put into that position because the dice rolls go your way. Input randomness, when put up close enough to the player so that he can’t plan around it, is basically output randomness. Feedback is being artificially delayed.
Ironically, I agree with Dan’s sentiment that there’s no significant difference between output randomness and input-randomness-for-the-next-turn, although I think they’re equally bad.
To really drive the point home, imagine a scenario where you have a character who has a “to-hit” dice roll against a tough monster. He swings, and he misses! Well, that’s ok, it’s just input randomness for the next turn, after all! He tries to attack again, and misses again! At this point, you may already have lost, and it wasn’t because of any decision you made.
“Some games need output randomness to work.”
If you were to just rip the dice rolls out of Risk, it definitely wouldn’t work.
This simply means that they are shallow games. It’s understandable, because creating a coherent system that is deep is very, very hard to do. However, this is not a defense of randomness; more an indication of a weak design.
“If there’s randomness, then it’s all about risk management.”
A favorite of poker players. The idea behind this argument is that having random elements adds a “factoring in your odds” element to the game. You have to weigh the odds of outcome A happening against the odds of outcome B against the benefit of outcome A and the benefit of outcome B, and that makes games more interesting. Essentially, it’s combining odds and valuation.
This kind of risk management is not unique to random games. In any game that you haven’t solved, really every move you make is to some degree a risk that you must manage. In chess, there could be two major strategies – strategy A and strategy B. You might figure that A is more likely to work than B, but B has a bigger payoff than A, for instance. Randomness isn’t necessary.
As to the “calculating odds” aspect of this, determining odds is never interesting, especially not when you’re talking about something like counting cards in poker. Calculating odds in a deterministic system might be harder to do, but it would certainly be far more interesting due to all of the variables at play in a good, dynamic strategy game.
“Randomness doesn’t matter – just do the best you can!”
The argument goes something like, “if you care about randomness, you care too much about winning. Just have fun!”
This argument is not actually a defense of randomness in strategy games; rather, it is a defense of randomness in toys. Strategy games have a win/loss condition. If you are telling us to ignore that in FTL, then you are saying that FTL is a toy and that’s why randomness is OK.
“Players with a wider skill range can compete against each other.”
If a grandmaster and a newbie play chess against each other, the result won’t be interesting or fulfilling for either party. That much is true! This argument suggests that the answer to that is to throw in some randomness.
Of course, that’s throwing the baby out with the bathwater. You’ve now severely damaged your game for the sake of presenting people with the illusion of more-similar skill levels. The real answer to this problem is good matchmaking.
“Randomness makes a game more like real life.”
To quickly counter this argument, let’s simply assume that there is a set of values for strategy games which we can separate from the set of values for a simulator.
“Games with randomness still have skill to them!”
True, and I haven’t argued otherwise. The issue is that on a practical level, you will be able to actually explore less of that space in your lifetime, since so many of the games are essentially wasted on false random outcomes.
Other Feedback Distortions
I should also note a few types of output randomness that are not usually regarded as such, but function so similarly that they have many or all of the same pitfalls.
Simultaneous Action – Trying to guess what the opponent will do in RPS, for example, is effectively random. In fact, that’s why we use it to decide who has to go take out the trash – we consider it fair, because it’s random. The whole reason people agree to use RPS as the determining factor for who will take out the trash is because they know that there is nothing that they or their opponent can do to increase their chances. (Sure, there’s some study that says people are slightly more likely to play rock. But did your opponent read that study, or not? You’re now back to square one.)
Execution – Execution in games is a matter of “can”, not “should”. Can you press this sequence of buttons before my jump kick hits you in the face? Execution is still slightly better than randomness probably, due to the fact that you can at least get better at it. However, inside of a single match, it’s basically the exact same thing. The complex chemicals, nerves, muscles and tissues that stand between “what you wanted to do” and “whether your body actually makes the desired input” has tons of room for error. When you choose to make the input for your Dragon Punch, will it actually work? It’s effectively random.
Our collective perspective on randomness in game design really hasn’t budged much in 4,000 years. It’s time that we really gave this question some serious thought.
I’m not arguing that there is no place for any kind of randomness in game design. In fact, I argue strongly in favor of well-balanced, low-variance input randomness in multiplayer games. And single player games require input randomness.
However, output randomness in all its forms is to be avoided. The only time you should use randomness of that kind is if you’re making a gambling machine, or if you’re insecure about the depth of your system.
篇目4，Luck In Games
The amount and type of luck involved in a game has a profound impact on the feel of that game. Some games have no luck whatsoever, and all the variation comes from what the opponent does (chess), some of them are all about luck with not much else (roulette), and most of them fall somewhere in between, creating a wide spectrum of possible experiences.
We don’t talk much about the role of luck in video games, probably because it’s hidden away under the black box of the computer simulation, but just like with board games, it can have have a large impact in the type of experience the video game provides.
Thinking about luck in these terms was crucial for the game I’m working on (still unannounced!). We made some crucial decisions thinking about how luck was part of the game and kind what kind of experience it created for the player. I’m hoping this post helps people with similar design challenges.
This post should apply to any kind of game in general (board or video games). Next time, I’ll be focusing especially on luck in video games using this as a launching point for a deeper look. Also, I’m limiting the definition of luck to random effects built into the game system itself, and not due just to player interaction.
In games with no luck, players rely completely on their skill to win. In that way, they’re closer to sports. Games become an intense, straight competition, pitting players’ brains against each other. Right there it shows how luck (or in this case, the absence of luck) creates a very specific feel to a game.
Good examples of games without any luck are classics such as Chess or Go. There are also plenty of modern board games with no luck, like Puerto Rico, Caylus (they both have a minimal amount of luck in the initial tile order), or Hive.
It’s interesting that a lot of abstract games tend to have no luck, and the more thematic a game gets, the more they seem to rely on luck.
Are You Feeling Lucky?
Having some amount of luck in a game can be very beneficial for most kinds of board games. It accomplishes many things:
Keeps things varied from game to game
Keeps players feeling they have a chance to win even if they’re not currently ahead
Removes pressure from winning players (“If someone beats me, it’s because they had a lucky streak”)
Makes players who didn’t win feel they stand a chance next time they play (“next time I’ll catch a break and I can win!”)
Points 2, 3, and 4 all encourage more people to play the game and feel they’re competitive at it, even if they didn’t win (and even if they’re not really competitive). One of the best examples of this is poker: Everybody feels they can do great at poker, if only they get good cards. In reality, this is not true in the long term, but poker introduces plenty of luck that it really is true in the short term.
A consequence of all those points is that having some amount of luck allows players of different skills to participate in the same game and enjoy it equally. For games that rely on having multiple people looking to play it, it can be a big factor.
Types of luck
For games that choose to add some luck element, there’s a whole range of amounts and types of lucks they can use for different effects. Unfortunately, it’s also possible to mix the wrong type of luck with a given game feature and create a frustrating experience instead of an enjoyable one.
Post-action luck. This is luck introduced after the player has made a decision and executed an action. It can be in the form of flipping a coin to see if you unlock a chest, or rolling a dice to see if your armies invade a territory.
Pre-action luck. Pre-action luck consists of the random events that happen before the player performs an action. The player is able to take them into account and make a decision based on them.
Hidden information. Hidden information is the third kind of luck. I was a bit hesitant to include it as its own category first, but it seemed different enough from the other two to warrant being listed on its own. Hidden information refers to things that are known only to some players and will affect other players or the game scoring.
OK, I’m going to say it: I’m not a fan of post-action luck. The player has already made its action and the outcome is random (even if it’s based on a probability curve the player is aware of, like rolling 3 six-sided dice). Since it doesn’t add to the choices the player has, it’s mostly uninteresting. This is the kind of luck that can add a bit of spice to an otherwise boring game, it doesn’t do much to make the game more interesting.
When used incorrectly, this kind of luck is extremely frustrating. The player can feel they chose the “best” action, but they rolled double 1s and their move backfired on them. Sure, there was some tension knowing that could happen, but was it really fun? Maybe the first time or two, but probably not long term.
While I typically really don’t like this kind of luck in my games, there are some situations in which even I will add it can add some interest to the game.
The first case is when the player can choose to perform one action or another, being aware of the different probability curves for both actions. For example, you can roll a single die and deal that damage to an enemy, or you can roll two dice, but if you roll two 1s, your character gets hit instead. In a situation like that, even though it’s still post-action luck, the player was presented with a meaningful decision ahead of time and had to weight the risks and rewards of both options.
The second case where post-action luck can work is when the action is repeated many times over the course of a game. That way, the outcome of each individual action in themselves is not game-breaking, and all the actions will eventually add up to the average over the course of the game. Luck in this case introduces a bit of noise and slight excitement without affecting things much.
This is a good situation to combine with the ability for players to slowly change their probability curves over the course of the game. That way, they can increase their chances of success for an action as the game progresses, presenting the player with a way to feel more powerful. This is often used in RPGs and video games.
Having some kind of post-action luck that affects the outcome of an action can also give players hope that they can do something, even if those chances are small. Otherwise, without any luck involved, they would see the situation is hopeless and lose interest in the game. At the same time, having that luck element makes predicting every possible outcome nearly impossible, so it encourages players to make a decision without spending a long time figuring out an ideal outcome.
Finally, another situation where post-action luck isn’t always a bad thing is in very short games. I love King of Tokyo even though it’s a complete dice fest with lots of post-action luck. Even if you get some really bad dice rolls, a game maybe only lasts 10-15 minutes, so it didn’t feel like a complete waste of time. On the other hand, losing a 4-hour game to a dice roll can be extremely infuriating.
The dark side of post-action luck is the human addition to random rewards, which is the reason why gambling or slot machines are so popular. Games can exploit that human quirk to their advantage and hook players in a game that would otherwise not be very interesting or fun.
A very meta post-action luck is buying “booster packs” of collectable card games (like Magic The Gathering). Purchasing the cards is the action, and the luck happens when you open it and see which random cards were in the pack. As most ex-Magic The Gathering players can attest, this can be extremely addictive.
This type of luck can add just as much randomness as post-action luck, but creates a very different feel for the game. Since the random event happens before the player action, even if you didn’t get the ideal outcome you were hoping for, you can choose to do the best action given your situation.
To illustrate the difference, consider power-ups in a first-person shooter. You open the door to one room and there’s a mysterious gift package power-up. You have no idea what it is, you pick it up and… it turns out it was health. Maybe that’s great because you were low in health. Or maybe you were maxed out and it was useless. That’s post-action luck.
Alternatively, imagine you open that door and you see 3 power-ups side by side. You see what they’re going to give you (health, ammo, or a new weapon). As soon as you take one, the others go away. Maybe neither one of them is exactly the ideal, but you can make a decision and pick the best one for your situation. That’s pre-action luck.
In board games, Stefan Feld is the master of pre-action luck. A lot of his games involve some kind of luck mechanism that limits your actions. For example, in The Castles of Burgundy or Bora Bora, you roll dice, and the numbers on those dice determine which actions you can take.
Without going that far, just about any games that involves drawing cards from a deck and having a “hand” of cards uses pre-action luck. The cards you’re dealt are the pre-action luck, and then you have to do the best you can with those cards.
An extreme type of pre-action luck is initial game layout. That happens only a single time during the game, and before players make any actions, so it has the potential to affect the full course of the game. Even players who are adamantly opposed to luck in games, are often willing to accept game setup randomness because it can be fully taken into account during the game without any surprises.
Pre-action luck isn’t as common in games as post-action luck, but it could be used just about anywhere that post-action luck is used. Consider the classic situation of a character attack some monsters and rolling a set of dice that determine whether he hits and how much damage it does. We could change that into pre-action luck by having players roll the dice (either all at once or separately), and having the dice restrict the options of what they can do. For example, low rolls on one dice could indicate that they can only do an attack close to the ground, while high rolls means they can attack flying enemies. Then the player can choose which of those actions to take, or maybe he can instead take a defensive stance or run away.
The main downside of pre-action luck is that it can extend every player action. The more it’s used, and the more possible choices it presents to the player, the longer the game might take, so it’s best to save it for times where the decisions really matter. If not, either post-action luck or no luck at all, might be better choices.
The most common example in board games is hidden end of game bonuses. For example, in Shipyard players get a set of goals that will score them points at the end of the game. There are two reasons for these goals: By giving each player different goals, it encourages players to focus on different aspects of the game instead of fighting over the same set of “optimal” actions. It also encourages players to pay attention to what other players are doing, and potentially try to anticipate or even block other players from getting too far ahead in their goals.
An even more interesting case is the game Troyes (one of my favorites!). Not only does each player get a set of end-of-game goals to get extra points, but all players, not just the player holding them, will be scored based on those goals. That makes paying attention to other players and trying to guess what they’re doing even more important.
At the extreme end of hidden information there are games like Discworld: Ankh-Morpork, in which each player gets a hidden winning condition. Players go about doing their actions until someone announces at the beginning of their turn that they have won the game, and they reveal their hidden victory condition card.
The higher the importance of the hidden information, the more casual and random the game becomes (and so, the shorter the game should be ideally).
篇目5，A Look at Luck in Game Design
by Darran Jamieson
The luck vs. skill aspect of games is one which is fairly central to good design—indeed, it’s something we’ve covered before. But before we worry about trying to balance luck and skill, we really need to ask: what is chance, and to what extent is it necessary in a game? Furthermore, how can we implement chance in a way that feels rewarding rather than punishing, and use it to improve rather than detract from the overall playing experience?
Is Chance Required?
It’s nearly impossible to create a game without luck. A game without luck isn’t really a game—something like “who’s the tallest” or “who has the most fingers” doesn’t really involve any sort of challenge. These are simply measurements that the players are unable to change, and so are unlikely to provide much entertainment. A game must have an element of uncertainty—something like “who can balance on one leg the longest”, while not terribly in depth, is at least not predetermined. Even when one player is better, their success is not always guaranteed.
For many games, we use cards, dice, or a random number generator to create this unpredictability. But not all games use randomisation tools, and a serious strategy game like chess still requires an element of randomness: this element comes from the players themselves. Players are unpredictable, and will often adjust strategies and tactics on the fly, based on what they consider the best probable outcome. This is why, despite being a fairly static game, chess games can vary wildly: no two players approach the game the same way.
The reason humans can provide chance to chess is because chess is incredibly complex – in fact, we can describe chess as a complex game. Unfortuntely, unlike concepts such as “flow” or “zero sum game”, the term “complex game” isn’t a recognised term. Since we’ll be talking about complexity a lot, we should probably define what we mean by it.
So what is a complex game?
If we look at Tic-tac-toe, we can see a game with fairly simple rules. There are nine spaces, players place an X or an O, trying to make a straight line, and the game is always over in nine moves or fewer. It’s fairly easy to predict the results of a Tic-tac-toe game, even before the first move is made—assuming the two players play “correctly”, then the game will always end in a draw.
We can say then, that tic-tac-toe is hard to justify as a complex game. In fact, Tic-tac-toe has been solved, which is to say that we’ve calculated every set of possible moves, and essentially proven the best moveset. To make matters worse, humans are capable of “solving” a tic-tac-toe game without much mental agility.
Compare this to chess, which has 64 pieces and six different types of piece, each with their own moveset, special moves such as castling and en parssant, and a ruleset that means a game could (technically) last forever. Given these conditions, it’s perhaps unsurprising that chess has never been solved, even by the most powerful computers.
So, essentially, a complex game is one which has not been solved, or that cannot be solved by the players.
This addendum “cannot be solved by the players” is important. It means that games can continue to be fun, assuming the players are incapable of solving them. This is why Four-in-a-row (also known as Connect 4) remains a fairly popular game; although computers have solved it, when players sit down they are unlikely to be capable of calculating the perfect game in their heads, so they play non-optimally. Tic-tac-toe, while trivial for most players, is still a good game for young children who are unable to plot out every move in their head. Complexity is subjective.
So why is this important? Because a non-complex game (a simple game) is a boring game. If the game is not complex, then it is solvable. If it is solvable, then the outcome is predetermined; all the player is required to do is work out the best moveset, and they’ve won. And at that point, they may as well go back to playing “who has the most fingers”.
A small sidenote here, a solvable game can be better described as a puzzle. And while puzzles are popular (many newspaper print daily crossword puzzles), a puzzle is only fun up until it’s been solved – which is why crossword enthusiasts generally don’t sit and solve the same crossword over and over. Theres certainly nothing wrong in deciding to make a puzzle game, but be aware of what it is you’re aiming for, and how that will impact replayability.
Tools of Fate
So, when we look at games like chess or Tic-tac-toe, we can see they are all strategy games with no inbuilt randomisation: basic strategy games. There are, however, many games which do use dice, cards or other tools as an inbuilt mechanic, like snakes and ladders or poker. As most of these games can’t be considered complex, the inclusion of these dice or cards is necessary to prevent the game from being solvable. If, in the game of Snakes and Ladders, rather than rolling, players chose a number between one and six spaces to move every turn, then even children would quickly work out that “always choose six unless you land on a snake” is an optimal strategy.
Of course, adding randomness does not automatically make a solvable game good. In fact, you simply change the aim from “find the solution” to “find the best probable outcome”. You still essentially have a puzzle game, except that the win condition is not guaranteed. Too much randomness is just as bad as none; here again Snakes and Ladders is an obvious example. Almost no-one other than children plays the game, as it lacks any sort of interactive challenge and, therefore, people see it as ultimately pointless.
So why does a game like poker continue to work? Poker is, essentially, a series of mini puzzles. You are given a hand, and you have to “solve” how probable it is for you to win. You can then bet on your hand, based on how likely you are to win the game.
This is an oversimplified view of poker, and if this was all there was to the game, it would be fairly boring. It would be trivial to write a program to calculate the odds (although people do that anyway), and simply run it to maximise your wins.
The fun of poker comes from player interaction: from bluffing and confidence. You are not required to bet on a good hand, and you are able to bet on junk. In fact, this is arguably what the game of poker is truly about; the cards are simply there to facilitate this, and to provide a fresh round of lying every few minutes. By adding the random element, we’ve eliminated player knowledge, which means that we can use uncertainty as a game mechanic. Players are required to perform based on what they know, and it is the combination of calculating winning odds and outfoxing other players that lets poker maintain its fanbase.
Bored of Boards
So, although we’ve been talking about about traditional gaming, computer games use exactly the same principles of design. Games like Tetris or Bejewelled can be considered simple (with added randomness), and games like Starcraft or Team Fortress can be considered complex.
In almost all games, there is a certain puzzle-like quality. Even in an RTS or FPS, players are constantly making decisions based on optimal play: should I build tanks or planes? Should I choose the machine gun or grenade launcher? Should I turn left or right? Like in chess, the player attempts to make decisions based on what they think will result in the best outcome. The randomness isn’t (generally) provided by computer dice, but by the choices of the players in the game. Players are trying to outwit each other, as well as outskill them.
In fact, its possible to argue that the only randomness in a PvP game (like an FPS or RTS) should come from the players themselves. As we’ve talked about before, crits in TF2 are a subject of much contention in the playerbase—to summarise, any shot in TF2 has the possibility of being a crit shot. Crit shots require nothing more than the roll of a dice, and any damage dealt by a critical bullet will be twice or three times as much normal, which causes crits to be frequently lethal. While new players may enjoy the thrill of randomly getting a kill, “pro” players will see the crit mechanic as unnecessarily spoiling their skills.
The range of numbers we use for randomness also play a large effect on how things pan out. If a rifle deals 90-110 damage a shot, then if we have 150 health the random element is really a flavour effect: no matter what happens, we need to be shot twice to die. However, if we have 100 health, than a rifle will randomly kill us in one shot half of the time. Despite there only being a small range in randomness, the numbers used matter a great deal.
The Effects of Randomness
So why is it that “pro” players bemoan crit systems (and improperly implemented damage ranges) whereas “casual” players don’t? The answer, simply, is player expectation.
A pro player will have played their game of choice a lot. They will know it inside and out. They will know what damage they can take, what they can deal out, and what the outcome of any situation should be. And while they may sometimes judge things poorly, it is generally due to underestimating the opponent’s skill level, or making bad split-second decisions.
So when a pro player enters a battle, and they are instantly gibbed by a bullet for no reason other than luck, they might feel cheated. They knew what they wanted to happen, but because of an electronic dice roll, they were instantly killed instead.
New players will generally not feel this sting as sharply; they don’t know the game as well, they have fewer expectations of what should happen, and so they can enter a battle not really expecting to win. To them, battles are as much a learning experience as a test of skill.
This randomisation destroying expectation is something that can happen in almost any game with randomness. When you’re waiting for a line block in Tetris, and the computer instead gives you six S blocks in a row, the player might feel a little cheated. The popular game Puzzle Quest (essentially a bejewelled clone with RPG elements) received many player complaints about “cheating AI”; there are enough forum threads about it that the developers had to specifically come out and say that the AI doesn’t cheat.
So why does it feel this way? Why are so many players upset over randomly falling jewel colours? Because the randomness is subverting player expectations. When a player goes into a game, they are (generally) expecting to be challenged, but they’re also expecting that if they play well, they can win. When the game randomly throws some bad numbers at you, and you immediately lose, then you can feel cheated. You had an idea of how the game was going to play, and despite your best efforts, you were defeated—not by your own lack of skill, or superior opponent strategy, but by electronic dice. This, for most players, is incredibly infuriating.
This “luck subverting player expectation” extends into all sorts of game. In fact, the more luck involved in a game, the more likely it is to be frustrating. RPGs are a notable example, especially because of crit systems. Crits systems often seem like a fun little addition, but by the numbers they will almost always punish the players. This is because:
1.Players are, generally, expected to defeat most enemies.
2.Crits add randomness to battles.
3.Randomness in battle means unpredictable results.
4.Therefore, players will (occasionally) win battles they should have lost, but more often:
5.Players will lose battles they should have won.
This is, of course, assuming that the encounters are designed or tailored towards the player. Some RPGs simply throw the player at giant monster and be done with it; however, as professional designers, we should be looking to ensure that the game is tailored towards our players, rather than just throwing some dragons in and calling it a day.
Balancing Turn-Based RPGs: The Big Picture
Balancing Turn-Based RPGs: Party Members
Balancing Turn-Based RPGs: Enemies
The other problem then, assuming we have designed our combats carefully, is that a crit system over-favours the player. Imagine if, after a harrowing journey through time and space, the hero of our game walks up to the ancient demon terrorising the planet and kills him in one (critical) blow. Its not quite the epic battle of legend, and is likely to leave the player feeling underwhelmed and unsatisfied. A player wants a challenge, and denying them that challenge because of randomness is unlikely to provide satisfaction.
In the case of Puzzle Quest, whether or not the AI actually was cheating isn’t actually important: what is important is that to some players, it felt like the AI was cheating. The lucky streaks gotten by the player are likely to be ignored (due to their expectation of winning anyway), but having your victory snatched away by a series of unfortunate dice rolls may seem unfair and punishing.
So how do we fix things? It might seem like so far all we’ve really said is “randomness is bad”. And essentially, that’s true. We’re professional games designers; we shouldn’t be doing things randomly. Every decision the player makes should be the result of a carefully crafted experience, and putting in randomness can endanger that.
When we look more closely at it, we realise that randomness can be added for two primary reasons:
To make the outcome unpredictable, or
to generate content.
Let’s examine these:
As we talked about in our previous article, players enjoy winning.
As we talked about here, randomness somewhat replaces the need for skill.
Therefore, adding randomness to a game allows (in some sense) bad players to win against good players. In a game with no randomness, a good player will always win against a bad player.
Because of this, having this unpredictability can be an important part of a game: it allows bad players to influence the game, and (hopefully) become better. If a player is constantly matched up against superior opponents and is losing, chances are they will quickly lose interest.
However, good players will often dislike this randomness, and will often be put off by a game which “punishes” their skill.
So how can we fix this?
Well, one option is to have an Elo rating system. This essentially gives players a number based on their skill level: beat a grandmaster, and your Elo rating goes up; lose games to newbies, and your score will probably go down. It originated as a way for chess players to measure their skill, but many MOBAs (Multiplayer Online Battle Arenas, such as League of Legends and Defense of the Ancients) do this, so that when you enter a battle you are (theoretically) placed with people around the same skill level. Some first-person shooters have also attempted this, allowing players to rebalance the teams if one side is continually getting crushed.
Another option would be to have a handicap system. Not too dissimilar to an Elo system, a handicap system allows players to give themselves an artificial advantage based on their skill level. Fighting games will often do this, giving the weaker player a variable health and damage output bonus. Although a handicap system might not solve all skill imbalance issues (it’s easy to imagine online players abusing a system like this), it’s a good way to allow casual players to compete more equally with their hardcore friends.
In both these cases, you can reduce the randomness of innate game elements, leaving the players as the only randomness generators.
The problem with generating content randomly (or gameplay elements, like in the game of Tetris’s falling blocks) isn’t so much that we’re generating unpredictable content; it’s that, often, certain sequences of random elements are extremely punishing to the player.
If, in Tetris, the player is waiting for a line block, but we only generate S blocks for the rest of the game, then the player will have every right to be annoyed. And, while it’s improbable, it can happen.
In other games, such as a dungeon crawl RPG, we might have a 1% chance of generating a boss every time a monster spawns. If, by chance, we generate three bosses in a row, then the player might find themselves in an unwinnable battle.
By the same token, we might go through the game and never generate a boss. This could make the game incredibly easy, or (if the bosses drop equipment upgrades) incredibly hard. In either case, randomness has essentially destroyed our players’ enjoyment of the game.
In certain cases, randomness can completely remove a player from the game. In the popular collectible card game Magic: The Gathering, players build decks that require a combination of lands (power sources) and spells to defeat their opponents. The use of lands is an important balancing mechanism: a simple goblin might require one land in play, while a mighty dragon might require ten. However, if the player happens to draw no land cards, then they are unable to play anything; they are essentially forced to sit there with zero options until their opponent defeats them. While it’s possible to mitigate this to some extent, it’s a serious design flaw that a non-insignificant number of game losses are the result of bad luck, rather than being outplayed.
People feel loss more strongly than they feel gain. It’s an interesting psychological phenomenon; consider these two scenarios:
You are given $1,000. I ask if you want to gamble on a coin toss: heads you win an extra $1,000, tails you don’t. Alternatively, you can just have an extra $500 (no coin toss required).
You are given $2,000. I ask if you want to gamble on a coin toss: tails you lose $1,000, heads you don’t. Alternatively, you can just give back $500 (no coin toss required).
In general, people tend to take the guaranteed extra $500 in the first case, but gamble on the coin toss in the second… even though the outcomes for gambling are the same in each scenario! (Do the maths: whether you choose to flip the coin or not, and whether the coin comes up heads or not, the amount of money you end up with in the end is the same regardless of whether we’re talking about Option 1 or Option 2.)
This means that, if you have a mechanic in game which randomly rewards or punishes they players, the losses will, psychologically, outweigh the gains. If the gamble is optional then it opens up extra avenues of gameplay, but a forced gamble will mostly feel like punishment.
A final problem with generating content randomly is that it can be very difficult to generate content which is interesting. A great example of this is MMOs; World of Warcraft has dozens upon dozens of dungeons, each of which can take hours to complete, and weeks to successfully master. However, once the dungeons are mastered, they (arguably) offer few variations and little replayability, save for the obvious grind for equipment. In Anarchy Online, the number of designed dungeons was tiny: however, players could enter randomised dungeons. In theory, no two dungeons the players encountered would ever be the same: however, in practise, every dungeon felt the same. Because dungeons were randomised, they had no narrative structure or overall design concept. Instead of feeling unique, every dungeon felt the same.
A lot of this is down to how many rules are put in place and how the generation is implemented: Nethack and Spelunky both use randomly generated levels, and have massive fan bases. The generation of rules for interesting map design is, however, a slightly different issue from randomly generating gameplay elements, and is probably best left for another discussion; it suffices to say that a good designer should be aware of the limitations of generating maps. We can still apply much of this randomness discussion to the generation of these maps, however.
A More Serious Solution
So where does this leave us? Well, sometimes we can actually just remove randomness from a game entirely. In the case of an RPG, instead of spawning a boss 1% of a time, we can spawn them after every 100 kills. In the case of collectible card games, one of Magic’s competitors (Versus system) solved the issue of players needing land by making every card playable, face-down, as a land instead of a spell; this meant that you would never find yourself “stuck”, while maintaining the momentum that lands crucially provided.
However, a total removal of randomness can often be an overzealous case of throwing the baby out with the bath water. In the example of the RPG, making a boss spawn every 100 kills exactly is likely to make them too predictable, and when a game gets too predictable, it becomes a puzzle. A better option would be making a boss spawn somewhere between every 50 and 150 kills. This means that bosses are still within a random range (making them hard to predict), but aren’t so random you can get attacked by three at once.
This use of carefully controlled numbers is pseudorandom generation. There are many ways to do it: in Tetris, if we spawn an L block, then for the next three blocks we “re-roll the dice” once if an L block is spawned again. Normally, the L block has a one-in-seven chance of spawning, but giving it a re-roll makes it a 1/49 chance for those threee turns. It can still happen, but is much less likely.
This isn’t the best way, of course: there are many ways to generate numbers randomly, ranging from simple re-rolls to weighted random numbers; plus, sometimes, in a case like Tetris, just leaving it as a one-in-seven chance to generate any block might be the best option.
If we do use randomness, we also have the opportunity to introduce seeds. This simply means that the random numbers we use in our game aren’t actually random; the “random” sequence is entirely defined by a number called a seed. In Tetris, it appears that we can’t predict what blocks are going to fall; however, if we seed a tetris game with the number 42, and we start off with square, L block, T block, square, then every game that uses the 42 seed will begin with those blocks. Seeds aren’t used often in gaming (Minecraft and FreeCell being two notable examples), but can be a nice addition.
The ability to seed randomness comes from the fact that computers aren’t actually capable of generating random numbers: often, they simply take a base number (such as the time in milliseconds), and then perform a calculation to get a “random” number. By ensuring the base number is the same every time, the calculations will give us the same “random” numbers.
The alternative to removing randomness is to use more of it. This might seem crazy initially, but can actually be extremely effective: roll two dice, add them together, and you have a one in six chance of getting a seven. Roll 2,000 dice, add them together, divide by 1,000 (and round), and you will almost always get a seven. In this case, using so much randomness has almost entirely removed randomness.
At the end of the day, randomness isn’t inherently evil; it all comes down to perception. Players want to be be challenged, or to have an interesting experience, and there’s nothing challenging or interesting about throwing a bunch of random monsters at a player, with little regard to whether they live or die. By tempering the randomness, we can craft the results we want, and hopefully make a game which interacts with the player, rather than ignoring them.
A Few Final Notes About Randomness
Randomness is generally a bad way to solve conflict, because (by its very nature) it creates unpredictable results. Randomness can also be a poor way to generate content, but is often the only sensible way to approach it; imagine designing a Tetris game which had a list of every block that should drop, in order.
When randomness does occur, it should generally favour the player (which is hard to achieve in a player vs player environment). If game elements are generated randomly, they should allow the player to react to a worst case scenario in a way that still allows a reasonable chance of success.
However, we have to accept that sometimes randomness is necessary. RPGs would be a lot less exciting without dice to determine combat. Board games, in particular, are unlikely to resolve the issue anytime soon: throwing 1,000 dice and averaging out just isn’t practical for a game of Snakes and Ladders.
And of course, the final big caveat: if we remove randomness entirely, are we making a game, or a puzzle?
篇目6，Random Thoughts on Randomization in Game Design
When it comes to game design, randomization is one of my favorite words. When used properly, it enhances a game’s replay-ability dramatically. Classic titles like X-Com and Diablo 2 make excellent use of randomization to keep gamers playing, and the rogue-like genre is famous for its use of randomization. Recent indie titles:
Dungeons of Dredmor, Din’s Curse and Space Pirates And Zombies each use randomization and are examples of the pros and cons of it.
Before we talk about the pros and cons of randomization, it’s important to define the degrees of randomization that can be implemented in a game. The degrees are not ranked in terms of preference, but just the ways that a designer can have randomization.
Low: Just equipment placement and probability of finding them. Action RPGs usually have this degree of randomization. Note, you can still have important items in set locations and have common items and equipment randomized.
Medium: Enemy placement along with the low category. There are two ways of implementing this, first is with having “unique” enemies. In Diablo 2, there was a chance of running across an enemy who had a name, these enemies looked different from their cohorts and had a unique modifier such as: increase damage, fire resistance, etc, and the other way is randomizing enemy positions as well.
High: Everything in the last two categories, along with world randomization. Rogue-likes fit the bill here, but this category is not mutually exclusive to rogue-likes. Space Pirates And Zombies allows players to create a random Universe from the get-go. TBS games like Civilization also allow players a chance to play on a randomized world, or preset map conditions.
With that out of the way, let’s move on to the pros of randomization. First, is that randomization is a great way to have replay-ability in your game. You’ll never know what that treasure chest will have, or what is behind the next door, and that can be an excellent motivator to keep playing. The more elements that are randomized in the game, the longer the experience will stay fresh.
While talking to a friend about Rogue-likes he told me that to him, they were like a slot-machine. In a way he is right with that analogy, you never know if you’re going to get lucky and get all the equipment you need and blaze through the game, or if the odds are going to be stacked against you.
Randomization can also be used as a difficulty modifier, allowing the game to generate a smaller or easier world for newcomers, or a larger more challenging world for experts. This is something that Din’s Curse does well, as players can choose the levels of the enemies, how big the world is, among other factors.
With that said, there are some cons to randomization. Going back to the slot machine analogy, while the lure of a jackpot can be motivating, losing thirty times before you get there can be demoralizing. In Dungeons of Dredmor, playing the game at the hardest difficulty setting, it felt like 9 out of my 10 runs ended before I even got off the first floor due to unlucky enemy and equipment placement.
Depending on the degree of randomization, it’s very easy to generate maps that completely screw the player. Going back to Din’s Curse, there were plenty of times that the game spawns hordes of enemies at the entrance to the dungeon that overwhelmed me or having a boss appearing on the very first floor with the hardest modifiers attached to it. Din’s Curse also features modifiers to the world that makes things harder; getting stuck with the worse modifiers at the beginning can be a big hole for the player to crawl out of.
Next, is that when it comes to randomized levels, most often quality takes a hit. Creating a randomize level using functions and basic assets is easy, creating a level that not only looks aesthetically pleasing and is crafted well is another story.
The perfect example of this would be Demon’s Souls, while you could argue that randomized levels would have helped the game, no one can say that the levels weren’t carefully designed. Each level was developed with a specific challenge in mind to the point that each level had its own mood and style. From the vertigo inducing heights of stage 3-2, to the poison gauntlet of 5-2, you could tell that the designers went to great effort to design the levels.
The first poor example that I had with randomized levels was with Phantasy Star Online for the Dreamcast. In the game, every dungeon’s layout was randomized, but the game only had a few room assets per world. What this meant was that every floor had maybe 4 different room models and that’s it. The level design had a very “Frankenstein” feel, in the way that the level design felt like it was just stitched together from various elements. That is also something you want to avoid when creating randomized levels as there should be a sense of cohesion in how the world is set up. The first retail build for Dungeons of Dredmor had door assets show up where rooms were supposed to be, and it brought the quality down somewhat.
The second problem is that the more game mechanics you have in mind, the harder it will be to create a decent system. The reason is that, the more mechanics the player has access to, the more variables will have to be programmed and implemented into the engine. In Mine Craft, on each new game, the world is randomly generated for scratch and it works because the only interactions the player has is putting a block down, interacting with objects and attacking.
Let’s say that someone designs a randomized level for Deus Ex: Human Revolution, in order for that level to work, the engine must be able to create a randomized setting that must also allow for the variations in play-style, meaning it must have breakable walls, vents, areas to reach and terminals to hack. If it doesn’t have all these elements and have them presented in a way that allows progress, then players will become very frustrated if the game gives them a level with a solution that is impossible for their build.
To create a randomized system that works, it has to be built on top of a layer of linearity. What that means, is that for every random element, there must be something guaranteed. For example, in Dungeons of Dredmor, while the world is randomized each time, enemy types are limited for the most part, to specific floors. You will never see an enemy who appears on floor 5, on floor 1 and vice versa.
Same goes for Din’s Curse, on every floor no matter what; there will be a way up, along with a portal back to town. In terms of enemies, the enemies will progressively get stronger the further the player descends into the dungeon based on what level the player set as the starting level at world generation.
Going back to Mine Craft, while the world is completely randomized at creation, the same basic rules apply to each new world: better materials are found deeper underground, enemies spawn in darkness and the player has complete freedom of where to go. With these three constants, the player still experiences the world fresh each time due to the scale of the randomization.
For one of my game ideas I envisioned the game taking place in a randomized world. Where ever the player is placed, the world will be built in a sense around that position. Incredibly dangerous areas would be further away, while easier areas will be closer. The majority of the buildings will be randomized, while special buildings that act more like dungeons are linear in their design. This will allow players to experience the game differently each time, but still have a sense of progression that they can base their play through on.
A well designed randomization system can be the cherry on top for your game design, giving players added value. However, like all good mechanics, it must be properly designed and implemented.