作者：Sirlin

说到平衡游戏，我们面临的问题其实比我所说的还严重。所谓的问题就是，你不可能完全解决你的游戏的平衡问题，但你无论如何都必须平衡它。（请点击此处阅读本文第1、2、3部分）

我所谓的解决是指，你不可能决定最佳的游戏方法是什么。如果你可以决定，你的游戏中就不可能存在什么真实的策略了，那么这个话题从一开始就没什么可说的了。如果你可以解决，那么你的玩家也绝对可以解决一。如果你不能解决，你的玩家可能仍然解决。无论如何，我们知道你不可能解决，因为那意味着你一开始就没把游戏设计好。

当不可能知道最佳方式时，到底如何实现平衡？如果你不担心这个，那就说明你并不理解这个问题有多恶劣。我在前面三个部分所探讨的技术是有帮助的，但它们让我想到美术总监Larry Ahern在准备画《猴岛的诅咒》的背景时说的话。他表示通过遵守经典美术作品的原则，他认为他可以获得“不太糟”的效果。但是，他说，从不太糟进阶到非常好才是他的期望，而那是不可能通过遵循某些人的原则得到的。

挑选尖顶玩家

我们先回到更早的一个问题。想象一下，在你面前有一个房间，里面都是某款游戏的玩家，我要求你判断出谁是最优秀的玩家，谁是次优秀的玩家吗。你要怎么判断？答案：你会让他们互相游戏。

但如果我不允许任何人玩游戏，那怎么办？我允许你采访玩家或让他们提交关于他们自己如何玩游戏和对游戏有什么了解的问卷。你可以通过这种方法判断谁是最优秀的玩家吗？我打赌你得到的答案不会比猴子掷飞镖好多少。根据我组织和参与比赛的经验看，我可以带着一定权威的口气说，获胜的能力和解释自己的能力几乎没有关系。

为什么最优秀的玩家不一定能够在采访或谈话中以最好的方式表达自己的看法？我认为主要有两个原因：

1、说出来的和写出来的答案是很狭隘的。

2、有许多能力是不可能通过意识思维体现出来的。

以上两个原因都与“精神冰山”的概念有关。

精神冰山

想像一下，冰山代表你的关于某事物的全部知识、技能和能力，例如玩某款竞技游戏。冰山露出水面的一小部分是你可以直接意识到的，也就是你能解释的东西。而水面之下的部分是你不能用语言解释的，但其份量却远远超过你能表达的那一小部分。当我们采访玩家或让他们写下关于自己如何玩游戏的答案时，我们只能认识到冰山的一小部分。如果一名玩家的露出水面的部分更大（他能更好地解释自己如何获胜），那么，他隐藏在水下的冰山部分其实比其他玩家的更小，这是完全有可能的。而这才是问题的关键。

（露出水面的部分代表你可以解释或意识上理解的；而庞大的水下部分则表示你没有意识到的。）

狭隘性

与你储存在头脑中的全部知识和决策规则相比，你写下来或说出来的答案所包含的信息量其实是相当有限的。另外，写下来和说出来的语言支持线性思考，而你的实际决策可能更加复杂，需要权衡许多不同的关联因素。在书面答案中，玩家可能说“移动A打败B，所以我专注于在这场比赛中移动A。”但真实操作取决于许多因素：移动A的时机、距离、角色的相对命值、对手的心理状态，等等。玩家不可能把这些在真实游戏过程中感知到的细微之处用精确的语言表达出来。

无法直接访问的部分

一开始，这个概念可能很难理解，但当你思考一会儿以后，你就会觉得很明显了。你不是意识到你的消化系统是如何运作的。你不可能直接问你的细胞如何接通和打断ATP和ADP的关联，以供给身体能量。当你看到飞盘掠过天空时，你没有意识到你的眼球以某种全人类都有的方式移动（你以为你的眼球是跟着移动中的物品转动的）。

有研究估计，人类大脑每秒通过五官接收约1100万个信息碎片，然而我们可以意识到的部分最多只是其中的40个。还有大量信息是默默接收的，我们不能意识到的，即使我们仍然能够决定如保利用所有那些信息。

盲视

盲视就是一个特别有说服力的例子。盲视是因为部分视皮质受到伤害而产生的眼盲。人的视觉事实上有两条不同的神经通路，而得了盲视的人的其中一条神经通路被阻挡了。结果是，他们眼瞎了，也就是不能有意识地体验到看这一活动。即使他们说看到一片黑暗，他们仍然可以根据视力作决定。在一个对盲视患者DB做的实验中，研究人员让实验对象看一个具有垂直或水平黑白条的环形然后回答条是竖直的还是水平的。即使他看不到，有时候被问得焦虑了，他“猜”的正确率仍然介于90%-95%。换句话说，有盲视的人对世界的感知比他们的意识能解释的来得更准确。

迅速决定

这个概念的另一条线索就在迅速决定中。意识不是立即联合的；需要0.3-0.5秒。我知道这个说法在脑研究专家中是具有相当的争议的，但我认为通常情况下可以说，在比那更短的时间内，我们还没有反应过来发生什么事然后形成事件的意识。然而，实验表明，我们根据外部刺激做决定比那个时间更快。例如在一个实验中，实验员要求测试者看到杆亮起某种颜色时就抓住它。实验时，实验员故意点亮一根杆，在测试者正要抓住它时立即暗掉它转而点亮另一根杆，然后估计测验者转向新点亮的杆的过程。这个修正过程几乎是立即发生的，比0.3秒还快，然而测验者认为他们只在最后一刻，也就是0.5秒后才调整行为。事实上，他们在做出调整以前甚至没有意识到杆的颜色改变了！他们在意识到发生什么事情以前就做出决定了。

网球是一个更加贴近现实生活的例子。网球职业选手可以把球以130英里每小时的速度打出，而对手双方之间距离是78英尺，这意味着球从一边抵达另一边只需要0.41秒。《纽约时报》的写手David Foster Wallace提到：

这段时间太短了，来不及深思熟虑。当时，我们更多地是依靠条件反射，也就是绕过意识思维的纯身体反应。然而，有效的把球回传取决于大量决定和身体调整，其涉及的行为比受到惊吓时的眨眼和惊跳更有意识和计划。

网球职业选手Roger Federer在采访时解释道，他不喜欢被叫作天才，因为在接球的紧张时刻他并没有想什么，他只是在意识到情况前就发动潜意识的技能。

冰山一角

还有另一个重要的例子是棒球。外野手如何接住飞来的球？这似乎是一个涉及速度、轨迹、重力、空气摩擦阻力、风力等因素的复杂数学题。外野手能尽快地跑到球一般会着陆的位置，然后根据上述计算做出调整？

不可能。抓住飞来的球的最好办法就是《Gut Instincts》一书所说的凝视捷思；也就是，看着球，开始跑，调整奔跑速度使凝视角度保持不变。这样，当球着陆时，你就能在刚好的位置抓住它了。实验人员发现，优秀的专业棒球选手正是使用这种方法（狗也是），但大多数选手并没有意识到自己使用了这种方法，也不能解释他们自己接球的方法。

这个例子表明正确的答案可能隐藏在你的精神冰山的水下部分，但这不一定是典型案例。我选择它作为例子是因为我可以通过简单地描述这个潜层决策过程，使读者明白。但潜层的决策过程要依靠不易描述的复杂的变量权衡，怎么办呢？解释如何解决复杂问题的另一条线索只是冰山一角，不一定是准确的。

在我们回到解决平衡游戏这个不可能的任务以前，我想让大家看看两个游戏之外的案例。在这两个案例中，专家解决难题的方法非常适合用于我们的问题，也适合解决其他所有高复杂度的问题。

希腊雕塑的案例

在《Blink》一书中有一个案例：加州的Getty博物馆正在考虑斥资近1000万美元购买具有2600年历史的希腊雕塑.为了鉴定雕塑的真伪，博物馆方面派律师研究雕塑所有者的书面记录和过去几十年的下落，还让一位名为Margolis的地质学家分析雕塑的组成材料。这位地质学家从雕塑上提取了2平方厘米的样本，使用电子显微镜、电子微探针、X射线衍射仪和X射线荧光仪作分析。他发现，这座雕塑是用希腊的Thasos岛的白云石制作而成的，并且雕塑的表面覆盖了一层薄薄的方解石——这不重要。Margolis告诉博物馆方面，因为白云石转化为方解石需要至少数百年的时间。

经过律师和科学家的14个月的分析，Getty博物馆决定购买这座雕塑。这时问题出现了。当博物馆方面揭开雕塑的遮盖时，几名艺术行家看过后觉得不对劲。他们觉得这座雕塑是伪造的。

其中一名专家是纽约的大都会艺术博物馆的前馆长Thomas Hoving。当看到雕塑时，他头脑中冒出的第一个词是“新的”。Hoving认为用这样一个词来形容经历上千年历史的雕塑太奇怪了。

Getty博物馆方面很担心，所以他们把雕塑运回雅典，邀请艺术行家召开讨论会。大多数专家也认为雕塑是假的。“指甲盖不对”或“手不对”或“在土里埋了那么多年的雕塑不是那样的”，人们这么说着。他们不知道为什么，但就是觉得。接着，博物馆的律师发现，雕塑所有者的某些文件作假。刚才说到的那位地质学家发现，使用土豆霉菌可以在短短几个月内把白云石转化为方解石。

Thomas Hoving怎么能立即发现律师和科学家经过14个月的研究调查都没有发现的问题呢？他知道因为他在这个领域已经积累了如同冰山一样庞大的知识量。他在西西里岛自己挖雕塑。他还说：

“我在大都会艺术博物馆工作的第二年，我有幸遇到这位欧洲馆长，并一同经历了那么多事。我们每天晚上都把东西摆在桌上研究。我们还进储藏室。里面的东西真是多得令人眼花缭乱。我们每天晚上都呆到10点，我们可不是走马观花，而是非常非常认真地一遍又一遍地观察藏品。”

律师和科学家在这个案例中有很大的“冰山一角”。他们可以拿出很多证据说明雕塑是真的。但说到关于希腊雕塑的知识，律师和科学家的冰山藏在水下的部分就太小了。Hoving的冰山一角很小（他只是有感觉），然而他的水下冰山部分是非常大的。

让Hoving给你一个假雕塑检测的理论吗？如果他的理论遗漏大量他不知不觉就用于解决问题的东西，怎么办？

如果他的理论其实是错的，且并不能反映他的方法（因为他自己也解释不清楚），怎么办？问题是必然存在的，因为理论要求的所有专家综合他所有知识经验。

解决复杂问题的方法是开发庞大的水下冰山部分。但那是不是说你需要“经验”？对我来说，经验是个脏词。布什有当总统和处理外交事务的“经验”。你希望他治理国家（或其他地方）吗？而林肯几乎没有任何经验。经验只对拥有它的人来说是好的，且我们通常使用完全错误的方法来衡量经验。

例如，如果你有“发布10款游戏”的经验，那很好，但与特定类型的经验——知识冰山没有任何关系；后者与平衡复杂的非对称游戏有关。在我们开发这座冰山前，我们再看一个例子。

航天飞机的案例

想象一下，你面临的问题是判定航天飞机挑战者号是如何以及为什么坠毁的。你是调查委员会中的一员，你正在寻找答案。谁才是解决这个问题的最佳人选？顶尖的航天工程师？一流的事故调查的专家？答案是Richard Feynman。

Feynman是一个光辉灿烂的人物，作为一名物理学家，他以非凡的能力攻克了许多自己专业之外的复杂问题。Feynman不是工程师，但航天飞机问题需要工程分析。他是调查委员会中不按理出牌的一位成员，没有相关的经验。他只有分析一般问题的经验。收集海量信息、在头脑中组织、分析出什么是重要的什么是不重要的。

Feynman不看表面的东西，无视委员会的原则，询问所有相关人员，无视权威人物和调查政治，而是专注于收集真正的信息。他的第一波调查对象是设计坠毁的航天飞机的工程师。他们有他需要的知识冰山，且他知道如何将至少一点点儿那种知识转化为自己的。他不管谁有高级头衔、谁应该知道真相，而是专注于谁真的有相关的知识冰山，只有Feynman—-委员会中没有其他人，最终发现挑战者号坠毁的原因是在寒冷气候条件下O形环没有恢复弹性。

如果你想解决复杂的问题，你有两种思路，Hoving式或Feynman式。当我参与开发《街头霸王》时，我采用的是Hoving的方法。我有大量关于那种游戏的知识，所以我的专家观点，即使我表达得像感觉，也是很有份量的。在我参与的其他项目如《Kongai》和《Yomi》，我表现得更像Feynman。我知道如何解决一般的平衡问题，但与我相比，有些测试员掌握了更多关于如何玩游戏的知识冰山，所以我要向他们讨教、观察他们、依靠他们。

开发冰山

在平衡竞争游戏领域，你要如何获得知识冰山？理想地说，你需要有Feynman式的、可以运用于许多不同类型的问题的才能，而不是专注于狭隘的一种游戏。

开发这种冰山的问题在于时间。如果我们想成为专家级玩家（而不是专家级游戏开发者），我们可以利用非常快的反馈循环。与比我们强的人一起玩游戏，看看什么策略管用，调整然后再玩。《街头霸王》这样的游戏一回合只持续几分钟上，即使是RTS也不过1小时。但开发一款游戏并平衡它却需要数年的时间。这是一个非常缓慢的反馈循环，几乎没有什么人会坚持下去。

但我认为获得必要知识的办法还是有的。以下是我研究过的游戏：

1、《街头霸王》。这款游戏我知道的版本超过20种。

2、《快打旋风》。据说盒装第5版是最新版本，但其实这款游戏已经有至少15个版本了。

3、《罪恶装备》。我认识这款游戏的8个版本。

4、《万智牌：旅法师的对决》。在诞生的10多年里，这款游戏每年三变（增加新牌组）。

5、《魔兽世界》。我玩这款游戏两年，我甚至不知道它发布了多少次更新。50还是100？

关于如何改变游戏的平衡性，数据太多了。你可以从游戏的第一版到下一版的变化中研究游戏受到什么影响，以及玩家如何感知那些变化。我其实把这些当成两回事，在《街头霸王》，我有两个独立的顾问：一个知道改变会如何影响游戏系统本身，另一个精通玩家会如何感知变化。

但，你必须认真地研究我在上面列举的游戏。出于兴趣的研究并一定给让你学到太多东西。另外，在游戏公司工作的经验几乎是有害的，因为我供职过的游戏公司不花任何时间考虑如“为什么《快打旋风》把这个动作的恢复改成8帧？”这类问题。相反地，它们专注于开发和发布游戏。

我也认为，你不可能假装。如果我不想成为更加出色的游戏开发者，我是不可能积累下像现在这么深厚的知识。我的动机是，我确实对那种东西有兴趣。Thomas Hoving确实对艺术史感兴趣。你必须在你选择的兴趣领域成为权威，积累深厚的知识。

分析VS.直觉

在《街头霸王》，不可能制作一种“平衡算法以”来告诉你Chun Li的行走速度应该更快一些。与她的重拳相比，与她的脚踢相比，更快的行走速度有什么意义？你计算上一年的结果可能还不如我两秒钟的猜测来得正确。

当我设计《Kongai》时，我也很清楚这一点，因为各种效果，我尽可能增加它的难度，使之与动作的相对值匹配。我希望评估（玩家直觉上知道在某种情境下的某种动作的相对值的能力）和“yomi”（玩家揣摩对手心理的能力）成为游戏的两个主要技能。然后我遇到了一位名为garcia1000的《Kongai》玩家，他是扑克牌粉丝。虽然我作为设计师的目标是便利评估和yomi，garcia1000作为玩家的目标是以最佳方式玩游戏，不需要做任何判断。他想计算这个可能性并解决平衡性问题。你可以说，他是我的恶梦，但他的工作也是相当有意思的。

garcia1000先是在《Kongai》中制造了若干“终极游戏问题”。他选择非常特定的情境，比如角色A vs.角色B、其他所有角色都死了、生命总量达到一定值、战斗范围设得很远，指定道具卡，等等。他可以给出非常特殊的情境（更简单得多，因为在这种终极游戏中选择更少），然的邀请其他玩家去想出最佳玩法。各个特定的情境都在论坛上占用了若干页面。他们得出一个有趣的结论，最佳玩法比一般玩法增加了3%的优势。更有趣的是，解决这些终极游戏情境的数字运算远比我用于设置所有这些调整变量的计算来得复杂（因为我基本上用的是直觉……）。

但你要记住的是，这种终极游戏情境的解决方案有多么大的局限性。你可以知道解决许多个问题的一个方法，但你不会解决甚至0.00001%的问题。可能的游戏状态的数量是非常大的，每一个终极游戏的问题都要花好几个页纸才能计算出唯一的一种游戏状态。如果我使用严格的数学来解决《Kongai》的平衡问题，那么我要在它身上耗费100年。

相信直觉

如果你有这种知识冰山，或者如果你像Feynman一样依靠其他人的冰山，那么你仍然应该知道关于最比化直觉价值的两件事。凭直觉的专家比分析师更擅长解决复杂的问题，但是：

1、直觉的专家不会很肯定自己的答案，而不胜任的人肯定自己（错误）的答案。

2、解释你自己会首先降低你利用直觉的能力。

对于本文，这个话题太大了，所以我只能做一个简短的总结。有一个关于不胜任的研究表明，不胜任某事（逻辑、幽默、语法，等等）的人往往会高估自己在这方面的能力，不能发觉其他真正擅长这个领域的人的专业表现。原因是，他们做某事所缺少的知识正是他们评估自己和他人必须具备的知识。

（我不知道这个图表是什么意思，不过看起来很重要的样子。）

结果是，你不得不应付许多不专业但对自己非常有信心的人的抱怨，那些人可能甚至没有冰山一角的推理能力，更别说水下冰山。我认为要让你在平衡问题上模糊的感觉获得足够权威的办法就是，能够克服他们大声的抱怨。你可能甚至庶务解释为什么那对游戏是最好的。

有若干研究表明，解释你自己会破坏你的直觉。如果让你看到一个人的脸，过一会儿后让你在一组人中认出那张脸，如果不要求你解释那张脸的细节特征，你会表现得更好。你的解释是不完全的，因为语言是很狭隘的，而你对脸的知识却是非常微妙的。你对脸所做解释会覆盖你对脸的真实知识，导致你在认脸测试时表现不佳。其他研究表明，要求解释思绪过程会导致测试对象更难想出创造性的解决办法。

在平衡《街头霸王》时，我很幸运不必向任何人解释自己的观点，这是一个大优势。注意，事后我会高兴解释一切，但我在开发最激烈的阶段时一直在说。如果我想平衡一个想法，且不能肯定为什么我想那么做，那我就去做。我不需要召集人员开会，演示计划让人投票。我只要去做，去测试就行了。

有一小段时间对我来说是灾难，因为制作人想跟进我在平衡过程中所做的每一件事。我很不情愿地提交未来的改变计划，因为每天都有一些东西会修改。明天我可能想执行一些我以前认为不可能执行的东西；后天我可能会根据测试结果，为了一些日后的变更需要而把最近做的修改撤销了。每一天，我所做的事就是做我当天认为最重要的事。

那种方法的敏捷性让我很满足，它是我能想像得到做事的唯一方法。我认为按照制作人的想法跟进我的工作是没有意义的，因为那么做并不能给项目带来任何好处，反而损害了我的利用直觉的能力。无论是我曾经做的任何游戏，平衡都不是开发的关键途径，总是有一些其他事情要占据开发周期。对于平衡，你能做的就是不停地做，直到有人说要发布了。

顺便一提，不久后，我继续做我想做的任何事，无视任何监督。所以，基本上忽略制作人的要求算是成功的策略。

很不幸，我提出的不解释自己和无视不胜任者的抱怨的建议，听起来好像会成为摧毁项目的自我为中心的命令。然而，利用直觉的最好办法就是在项目中获得一定的权威，然后不要经常使用权威。毕竟，你也希望你的下属好好做他们的工作，不必每一点小事都向你解释。

总结

当我们知道我们不可能知道什么才是最佳游戏玩法时，平衡游戏就是一件非常麻烦的事了。逻辑分析通常不适合用来解决这种复杂的问题，因为它不能像我们的无意识思维和直觉那样考虑到所有微妙之处。为了解决这个平衡问题，或任何类似的问题，我们应该积累这个领域的知识冰山和经验。我指的不是像在游戏公司工作或你的名字出现在制作人员名单中的那种伪经验，我指的是只能来自努力研究的那种真正的经验。以直觉的方式使用你自己的知识冰山，寻找其他具有知识冰山的人并倾听他们的建议。最后，在项目中获得一定的权威，不要让那些不胜任者的大声抗议盖过你的可靠的感觉，不要那些要求你事事给出解释的人破坏你的直觉。（本文为游戏邦/gamerboom.com编译，拒绝任何不保留版权的转载，如需转载请联系：游戏邦）

Balancing Multiplayer Games, Part 4: Intuition

by SIRLIN

We’re in much deeper trouble than I’ve been letting on when it comes to balancing games. The problem is that you cannot solve your game–you definitely cannot–yet you must somehow balance it.

By solving, I mean you cannot determine how to play your game optimally. If you could determine this, there would be no actual strategy left in your game, so it would be boring and not worth talking about in the first place. If you can solve your game, your players can definitely solve it. If you can’t solve your game, your players might still solve it. In any case, we know you can’t solve it because that means you did a bad job designing it in the first place.

How in the world can you balance something when it’s impossible to know the best ways of playing it? If you aren’t worried about this, then you don’t understand how wicked the problem is. The techniques I discussed in the previous three articles will help, but they remind me of what art director Larry Ahern said when he was preparing to draw all the backgrounds in The Curse of Monkey Island. He said that by following the rules of composition from classical painting, he believed he could get results that were “not terrible.” But, he said, going from not terrible to great was something he hoped he had within him, and that it’s not exactly possible to get there by following someone else’s cookbook of rules.

Picking The Top Players
Let’s back up to an easier problem. Imagine I gave you a room full of players of a certain game and I asked you to determine who the best player is, and who is second best. How would you do it? Answer: you would have them all play each other.

What if I don’t let anyone play the game, though? I’ll let you interview the players or have them submit written answers to your questions about how they will play the game and what they know about the game. Can you determine the best players from this method? I bet you will do only slightly better than monkeys throwing darts to determine the answer. In all my experience running and competing in tournaments, I can say with some authority that there is little correlation between ability to win and ability to explain yourself.

Why are the best players not necessarily able to reveal themselves as best through interviews or speaking? I claim there are two reasons:

1) Spoken and written answers have extremely narrow bandwidth.
2) It’s impossible to access many of our own skills with conscious thought.

Both of these ideas have to do with the concept of the mental iceberg.

The Mental Iceberg

Imagine an iceberg that represents your total knowledge, skill, and ability at something, for example in playing a certain competitive game. The small part of the iceberg above the waterline is what you have direct conscious access to; it’s what you can explain. The gigantic underbelly of the iceberg is the part you do not have direct access to, and yet it accounts for far more of your overall skill than the exposed tip. When we interview players or ask them for written answers about how they might play, we are only accessing the tip. If one player’s iceberg has a larger tip (he tells a better story about how he will win), it’s entirely possible that his hidden below-water iceberg is much smaller than another player’s, and that’s really what matters.

The tippy-top part represents what you can explain or consciously understand. The huge underside represents your vast unconscious.

Narrow bandwidth

The amount of information you can convey in a written or spoken answer is actually very small compared the storehouse of knowledge and decisions rules you have stored in your head. Also, spoken and written language encourage linear thinking, while your actual decision-making might be a more complex weighting of many different interconnected factors. In a written answer, a player might say “move A beats move B, so I will concentrate on using move A in this match.” But really it might depend on many factors: the timing of move A, the distancing, the relative hit points of the characters, the mental state of the opponent, and so on. Players cannot communicate these nuances in an explanation the way they can enact them during actual gameplay.

No Direct Access to Parts of Our Own Minds

This concept might be hard to swallow at first, but it should be incredibly obvious if you think about it for a moment. You are not conscious of how your digestive system works. You do not have direct access to how your cells make and break the bonds of ATP and ADP to give your body energy. When you see a frisbee travel across the sky, you are not aware that your eye moves in a particular pattern of jerky movement that’s common in all humans (you believe that you smoothly follow the moving object).

One study estimates that the human brain takes in about 11,000,000 pieces of information per second through the five senses, yet the most liberal estimates say that we can fit at most 40 pieces of information in conscious memory. There is A LOT going on behind the scenes, and we do not have conscious access to it, even though we are still able to make decisions that leverage all that information. (Wilson, p.24.)

Blindsight

This is what blindsight looks like.

The medical condition of blindsight is a particularly telling example. Blindsight is blindness that results from having damage to a certain part of your visual cortex. There are actually two different neural pathways for vision, and people with blindsight have only one of these pathways blocked. The result is that they are blind, meaning specifically that they don’t consciously experience seeing. Even though they claim to see black, they can still make decisions based on eyesight. In one experiment with a blindsight subject named DB, experimenters showed him a circle with either vertical or horizontal black and white stripes. Even though he can’t see so he has no idea whehter the stripes are horizontal or vertical, and sometimes become agitated when asked to guess, his “guesses” were correct between 90 and 95 percent of the time. In other words, people with blindsight can perceive the world more accurately than their conscious minds can explain. (Blackthorne, p.263.)

Instant Decisions

Another clue to this concept lies in decisions that we make extremely quickly. Consciousness does not coalesce instantly; it takes somewhere between 0.3 to 0.5 seconds to form. I know that that sentence is highly controversial amongst brain researchers, but I think it’s generally safe to say in times shorter than that, we have not yet formed enough of an awareness about what’s happening to be conscious of it. And yet, experiments show that we make decisions based on outside stimulus faster than this. For example, when people are asked to grab wooden rods as they light up a certain color, and the experimenter cleverly lights up one rod, then as you are reaching for it, darkens that rod and lights up a different one, he can measure when your hand made the course correction to go for the newly-lit rod. The course correction occurs almost immediately, much faster than 0.3 seconds, and yet the subjects believe they course correct only at the last moment, after 0.5 seconds. In fact, they don’t even consciously percieve that the lights on the rods changed until after they made the course correction! They are making decisions before they are conscious of what is going on.

Tennis is more real-world example of this. Tennis pros can serve the ball at 130mph, and the distance between baselines is 78 feet. That means it takes 0.41 seconds for the ball to reach the opponent. New York Times writer David Foster Wallace said:

The upshot is that pro tennis involves intervals of time too brief for deliberate action. Temporally, we’re more in the operative range of reflexes, purely physical reactions that bypass conscious thought. And yet an effective return of serve depends on a large set of decisions and physical adjustments that are a whole lot more involved and intentional than blinking, jumping when startled, etc. (New York Times.)

Tennis pro Roger Federer has explained in interviews that he doesn’t like to be called a genius at the game, because he doesn’t think during the incredible moments when he returns balls few other players can. He acts before he is conscious of the situation by leveraging his unconscious skills.

Heuristics We Use But Can’t Explain
Baseball gives us another important example. How do fielders catch fly balls? It seems like a very complex math problem with variables for speed, trajectory, gravity, friction from air resistance, wind influence, etc. Should fielders run as quickly as they can to the general location where the ball will land, then make adjustments as they solve these equations somehow?

No. The best way to catch a fly ball is to use the gaze heuristic, as described in the book Gut Instincts. The method is to look at the ball, start running, and adjust your running speed so that the angle of your gaze remains constant. You will then reach the ball just as it lands, and you’ll be in the right place. Experimenters found that the best professional baseball players use this method (and so do dogs), but that most of the players don’t know that they use it, and are unable to explain any method they use to catch fly balls. (Gigerenzer, p.10.)

This example shows that it’s very possible for the correct answer to be hidden in your mental iceberg’s underbelly, but it’s not necessarily a representative example. I chose it on purpose because the underlying decision process can be simply described, which allows me to describe it to you. But what if they underlying decision process relies on a complex weighting of variables that isn’t easy to describe? This is another clue that explanations of how to solve complex problems are just tips of the iceberg, and not necessarily accurate.

Before we get back to solving our near-impossible task of balancing a game that we can’t possibly know how to play optimally, I’d like us to look at two cases outside of games where experts solved very difficult problems. The different methods they used are extremely applicable our problem, and to solving any other highly complex problem.

The Case of the Greek Statue

From an example in the book Blink, the Getty Museum of California was considering purchasing a 2,600-year-old Greek statue for almost $10 million. To determine if it was a fake, the museum had its lawyers investigate the paper trail of the statue’s ownership and whereabouts over the last several decades and had a geologist named Margolis

…analyze the material composition of the statue. The geologist extracted a 1cm by 2cm sample from the statue analyzed it using an electron microscope, electron microprobe, mass spectrometry, X-ray diffraction, and X-ray fluorescence. The statue was made of dolomite marble from the island of Thasos, Margolis concluded, and the surface of the statue was covered by a thin layer of calcite — which was significant, Margolis told the Getty, because dolomite can turn into calcite only over the course of hundreds, if not thousands, of years.

The statue in question.

After 14 months of analysis by the lawyers and scientists, the Getty was ready to buy the statue. And then the trouble started. When the Getty was nearing the unveiling of the statue, a few art experts saw it and each of them had an immediate reaction that something was wrong. They didn’t know what, but they thought it was a fake.

One of those experts was Thomas Hoving, the former director of the Metropolitan Museum of Art in New York. When Hoving saw the statue, the first word that popped into his head was “fresh,” which he thought was an odd word to describe a statue that’s thousands of years old.

The Getty was worried, so they shipped the statue to Athens where they invited art experts to a symposium to look at the statue. Most of them said it was fake, too. “It’s the fingernails” or “it’s the hands” or “statues don’t come out of the ground looking quite like that,” people said. They didn’t know just why, but they knew. Then the Getty’s lawyers discovered that some of the statue’s ownership documents had been faked. The geologist (who was so proud of his examination that he wrote an article about it in Scientific American) discovered that it was possible to convert dolomite to calcite in just a few months using potato mold.

How did Thomas Hoving know something instantly that the lawyers and scientists could not discover after 14 months of investigation? He knew because he had an enormous mental iceberg of knowledge and expertise in this exact area. He dug up statues himself in Sicily. He also said:

“In my second year working at the Met, I had the good luck of having this European curator come over and go through virtually everything with me. We spent evening after evening taking things out of cases and putting them on the table. We were down in the storerooms. There were thousands of things. I mean, we were there every night until ten o’clock, and it wasn’t just a routine glance. It was really poring and poring and poring over things.”

The lawyers and scientists had a large “iceberg tip” in this case. They had lots of explanations why the statues were real. But if there’s anyone in the world who has a tiny iceberg underbelly when it comes to knowledge about Greek statues, it’s laywers and scientists. Hoving’s iceberg tip was small (he just had a feeling), yet his iceberg underside was enormous. (Gladwell, pgs.3-11,184.)

Thomas Hoving knows statues.

Can you imagine trying to detect fake statues by asking Hoving to give you a theory of fake statue detection? What if his theory left out lots of things he unknowingly uses to solve the problem? What if his theory is actually wrong, and doesn’t reflect his methods at all (because he doesn’t know them himself)? That’s the inherent problem with requiring that any expert synthesize a theory of his own expertise.

The way to solve a complex problem is to develop an enormous iceberg underside. Is that just saying that you need “experience,” though? Experience is kind of a dirty word to me. George Bush has “experience” as a president and with foreign affairs. Do you want him running the country (or anything else)? Meanwhile Lincoln had hardly any experience. Experience is only as good as the person who has it, and even besides that, we usually use completely the wrong scale to measure experience.

If you have the experience of “shipping 10 games,” for example, that’s great but it doesn’t have anything to do with the particular type of experience–the particular iceberg of knowledge–that is involved with balancing a complex asymmetric game. Before we try to develop this iceberg, let’s look at one more example.

The Case of the Space Shuttle Disaster

Imagine that your problem is that you must determine how and why the Space Shuttle Challenger crashed. You are on the investigative committee, looking for this answer. What is the best way to solve this problem? Is it to be an extreme expert in aerospace engineering? Is it to be an expert at investigating disasters? The answer is to first live the life of Richard Feynman, then solve the problem.

Feynman is one of the most brilliant people who ever lived, and he demonstrated his ability to solve complex problems in many fields outside of his own field of physics. Feynman was not an engineer, but the shuttle problem required an engineering analysis. He was a fish out of water on the investigative committee, and had no experience doing anything like that. What he did have experience doing was analyzing problems in general. Taking in vast amounts of information, organizing it in his head, figuring out what mattered and what didn’t.

Feynman dramatically reveals why the Challenger crashed with a glass of ice water and rubber.

Feynman took nothing at face value, ignored the rules of the committee, questioned everyone he could, ignored authority figures and the politics of the investigation, and instead focused getting real information. His very first interview was a marathon session with the engineers who designed the shuttle’s rockets. They had the iceberg of knowledge he needed and he knew how to get at least a piece of it out of their heads and into his own. By ignoring illusions like who had important titles or who supposedly knew anything and instead focusing on who actually had the relevant icebergs of knoweldge, Feynman–and no one else on the commission–discovered that the real problem with the shuttle was lack of resilience of the rubber O-rings during cold weather. (Feynman, pgs.113-153.)

If you are going to solve a complex problem, the two best ways are to be like Hoving or to be like Feynman. When I worked on Street Fighter, I was like Hoving. I have a mountain of knowledge about that particular game, so my expert opinion, even if it expresses itself as just a feeling, is worth a lot. On other games I worked on such as Kongai and Yomi, I was more like Feynman. I know how to solve balance problems in general, but there are playtesters who have bigger icebergs of knowledge about how to play the game at an expert level than I do, so I question them, watch them, and rely on them.

Developing the Iceberg

How do you actually get the iceberg of knowledge in the realm of balancing competitive games? Ideally, you want the Feynman-type of ability that can be applied to many types of problems, not just a very narrow domain of one game.

The problem with developing this type of knowledge is time. If we are instead trying to become expert players (rather than expert game balancers), we have access to a very fast feedback loop. Play the game against people better than us, see what worked and didn’t, adjust, play again. A game of Street Fighter takes only a couple minutes, and even an RTS game takes less than 1 hour. But creating a game and seeing how its balance turns out takes years. It’s a very slow feedback loop, and extremely few people get to even participate in it directly.

I think that there is a way to gain the necessary knowledge though. Here are the games I studied:

1) Street Fighter. I know about more than 20 versions of this game.

2) Virtua Fighter. It says version 5 on the box of the latest one, but really, there have been at least 15 versions of this game if you look closely.

3) Guilty Gear. I know of 8 versions of this game.

4) Magic: The Gathering. This game has changed (with new sets of cards) about 3 times per year for over 10 years.

5) World of Warcraft. I played that game for two years before it was released and I couldn’t even guess the number of mini-releases over that time. Maybe 50 or 100.

That is A LOT of data about how changes to a game’s balance out. You can study what the exact changes are from one version of a game to the next, then learn how those changes actually affected the game’s balance and how they players perceived the changes. I actually count those as two separate things, and on Street Fighter I had two separate main advisors: one who knew the most about how a change would affect the game system itself, and another who knew the most about how players would perceive changes.

You have to put in real, effortful study on following games like the ones I listed above, though. Just being along for the ride doesn’t necessarily get you much. Also, experience working at a game company is almost a detriment here, because game companies I’ve worked at don’t spend any time looking at things like “exactly why did Virtua Fighter change this move’s recovery to 8 frames?” Instead, the focus is on actually implementing and shipping games.

I also think that you can’t really fake this. There is no way I could have accumulated the knowledge that I have if my motivation was to be better at my career. My motivation is that I am actually interested in things like this. Thomas Hoving was actually interested in art history. You have to live an authentic life in your chosen area of interest to develop true, deep knowledge of it.

Garcia vs. Sirlin (Analysis vs. Intuition)

In Street Fighter, there is no possible way to create a “balancing algorithm” that will tell you if Chun Li’s walking speed should be faster. How good is faster walking speed compared to damage on her fierce punch, compared to priority of her ducking medium kick, etc? You could do a year of math on that and still be more wrong about it than my guess in two seconds.

I was very aware of this when I designed Kongai, and I tried to make it as difficult as possible to compare the relative value of moves because of their varied effects. I wanted valuation (the ability of players to intuitiely know the relative value of moves in specific situations) and yomi (the ability of players to know the mind of the opponent) to be the two main skills in the game. And then I encountered garcia1000, a Kongai player who came from the poker community. While my goal as a designer is to facilitate valuation and yomi, garcia’s goal as a player is to play optimally without needing to make any judgment calls on those things at all. He want’s to compute the odds and solve the game. You could say that he’s my worst nightmare, but he is work is also fascinating.

This is the Kongai virtual card game I designed for kongregate.com.

Garcia started by creating several “endgame problems” in Kongai. He chose very specific situations, Character A vs. Character B, all other characters are dead, life totals a certain amount, fighting range set to far, item cards given, etc. He would give very specific situations (which were much simpler because there are fewer chioces during the endgame), and then invite other testers to work out the solution for optimal play. Each specific situation took dozens of pages of forum posts to settle. They would also show amusing things such as optimal play giving a 3% edge over the more obvious plays, in one case. It was also amusing that the math reequired to solve these endgame situations was far more complicated than the math I used to set all the tuning variables. (Because I mostly used intution….)

What you have to keep in perspective though, is how limited these endgame solutions are. You could know the solution to dozens of them and you wouldn’t have solved even 0.00001% of the game. The number of possible game states is very large indeed, and each of these endgame problems that took dozens of pages of posts to figure out solved only ONE gamestate. If I had used rigorous math to solve Kongai during development, I could have been working on it for 100 years.

Trusting Intuition

If you have this iceberg of knowledge, or if you’re like Feynman who can rely on the icebergs of others, you should still know two things about maximizing the value of intuitions. Intuition by experts is better at solving complex problems than analysis, but:

1) The intuitive expert will be less sure of his answers, while incompetent people will be very sure of their (wrong) answers.

2) Having to explain yourself diminishes your ability to draw on your intuition in the first place.

This is too large of a topic to go into depth on here, so I’ll give only a short summary. There’s a wonderful study on incompetence that shows that people who are incompetent at a task (logic, humor, grammar, etc.) grossly overestimate their own ability at the task and are unable to detect expert performance in other people who actually are skilled at the task. The reason is that the very knowledge they lack to do the task is the same knowledge they need to evaluate themselves and others.

I don’t know what this diagram means, but it seems important somehow.

The result is that you will definitely have to deal with the loud complaints of incompetent people who are quite sure of themselves, and who might even have a well-developed tip-of-the-iceberg of reasoning, but no underside to their iceberg at all. I suggest somehow gaining enough authority that your vague feeling on a balance issue is able to trump their loud complaints. You might even try explaining why that is best for the game.

Several studies show that explaining yourself wrecks your intuition. If you see a person’s face, then must identify that person later in a lineup, you will do much better if you do NOT have to explain the face in detail beforehand. Your explanation is imperfect because the bandwidth of words is so narrow, yet your knowledge of the face is nuanced. The story you create about the face overwrites your actual knowledge and makes you perform worse in the lineup test. Other studies show that requring an explanation of thought process makes test subjects less able to come up with creative solutions for problems.

While balancing Street Fighter, I had the luxury of not having to really explain myself to anyone, and that was a great advantage. Note that I happily explained everything after the fact, but I’m talking about in the heat of development. If I wanted to try a balance idea, and I wasn’t exactly sure why I wanted to try it, I could. I did not need to convene a meeting and lay out a logical plan that people voted on. I could just do it, and test it.

There was a brief period of disaster where a new producer tried to track every single task I planned to do in the balancing process. I was reluctant to submit any list of future changes because every day, the landscape changed. Tomorrow I might learn how to implement something that I thought before was impossible to implement. The next day I might learn that a recent change removed the need for some other future change, based on playtest results. Every day, the thing I worked on was whatever thing I felt was most important that day.

The agility that method allowed was amazing, and it’s the only way I can imagine doing things. I think it’s pointless to track my work in the way that producer wanted to because doing so gives the overall project no advantage, while it damages my ability to draw on my intuition. Game balance has not been on the critical path of development on any game I’ve ever worked on, meaning there’s always some other thing that pushes out the ship date. In balancing, you keep doing it and doing it until someone says you have to ship.

By the way, I went back to doing whatever I wanted with no oversight fairly soon on the Street Fighter project, so mostly ignoring the new producer’s requests was a successful strategy.

My advice to not explain yourself and to have the authority to ignore incompetent complainers unfortunately sounds like a recipe for creating an ego-centric dictatorship that ruins a project. Yet, the best way to leverage intuition is to gain that kind of power on a project, and then not use it much. You want your subordinates to do their best jobs without having to explain every little thing to you either, after all.

Conclusion

Balancing a game when we know we can’t know how to play that game optimally is a deeply troubling problem. Logical analysis often fails at this type of complex problem because it doesn’t take into account all the nuances that our unconscious minds and intuitions can. To solve this balance problem, or any similar problem, we should build up a vast mental iceberg of knowledge and experience in the field. I don’t mean fake experience like working at a game company or getting your name listed in credits though, I mean real experience which only comes from effortful study. Use your own iceberg of knowledge in the form of intuition and seek out others with vast icebergs of knowledge and rely on their advice. Finally, somehow acquire enough power on a project that you don’t let your valid feelings about what to do get trumped by loud disagreement from incompetents and don’t let your intuition be destroyed by anyone who demands constant explanations of your every decision.(source:sirlin)