作者：kyoryu

复杂性是衡量玩家在特定时刻的可行选择，及其需要考虑的一系列因素的指标。

深度是衡量玩家在任何时刻可制定的非强势策略的选择数量的一种指标。

例子：一字棋

tictactoe(from historyofboardgames.wikispaces.com)

一字棋就是无深度游戏的一个绝佳典型。在每一回合，玩家只有一个最佳移动策略。数个移动看似比一次“最佳”移动更好，但这是因为这些移动的功能相同——在某次移动中挑选任意一个角落实际上并无不同。

一字棋很无趣，原因在于它缺乏深度——在每次移动过程中，玩家的回应基本上没有悬念。

有趣的是，游戏理论认为任何拥有完善信息的连续游戏都可以找到“解决”方法。所以，象棋就是可以解决的游戏。因此从理论上讲，如果你完全掌握了之后的布局和走向，就可以部署一个最佳的开局。

深度并非必要选择

许多成功游戏都没有什么深度，多数解谜游戏就属于这种类型。几乎所有解谜游戏都属于此列——它们只有一个解决方案。而多数冒险游戏也同样如此，这些游戏的挑战和趣味来源于分析谜题和决定正确解决方案。

如果你要制作一款不依赖于深度的游戏，那就有两种选择。你可以增加游戏规则的复杂性，或者为玩家呈现谜题的不同部署方式。

例如，九宫格游戏的规则就非常简单。但它之所以有趣，原因就在于玩家可以玩不同的谜题，可以在同一个规则集合中接受新挑战。纵横字谜游戏也同此理。

多数电脑游戏的深度并未随着复杂性的增加而提升——当玩家知晓如何在考虑因素1、2、3之后，在A、B和C之间制定正确决策时，游戏就只有增加可行选项，或者增加玩家的考虑因素。这两个选择都会增加复杂性，但不会增加深度。

增加复杂性会产生一种副作用，即阻碍新玩家接触游戏。当游戏增加了A至Z的选择，以及1-100的考虑因素时，新玩家可能就会发现自己难以掌握游戏要领，无法享受其中乐趣。

另一个让无深度的游戏富有趣味性的方法是关注其娱乐性（游戏邦注：例如图像、声音、文字、故事情节等）而非玩法层面的特点。这是一种行之有效的方法，但并不在本文讨论范围之列。

增加深度

那么，我们该如何增加深度？

很简单，在每个决策点都增加更多有效选项，并确保不陷入纯策略均衡状态。

纯策略均衡是指玩家每次都采取同样行动的均衡，而不是在特定时刻进行不同选择的混合策略均衡。人类是很缺乏随机觉悟的动物，所以执行混合策略对人们来说几乎是不可行的方法。在RPS游戏中，玩家双方选择三种标志的概率都是三分之一，这就属于混合策略均衡，但人们几乎不可能采用这种行动，这也是为何Roshambot之类的东西会难倒众生的原因之一。

如果是一款单人模式的游戏，那就需要在AI上多下功夫。如果AI总是选择“最佳”选项，那么它的行动就具有可预测性，并且之后很容易被玩家打败。有一个选择就是让AI从一些最佳策略中做出特定数量的随机选择，这可以避免游戏因AI具有可预测性而出现仅有单个最佳策略的现象。

另一个可行方法就是隐藏相关信息。不公开所有信息，这样玩家就不得不考虑情况来制定决策。

随机化是一种隐藏信息的形式——如果某个动作的结果是未知的，那么玩家就难以对其设计出单个最佳策略。

增加选项也会提升游戏的复杂性。但要慎用这种方法，并且不可操之过急，因为每添加一个选项都可能令其他选项失效，导致游戏降低深度，但却提升了之前的复杂性。

在某些情况下，你可以通过移除选项来增加复杂性。如果某个策略胜过其他两者，移除该策略就可以达到降低复杂性和增加深度这种一箭双雕的效果。在多数时候，这种做法是一种双赢策略。

Street-Fighter-II-HD-Shoryuken(from bireyselkisi.blogspot.com)

也可以通过添加技能要求来增加深度——要求玩家具备一定等级的技能才能执行某个策略，这可以有效随机化该策略的结果。例如，在《街霸》中，玩家可能无法每次都使用升龙拳。这就给玩家带来了决策点的概念，他必须权衡准确采取这项操作所带来的好处，以及操作失败所造成的影响。但这个方法也要慎用，因为如果有人每次都能成功执行某个策略，这就可能导致游戏深度大打折扣。

游戏邦注：原文发表于2008年5月20日，所涉事件及数据以当时为准。（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）

Complexity vs. Depth

by kyoryu

These are terms that are thrown around a lot, but are not well defined.  So, here’s an attempt at a definition.

Complexity is a measure of the possible choices a player has at any given moment, as well as the number of factors the player must consider.

Depth is a measure of the number of choices a player can  make at any moment that are not dominated strategies.

Example: Tic-Tac-Toe

Tic-tac-toe is a great example of a game with no depth.  At each turn, there is a single move that is definably the best move to make.  Some moves seem to have more than one “best” move, but that is because the moves are functionally equivalent – picking any corner on move 2 is essentially the same move.

Tic-tac-toe is boring.  The reason tic-tac-toe is boring is that it has no depth – at any given move, the player’s response is dictated.

Interestingly, game theory states that any sequential game with perfect information can be “solved.”  So chess, for instance, is solvable.  There is, theoretically, a single best opening move, if you have full and perfect knowledge of every possible move after that.

Depth Isn’t Necessary

Many games are successful without much depth.  Almost all puzzles fall in this category – there is a single solution.  By extension, most adventure games fall into this category as well.  The challenge and enjoyment of these games comes from analyzing the puzzle and determining the correct solution.

If you’re going for a game that is not based on depth, there are two ways of approaching it.  You can either increase the complexity of the rules, or you can present different configurations of the puzzle to the player.

Sudoku, for instance, has very simple rules.  The reason Sudoku is fun is that players can play different puzzles, giving them new challenges within the same ruleset.  Crossword puzzles are similar.

On the other hand, most computer games that don’t increase depth increase the complexity – once players have mastered making the correct decision between A, B, and C while considering factors 1,2, and 3, games will either increase the options available, or increase the factors the player must consider.  Either of these increase complexity, but not necessarily depth.

Increasing complexity has the side effect of eventually becoming a barrier to entry for new players.  By the time our hypothetical game has choices A-Z, and factors 1-100, new players will find themselves unable to grasp the game sufficiently to play.

Another way to make a game fun without depth is to focus not on the gameplay aspects, but rather on the entertainment aspects – the graphics, sound, writing, plot, etc.  This is completely valid, but a bit beyond the scope of this blog in general.

Increasing Depth

How, then, do we increase depth?

Simple.  Make more valid options at each decision point, and make sure we don’t fall into any pure strategy equilibrium.

A pure strategy equilibrium is an equilibrium where the players do the same move every time, compared to a mixed strategy equilibrium where the players choose different choices with a certain probability – humans are very poor randomizers, so actually properly executing a mixed strategy, for a human, is very nearly impossible.  In RPS, choosing each symbol 1/3 of the time for both players is a mixed strategy equilibrium, however people are almost incapable of doing so, which is why things like Roshambot can beat humans.

If dealing with a single player game, one thing to look at is AI.  As discussed here, if the AI always chooses the “best” option, it is predictable and therefore defeatable.  One option is to have the AI randomly choose between a certain number of the best strategies (or between strategies that are within n% of the best, or…).  This will prevent the game from having a single, best strategy due to AI predictability.

Another thing that can be done is to hide information.  If not all information is known, the player will have to make choices to take into account a number of possible scenarios.

Randomization is a form of information hiding – if the results of an action are unknown, then devising a single, best strategy will be hard to do, if not impossible.

Complexity can also be increased by adding choices.  However, be careful when doing this, and do it slowly, as adding a choice can often invalidate others, leaving your game with less depth, but more complexity, than it previously had.

In some cases, you can increase complexity by removing choices.  If a particular strategy dominates two others, then removing that one strategy can increase depth while simultaneously reducing complexity!  In most cases, that’s a win-win.

Adding a skill requirement is another possible way to increase depth – requiring a certain level of skill to execute a given strategy effectively will essentially randomize the outcome.  For instance, in Street Fighter, a player may not be able to execute a Shoryuken 100% of the time.  This introduces a decision point for him – weighing the benefits of executing properly against the drawbacks of a failure.  Be careful with this, however, as it can lead to a situation where the game has less depth at the high end if everyone can eventually perform the skill 100% of the time (or at least close enough as to be functionally the same).  While I don’t like making general proclamations, I think a good general rule is that games should have more depth at the high end of ability, not less.（source:design）