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Published: October 15, 2023 (3 months ago.)
Tags:  Games

The book in...
One sentence:
A fairly wide examination of games from the most basic principles up to some (light) mathematical reasoning in 'game theory.'

Five sentences:
The book examines many micro elements of games and the surrounding metagames in a very casual and easy (and interesting) way. After breaking down the games into smaller units, it is demonstrated that there are often a few 'root' games that underlie what, on the surface, seems like a great many games; for example very many games can be decomposed into things like brawls, races, or chip-taking. The indirect comparison, through their respective treatments, of older 'classic' games, some of which that have have been around for millennia, to more modern computer games is very interesting. Beyond the intention of the book, I think there is a bit to be gleaned here in regard to a social commentary on how people no longer need other humans to play games and I would argue that the long term effects of this development may be socially disastrous; even the so-called social games (like MMOs) have been devolving into asocial parallel single played game (IMHO). Finally there is a decent amount of very interesting analysis on things like metagames, heuristics, and a decent treatment of Von Neumann Game Theory and Combinatorial Game Theory.

designates my notes. / designates important. / designates very important.


The two major components that games have (and they need not have both) are systemic and agential, or the explicit rules of the game and the human element that can be roughly thought of as the metagame.

Games can be broken down into smaller and smaller units, from campaigns to matches to atoms, and then these smallest bits can be examined to understand the strengths and weaknesses of the macro game.

Many of the older games we know of today have changed a lot since their inception and have ostensibly “evolved the bad out” to arrive at what we see as classics today (chess, checkers, bridge, etc).

Computer games adhere to a great deal of the same principles applied to board games, but they also break a lot of those principles; for a simple example things like finding people to play with is trivial compared to in-person gaming, computer games allow you to play alone with a simulated opponent that makes move functionally instantaneously, and the adjudication of the rules is done by the computer. Many things are still the same, albeit physical vs. digital. For example there is still a graphic design, there are “user interfaces” in both worlds (although we rarely would call the physical components a UI).

Many games can be broken down into a few simple categories, like brawls or races. There are essentially 2-player games that are “glued together.” Further, many games are rekinned version of one or several archtypical games like chip-taking. Political games are essentially the equivalent to chip-taking games, but unless you are trying to look under the hood, you might never make this connection. This is important because it lets you understand the game you are trying to design better by looking at it abstractly and without all the the trappings that look/feel good, but aren’t actually part of the game.

Sometimes the problems you game might face are very common and often times strictly unsolvable. You can probably never get rid of kingmaking in multiplayer games, but you can design in such a way that incentives people to play toward a particular spirit of the game.

This leads well into the next part of the book where rules and understanding the games are discussed. In simple terms there are first-order rules that are needed to play and there are second-order (and beyond) rules, that are needed to do well. A great deal of enjoyment can be had beyond the simple first-order understanding. Many people play many games specifically to learn more about a game and improve their performance. Think about a rating system like the Elo in chess. Understanding how the pieces move in chess (first-order) is quite simple. Understanding which moves to make is so complex that there are libraries of books written on the topic. When learning these second-order rules you will often have some kind of gut feeling of what move you should make. These are heuristics and there is much joy found in climbing the heuristic tree for many people.

Interestingly as you refine your heuristics games can sometimes reach “tipping points” where they become “solved” as with tic-tac-toe or nim or they can almost transform into very different games. Take for example games with hidden catch-up mechanisms. The naive player may think they are very far ahead or behind. You heuristics are working on a simple pattern of how many “points” behind you are. After playing the game more and integrating knowledge of the catch-up mechanisms you now have a revised heuristic that tells you that even if you are behind/ahead a large number of points, the game is actually still very close. You will likely make different choices in your naive vs. nuanced understanding of the game.

The final part of the book (appendix notwithstanding) goes into more detail on some of these patterns that show up again and again in games. The simplest example is the rock-paper-scissors metagame. It shows up in so many places. In Magic: The Gathering you have aggro beats control beats combo beats aggro. In RTS games you have melee-ranged-flying units. The aforementioned catch-up mechanism and its opposite, the snowball effect, can make games feel more or less competitive or balanced depending on your understanding. The cost/effect pattern is also seen time and time again. Balancing this is difficult at best and in many games there are after-the-fact balancing changes implements. In a game like MTG this is quite disrupting because you need to ban/restrict cards or errata their text. In computer games this can be handled much simpler (though still with disruption) by patching the game.

Table of Contents

· Introduction

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· Chapter 01 - Basics

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  1. Or tactics. No distinction between the two is intended here; the point is merely to emphasize “a choice that you as a player might make” over the evaluation of the state of the game itself.
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  1. Or indeed in almost any human endeavor - hardly surprising given that games are to some extent abstract and purified models of everyday human existence.
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· Chapter 02 - Multiplayer Games

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· Chapter 03 - Infrastructure

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· Chapter 04 - Games as Systems

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Snowballing and catch-up

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$$p_1 , . . . ,p_n$$ the variance is

$$\frac{( p_1 – 1/n )^2 + … + (p_n – 1/n)^2}{n} $$

  1. The square root of the variance is called the standard deviation, and is another common measure of spread. The variance is more convenient for our purposes — it ’ s easier to compute with — but it conveys essentially the same information.

  2. $(n - 1)/n^2$, not that it matters for this discussion.

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One common attempt to solve the problem of catch-up in very long games is to use dynamic difficulty adjustment. This basically amounts to catching up the player invisibly whenever she falls behind, and catching up the AI if the player moves ahead. The problem is that it is rather like your spouse cheating on you: arguably fine if you know nothing about it, but liable to make you feel bad if you do find out about it, which eventually you will (at least in the case of games, given the Internet). Players who are trying to play well want to feel that if they do play well, they will be rewarded. This feeling is hard to come by if the game tries to ensure equal outcomes regardless of player skill.

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However, such a mechanic — say the Green Shell in Mario Kart (which, being unaimed, typically is used against players who are close) — may not give large-scale catch-up. Instead, it may cause clumping: groups of players who are close together keep shooting each other, forming clumps, but one clump can’t affect another far-off clump (although occasionally a player will break away from one clump and push ahead or fall behind until pulled into the orbit of another clump). In this sense Mario Kart is almost exactly like a large bicycle race, with the Green Shell playing the same role as drafting: something that pulls together nearby vehicles but does not affect faraway ones. They are a catch-up feature within a given clump, but less so when viewed from the point of view of the race as a whole. 17

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· Chapter 05 - Indeterminacy

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Game Amount of luck Amount of skill
Poker High High
Chess Low High
Tic-tac-toe Low Low
Slots High Low

· Chapter 06 - Player Effort

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  1. Monopoly tends to come in for a lot of criticism among game designers. (A highly popular game that the “experts” all hate should be a warning flag for the thoughtful designer - if the game is so bad, why do so many people like it? Some answer beyond “people are stupid” is required.) While the game certainly has plenty of flaws, this one innovation, of exciting downtime in a turn-based multiplayer game, is enormously powerful and still not as widely appreciated as it should be.
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  1. “Pure” busywork Completely mechanical operations that must be performed according to some deterministic algorithm. No choices of any kind are involved. Shuffling and dealing, setting up the board, making change, or looking up results in a table.

  2. Incomprehensible busywork Actions that involve gameplay choices that are completely opaque to the players and are made essentially randomly. Logically these are quite different from pure busywork, but the effect on the player is much the same. These are actions that must be performed for the game to continue, but that don’t involve any meaningful choices and cannot be done better or worse, 21 and hence seem like work unrelated to the play of the game.

  3. Very low reward/effort ratio activities Not strictly speaking busywork, these sorts of activities might seem close to busywork to some players.

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  1. Interestingly, although computer game players are relatively tolerant of busywork, they are highly intolerant of downtime.

· Chapter 07 - Superstructure

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  1. Purely abstract: tic-tac-toe, Scrabble, Othello, most sports, most classic card games
  2. Theme only: Bejeweled, Candyland
  3. Very light conceit: chess, fox & geese
  4. Slight modeling of conceit: Battleship, Asteroids
  5. Some modeling of conceit: Clue, Donkey Kong
  6. Just barely a simulation: Monopoly, Diablo
  7. Very light simulation: Starcraft, Quake
  8. Simulation, but many sacrifices to gameplay: World of Warcraft
  9. Simulation, minimal “unrealistic” elements: Counterstrike, Civilization
  10. Full-on simulation (attempt to maximize modeling): Squad Leader
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· Chapter 08 - Appendixes

11.1. Von Neumann Game Theory

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11.2. Combinatorial Game Theory

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