# Analog vs. digital games

## Introduction

In the 2010s, there was a resurgence in the popularity of old-fashioned tabletop games, and cafes dedicated to serving board game players popped up. These games are non-electronic and are played with people face-to-face, contrasting with video games which have taken the spotlight for several decades and are often played online. (The dominance of video games is understandable given the continual and massive increases in graphics capabilities, game mechanics, world size, amount of detail, etc.)

Some writers refer to these tabletop/board games as “analog” games and video games as “digital” ones. But I will argue that from a computer science standpoint, this terminology is inaccurate. There are many subtleties involved, and in the end there is no clear answer.

Formally speaking, an analog domain involves a continuous space of values, whereas digital means working in a discrete (and often finite) space of values. These definitions will become more apparent when elaborated and exemplified.

## Rules

A game is defined by its rules, which generally comprise a set of allowed objects, states, and actions. The rules of any particular game dictate whether it has an analog quality or a digital quality. This analogness/digitalness of a game is independent of what physical objects are used to play the game (e.g. roulette wheel vs. computer).

To illustrate the ramifications of game rules, we’ll use two diametrically opposite examples: chess as a digital game, and basketball as an analog game. Monopoly will be sometimes used as an impure digital example.

State space

Chess has a discrete, finite set of states. There are 2 player colors and 6 piece types. There are 64 squares, each of which is either empty or has a single piece on it. There is nothing “in between” squares. It is either the white player’s turn or the black player’s turn. Most of the time, two states that differ only slightly will have wildly different behaviors (e.g. blocked, capturable, promotable, checkmate).

Basketball has a continuous, infinite state space (ignoring quantum physics concepts like Planck length). The positions and velocities of the ball, every player, their arms and legs, etc. are best described with real numbers. Various aspects of the game can be analyzed with calculus, which is a tool for functions acting on real-valued (not discrete) variables.

Monopoly has a discrete but infinite state space because the amount of money each player can hold is unbounded. In particular, a player can pass Go an unlimited number of times, collecting \$200 each time. The game rules explicitly say that the bank cannot run out of money (even though every physical game box contains a finite number of banknotes).

Actions

At any particular chess player’s turn, the number of legal moves he has available is finite and small (in the order of magnitude of 10). The possible actions are discrete and lack “in-between” actions like moving a piece by half a square or doing a quarter capture.

At any point in time, each basketball player has a continuous (and thus infinite) number of actions available to her. She can walk at any velocity, throw the ball with any force vector, etc. Small changes in the action generally yield small changes in the upcoming state.

Most analog games use intuitive physical processes (like the movement of a ball) to define how actions change the game state. It’s rare for analog games to use a complex and contrived mechanism or electronic circuit to implement the game rules.

Time

Chess is defined to progress in discrete turns, alternating between the white player and black player.

Basketball generally unfolds in continuous time, where any player can take any action at any time. But there are some discontinuous events like scoring a point, starting a free throw, and ending the game.

Some traditional sports games have more discrete turns than others. Baseball is structured as a sequence of batting attempts. American football is structured around downs. Soccer mostly runs continuously, except for goals and fouls.

Monopoly lets any player propose a trade during any idle time (i.e. not in the middle of moving pieces, exchanging money, manipulating cards, etc.), which means the action takes place in continuous time. The rest of the game happens in well-defined turns and actions which give players a reasonable amount of time to think. The trade-proposal mechanic favors players with fast thinking and reaction times, which can arguably be unfair to players with physical mobility issues. If needed, this game behavior can be patched and discretized by, say, enforcing a round-robin order for these actions.

Outcome

In chess, either the white player wins, the black player wins, or the game ends in a draw. This is clearly discrete and finite.

In basketball, the end result is an unbounded integer number of points for each of the two teams. This is also discrete and thus digital-like.

In horse racing, the outcome is a ranking of the horses (discrete) in their order of passing the goalpost, but also a finish time (continuous and analog-like) for each participant.

Miscellaneous

Pokémon GO is a video game with sizable analog-like and digital-like elements. For example, you walk on a continuous map of the real world and make analog throws of Poké Balls. But the management of items and owned Pokémon is inherently discrete.

Mafia has discrete states based on cards and discrete actions to kill players, but it is primarily a social game. Free-form discussion among the players is a major component of gameplay. When played face-to-face (this is the preferred environment), the discussion is inherently continuous in the oral messages and timing. This can be discretized in the form of turn-based text chat, but this would ruin the intimate and real-time atmosphere of the game.

## Examples

Mostly analog
• Traditional sports: Tennis, hockey, golf
• Driving/racing (e.g. car, airplane, spaceship)
• Running, jumping, throwing, swimming
• First-person shooter
• Darts, billiards, bowling, pinball, foosball
• Jenga, marbles, disentanglement puzzle
Mostly digital
• Chess, checkers, go
• Cards: Poker, big two, Uno
• Gambling: Slots, Bingo, blackjack
• Scrabble, Battleship, Connect 5, dominoes
• Rubik’s Cube, Sudoku, 15-puzzle

## Hardware

Analog devices dominate the history of games because digital computers are a recent invention. Generally speaking, an analog device has continuous state variables such as position and velocity. Examples:

• A chess piece has a continuous position on a board. However, we agree by the rules to mentally snap or quantize the position to a finite set of discrete states.

• A playing card has a continuous position and rotation. But we restrict the interpretation to discrete states like “face up”, “face down”, “in the deck”, “in player k’s hand”, “in the discard pile”, etc. (The fact that a playing card is an analog device can be seen in how messy a discard pile is.)

• A golf ball has a continuous position, velocity, rotation, etc. We generally accept the analog state as is, except for a few special cases like “in the hole” (which is defined by a continuous region of space).

Digital devices are characterized by discrete states and discontinuous transitions. While no device is perfectly digital because they are all ultimately implemented on analog physics (with the exception of quantum physics), devices can approximate digital behavior with conspicuous differences between states and fast transitions that exclude “in-between” values. Examples:

• We all know that modern computer microchips are digital devices (except for special analog circuits like audio output). The transistors in chips can handle electronic digital signals extremely quickly and accurately, so these devices are very close to ideal (except for small problems like metastability, glitches, radio-frequency interference).

• A whack-a-mole machine should be digital. A mole is either up or down, and the score is a discrete quantity. Ideally, a mole should rise or fall as quickly as possible because a half-up mole is not a meaningful state in the game. Note that the machine could be implemented as a fully mechanical device, without any computers or electronics.

• A coin (for flipping) or a die (for rolling) is digital because it’s easy to tell which face is up, and it’s very hard to do weird things like flipping a coin and having it end up standing vertically.

• Most board games are manufactured in a lazy way such that game-relevant regions are merely printed on a flat board. Because of this, players are expected to move pieces onto regions cleanly and avoid straddling a boundary. Alternatively, game boards could have walls surrounding each region. With this, pieces will stay in their region even if the board is lightly jostled.

Whether a game has analog or digital rules/mechanics, it can still be implemented on analog or digital devices. The choice of what device to use comes down to practical concerns, just to name a few:

• Universality: Analog devices are mostly special-purpose or single-purpose; e.g. a deck of cards can’t be used in a golf game, nor golf balls in poker. But a computer (or computerized game console) can convincingly mimic or emulate a wide variety of games just by downloading software code and showing visual images.

• Delivery: Games implemented on modern digital devices are software code, and can be transferred over the Internet quickly and automatically. Analog objects can only be shipped physically with human handling. But some analog items (e.g. standard 52-card deck) are reused for many different sets of game rules, so they are commonly available.

• Cost: Each analog object (which supports only one or a small number of games) must be paid for somehow, like buying a Jenga set or renting a horse. There may also be costs for travelling to a site and the risk of personal injury. By contrast, buying a computer (or game console) is a big one-time cost, but the device can play hundreds of different games. Although the marginal cost of copying a digital game is zero, games are priced such that the total revenue from all copies sold will compensate the time and effort spent by the game developers (programmers, artists, managers, etc.) to create that virtual game world.

• Remote: True digital games like chess can be played remotely, even over extremely high-latency communications methods like paper mail. This is because the rules are simple enough for both parties to understand and agree on, and the game is turn-based with clearly defined actions. While it’s not possible to play basketball remotely in any reasonable natural way, the game can be artificially digitized. The rules of the game become megabytes of program code that all the participating computers agree to interpret and execute in the same way, and the communication latency (e.g. 1 ms on a LAN, 100 ms on the global Internet) is low enough to not detract from the real-time gaming experience.

• Recording: Analog devices generally have unrepeatable behavior. For example, a machine that spits out tennis balls cannot be expected to land each ball in the same place, due to errors like the wind, the weight of each ball, the machine moving slightly after throwing a ball, etc. On the other hand, digital rules are mathematical and inherently repeatable. By agreement, feeding in the same list of chess moves will always give the same outcome. Similarly, a computer program like Super Mario, when fed the same sequence of controller inputs with the same timings, will yield the same game state. So digital games can be recorded and perfectly replayed as many times as we like. It’s also possible to slow down the playback (even frame-stepping), undo a move and try another one, and craft clever products like tool-assisted speedruns (TAS).

• Lifespan: Analog devices like cards wear out quickly after thousands of uses. Digital equipment like CPUs and LCDs never wear out, but physical controllers do wear out after years of handling.

• Errors: Analog objects have manufacturing tolerances (e.g. the dimensions of a die). Digital circuits have error tolerances too (e.g. bit error rate of 10−30 per transistor per second), but in practice they are either indistinguishable from perfect or obviously broken.

## Conclusion

Based on the definitions and examples given, it is incorrect to blindly label all tabletop games as “analog” and all video games as “digital”.

The vast majority of tabletop games are digital because they have a discrete state space, discrete and finite actions, and discrete time; chess would be an excellent example of these characteristics. Some tabletop games like Jenga are indeed analog, involving continuous actions and real physics.

Video games have mechanics that span the spectrum from digital to analog. Early video games were more often digital, implementing things like simple board games or card games, or forcing the character to move in a coarse grid (e.g. The Legend of Zelda (NES)). Some games use input timing as an analog control, like in Kirby’s Dream Course (SNES). The introduction of analog joysticks and movable 3D camera views significantly increase the analog nature of a video game. When computer hardware became powerful enough, more games could realistically simulate analog mechanics like running, jumping, throwing, and driving in a virtual world.

Everything on a computer is finite, from the number of frames per second, to the number of values an “analog” joystick can generate, to the number of different floating-point numbers that can be represented. But when so many different values exist (easily hundreds or more), the values are so closely spaced, and the game outcomes for two nearby numbers are so similar, it’s easier to think of the game as being analog and continuous instead of painstakingly modeling every bit of digital logic that comprises the game.

We can all agree that basketball in the physical world is an analog game. If someone creates a video game version of basketball that uses an analog joystick, takes place in continuous time, has realistic physics, and has decent picture resolution and frame rate, then this video game should be considered analog as well.