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Probability and Games

by Davide Bisso on 09/23/13 03:41:00 pm

The following blog post, unless otherwise noted, was written by a member of Gamasutras community.
The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.


Davide Bisso

Game Design student @ Full Sail

Probability in games

Most games of today have several elements of probability incorporated into their base mechanics. We’ve all heard about or played World of Warcraft, Texas Hold’em and the classic Pac Man right? Although, completely different in genres and motives, each one of these games has their unique probabilistic mechanics or “random events” integrated throughout its gameplay. Some, without a doubt more advanced than others but nonetheless still using the same laws of probability.

Lets take Pac Man for example. When you first start playing this game, you’ll most likely feel as if the ghosts are on a relentless pursuit to get you. You franticly eat away at the dots trying to completely avoid each colored wraith, but as you progress you find this to become more difficult. This may leave you wondering, does the game have a patter or is the chase at random? Thanks to probability we’ve figured out that the ghosts aren’t actually programmed to chase you. If they were, the game would be impossible. Instead, each one has different patterns: Only the red ghost (Blinky) is programmed to go after you. The pink and blue ones (Pinky and Inky) only want to position themselves at a specific place relative to you, and the orange one (Clyde) just moves around randomly.

This leaves us with a basic understanding for how probability works with many of the golden age games (1970-1980) but personally, I feel that there’s much more to probability in games than the above example. Lets take a look at card games and rolling dice for the next portion. Typically you’ll find these two utensils mixed into Casino games like Hold’em, slots, craps and so on. Your main priority when playing these games is to be wary of the “gamblers fallacy” but in order to understand this fallacy you must have knowledge of independent and related events. So what are independent and related events?

Independent Events: The chance of each event occurring does not depend in any way on what happened in the other event. For example, rolling a six-sided die (event #1) and then rolling it again (event #2) are independent events. The first and second rolls are not related in any way. The number you rolled in event #1 has absolutely zero influence on event #2.

Related Events: the chance of each event happening is related in some way to the other event. For example, drawing a card from a poker deck (event #1) and then drawing a second card from the same deck (event #2). The chance of drawing a King on event #2 is affected by event #1—if you drew a King on event #1, then there’s a smaller chance of getting one in event #2 because there are less Kings remaining in the deck.

As you can see we have a pattern. “The Gamblers Fallacy” is nothing but someone confusing independent and related events. DON’T FALL FOR THE TRAPS!

Now, because not all game designer work with cards and dice, we must also take the time to figure out how probability works with digital games. In digital games, random numbers generators aren’t necessarily random. They use a “seed number” which is a number used to initialize a pseudorandom number generator. This PRNG is an algorithm for generating a sequence of numbers that approximates the properties of random numbers. This can get pretty complex, especially when working with big games, as you will start to notice patterns (patters lead to boredom, which = people quitting your game).

What we conclude from this article is that probability has many key factors in board, card and digital games. As games and technology rapidly evolve, we must use our knowledge to create new immersive games.

Thank you for reading.


Omey, E. “A simple game to derive probability”. N/A. 9/23/2013.

Peter Webb’s “Layman’s Guide to probability”.

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