With my science background, I am sometimes intrigued by different mathematical concepts and how they might fit into a game. Today I am looking at one of these ideas, that of parity.

For those who might not have encountered the term before, parity refers to a property identifying a integer as either even or odd. While this might seem like a very straightforward idea with little application to games, it can have some surprising consequences. Notably you can often define a set of permutations of some set by their parity – whether you needed an even or odd number of moves to achieve the current state – and every move you make switches from an element in one set to another (the parity changes).

In games, this can produce two different states for a player, with different sets of available choices, depending on the parity of their current game state. How could this be applied in a game?

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Day 12: Exploring parity

Imagine an action selection game where each turn for a player is given a parity. A thematic way could be describing each turn as happening in the day or the night (with the player changing between the two states on alternating turns). Depending on whether it is day or night, players can take an entirely different set of actions. For example, say we were to take an Agricola-like strategy game and apply this mechanic. Maybe you could only plant crops or build buildings during the day, and actions such as family planning can only happen at night. Or a different theme – players play ghosts collecting dreams, which are collected at night, and are used to construct new magics during the day.

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Each different parity could give a very different feel for the player, providing a completely different set of options and concerns depending on whether it is night or day. With such a simple idea (indeed, maybe this is already present in an existing game) the players have to have some degree of planning and strategy, as they know if they don’t take a certain action this turn, they will have to wait at least another two rounds before they could take it again.

You can also spice up the idea with some complications: maybe there is competition to take certain actions, or there is some way players can speed up time and change the parity of their turn artificially, to be out of sync with the other players. It also opens some creative space to make different sets of actions, indeed completely different ways to play, between the two parities. How would you implement this concept?