Arithmetic Progression

A linear relationship between the investment put into an action and its potential reward or risk.

Arithmetic Progression described the relation between the effort players put into some part of the game and what type of effect can arise from the action. These effect can either be positive, i.e. rewards for wanted outcomes of the actions, or negative, i.e. penalties if the actions fail for some reason.

Examples

Unit construction in many strategy games have a linear relation between the numbers produced and its cost, e.g. each Longbowman in Age of Empires III costing 40 wood and 60 food (An exception can be found in the Hearts of Iron series which uses various modifiers through the version so that producing one unit can provide rebates on units produced afterwards).

Using the pattern

Drawing Stacks can be used to create Arithmetic Progression since they steadily increase the probability for drawing a specific Card, and this can be used to create implicit Time Limits (the game Pandemic uses this to guarantee that epidemics start semi-regularly). It should be noted though that when more than one Card of the same type is in the same range of a Drawing Stack the distribution is more like Geometric Progression. Using the pattern

Arithmetic Rewards for Investments use linear functions between the Resources and Rewards of Investments and are thereby incompatible with Geometric Rewards for Investments and Diminishing Returns. They make the planning of the Investments straightforward as there is no real incentive for hoarding the Resources before investing. As the Investments can be done in smaller chunks and do not represent so great Risk/Reward choices they give players a Freedom of Choice how to make Investments. The ease of understanding the Rewards received from Arithmetic Rewards for Investments makes them have Predictable Consequences, both for the players who are making the Investments and those observing the Investments being made.

Consequences

When implementing Arithmetic Rewards for Investments the costs involved have to be balanced compared to other possible Investments in the game. It is also possible to artificially limit the maximum possible amount used in single Investments or require minimum amounts to be invested to modulate the Risk/Reward choices that have to be made. Another way of modulating the Risk/Reward choices is to not make several identical Investments using arithmetic reward schemes possible at the same time by imposing Time Limits between such Investments.

History

An updated version of the pattern Arithmetic Rewards for Investments that was part of the original collection in the book Patterns in Game Design.

Acknowledgements

Jonas Linderoth