Arithmetic Progression

That the relationship between the time or investment put into some part of the game and the possible reward or risk associated with it is linear.

This pattern is a still a stub.

The possible rewards have a linear relationship to the investments, that is, if the investment is double, the comparable reward is doubled. Arithmetic Rewards for Investments are those rewards in game that are directly proportional with the resources used to gain them. As long as requirements of minimum and maximum investments are met, Arithmetic Rewards for Investments allow players to split resources into several smaller investments rather than one large investment with no other penalty than maybe not receiving all rewards at the same time.

Examples

the unit construction in strategy games is often based on Arithmetic Rewards for Investments. If it costs 100 production points to construct a tank, it costs 200 points to construct two tanks, 300 points to construct three tanks, and so on.

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