Difference between revisions of "Arithmetic Progression"

Revision as of 20:06, 17 February 2011

A linear relationship between the effort 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).

Most board games that use action points to determine how much a player can do each turn have a direct translation between how many points are used on movement and how far one can move. This is for example true in Pandemic and Space Hulk.

Betting in gambling games often make use of Arithmetic Progression. In Texas Hold'em the potential win is directly related to how many others follow while in Roulette how much can be won is a fixed multiple based on how much is bet (and which type of bet).

Using the pattern

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.

Resources Rewards Investments Penalties Extended Actions Value of Effort Risk/Reward Betting

Consequences

By definition Arithmetic Progression make use of different ways of translating between effort and effect than Geometric Progression and Discontinuous Progression, and are thereby incompatible with each other.

Arithmetic Progression makes the planning of the Investments straightforward since there is an intuitive and easy to remember relation between how much Resources are used and the potential Rewards or Penalties, or in other words: they support Predictable Consequences. As Rewards can be claimed whenever without ruining the value of later Investments, Arithmetic Progression lets players do Investments in smaller chunks, thereby not requiring so great Risk/Reward choices (there nearly always is some risk - either due to a possibility of losing the Investments or not having put them in the most profitable option) and giving players a Freedom of Choice as well as encouraging Experimenting (compared to Geometric Progression).

Relations

Can Instantiate

Experimenting, Freedom of Choice, Predictable Consequences

with ...

-

Can Modulate

Investments, Penalties, Rewards, Risk/Reward

Can Be Instantiated By

Drawing Stacks

Can Be Modulated By

-

Possible Closure Effects

-

Potentially Conflicting With

Discontinuous Progression, Geometric Progression

History

A renamed and updated version of the pattern Arithmetic Rewards for Investments that was part of the original collection in the book Patterns in Game Design^[1].

References

1. ↑ Björk, S. & Holopainen, J. (2004) Patterns in Game Design. Charles River Media. ISBN1-58450-354-8.

Acknowledgements

Jonas Linderoth