Difference between revisions of "Arithmetic Progression"
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== Using the pattern == | == Using the pattern == | ||
Implementing [[Arithmetic Progression]] is rather easy, the most demanding design choice related to it is actually if it should be used instead of [[Geometric Progression]] or [[Discontinuous Progression]]. | Implementing [[Arithmetic Progression]] is rather easy, the most demanding design choice related to it is actually if it should be used instead of [[Geometric Progression]] or [[Discontinuous Progression]]. | ||
| − | The actual choices consist of what efforts, most often [[Resources]], should be related to what effects, which may be either [[Rewards]] or [[Penalties]], or both. The relation needs to be based solely on one unit of whatever the effort consists of, for example adding a score of 1 for each time | + | The actual choices consist of what efforts, most often [[Resources]], should be related to what effects, which may be either [[Rewards]] or [[Penalties]], or both. The relation needs to be based solely on one unit of whatever the effort consists of, for example adding a score of 1 for each time an action is done. This since if the effect depends on the number of units the progression will become a [[Geometric Progression|Geometric One]], or, if the relation change depends on which unit in a sequence of units it is it will become a [[Discontinuous Progression]]. |
| − | + | ||
| − | When | + | When designing [[Arithmetic Progression]] the [[Investments]] they represent need to compared to the other ones 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. |
| − | [[ | + | [[Extended Actions]] |
| − | + | ||
| − | |||
| − | |||
| − | |||
[[Risk/Reward]] | [[Risk/Reward]] | ||
[[Betting]] | [[Betting]] | ||
| + | |||
| + | [[Budgeted Action Points]] | ||
== Consequences == | == 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. | + | Since [[Arithmetic Progression]] affect the relation between effort and effect, it can modulate [[Investments]]. 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]]). | + | [[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]]). While the [[Value of Effort]] provide by [[Arithmetic Progression]] may not be as strong as for certain varieties of the other types of progression, its value is known in advance and may be a safer option. |
== Relations == | == Relations == | ||
| Line 42: | Line 39: | ||
[[Freedom of Choice]], | [[Freedom of Choice]], | ||
[[Predictable Consequences]] | [[Predictable Consequences]] | ||
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=== Can Modulate === | === Can Modulate === | ||
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[[Resources]], | [[Resources]], | ||
[[Rewards]], | [[Rewards]], | ||
| − | [[Risk/Reward]] | + | [[Risk/Reward]], |
| + | [[Value of Effort]] | ||
=== Can Be Instantiated By === | === Can Be Instantiated By === | ||
Revision as of 20:30, 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.
Contents
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. Puerto Rico makes use of an Arithmetic Progression to make action more desirable the longer since they have been used - for each turn an action card has not been used a bonus doubloon is placed on it and this is given to whomever first chooses the action.
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
Implementing Arithmetic Progression is rather easy, the most demanding design choice related to it is actually if it should be used instead of Geometric Progression or Discontinuous Progression. The actual choices consist of what efforts, most often Resources, should be related to what effects, which may be either Rewards or Penalties, or both. The relation needs to be based solely on one unit of whatever the effort consists of, for example adding a score of 1 for each time an action is done. This since if the effect depends on the number of units the progression will become a Geometric One, or, if the relation change depends on which unit in a sequence of units it is it will become a Discontinuous Progression.
When designing Arithmetic Progression the Investments they represent need to compared to the other ones 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.
Consequences
Since Arithmetic Progression affect the relation between effort and effect, it can modulate Investments. 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). While the Value of Effort provide by Arithmetic Progression may not be as strong as for certain varieties of the other types of progression, its value is known in advance and may be a safer option.
Relations
Can Instantiate
Experimenting, Freedom of Choice, Predictable Consequences
Can Modulate
Investments, Penalties, Resources, Rewards, Risk/Reward, Value of Effort
Can Be Instantiated By
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
- ↑ Björk, S. & Holopainen, J. (2004) Patterns in Game Design. Charles River Media. ISBN1-58450-354-8.
Acknowledgements
Jonas Linderoth
