Difference between revisions of "Arithmetic Progression"

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[[Category:Patterns]]
 
[[Category:Patterns]]
[[Category:Needs work]]
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[[Category:Resource Patterns]]
 
[[Category:Needs revision]]
 
[[Category:Needs revision]]
[[Category:Needs examples]]
 
 
[[Category:Needs references]]
 
[[Category:Needs references]]
[[Category:Stub]]
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''A linear relationship between the effort put into an action and its potential reward or risk.''
[[Category:Staffan's current workpage]]
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''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.''
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[[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.
  
This pattern is a still a stub.
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See wikipedia<ref name="wiki"/> for more information on arithmetic progression.
 
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The possible rewards have a linear relationship to the investments, that is, if the investment is double, the comparable reward is doubled.
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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.
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=== Examples ===
 
=== 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.
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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 ==
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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.
[[Drawing Stacks]] can be used to create [[Arithmetic Progression]] since they steadily increase the probability for drawing a specific [[Cards|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 [[Cards|Card]] of the same type is in the same range of a [[Drawing Stack]] the distribution is more like [[Geometric Progression]].  
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Using the pattern
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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.
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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).
  
=== Diegetic Aspects ===
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== Using the pattern ==
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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]]. [[Repeat Combos]] is a specific example of how the pattern can be created by allowing the same type of goal to be reached several times with a linear relation between the [[Rewards]] given for each goal.
  
=== Interface Aspects ===
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The actual choices consist of deciding what efforts should be related to what effects. The efforts most often are uses of [[Resources]], but these do not have to be concrete [[Resources]] but can also be [[Budgeted Action Points]] or time invested in [[Extended Actions]]. The number of pieces of [[Sets]] collected is another possible effort that can be related to [[Arithmetic Progression]]. The effects can be either [[Rewards]] or [[Penalties]], or both, but affecting [[Scores]] or [[Vulnerabilities]] is another possibility. The relation needs to be based solely on one unit of whatever the effort consists of, for example adding a value 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]].
  
=== Narrative Aspects ===
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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; even if these uses of [[Resource Caps]] (or [[Action Caps]]) and [[Event Thresholds]] can be seen as a form of [[Discontinuous Progression]] regard how the [[Investments]] can be made it does not change the fact that the changes on effects are arithmetic. 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]] (although this can negatively affect players' [[Freedom of Choice]]). It should be pointed out that when the type of [[Investments|Investment]] involved can be done many separate times in the game (as compared to only once), the use of [[Resource Caps]] and [[Time Limits]] may functionally become the same for players.
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Since the consequences of [[Arithmetic Progression]] are more intuitive than other types of progression, they are often used in [[Betting]] situations, especially when players bet [[Resources]] against each other.
  
 
== Consequences ==
 
== 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.
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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.
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[[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 ==
 
=== Can Instantiate ===
 
=== Can Instantiate ===
 
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[[Experimenting]],
==== with ... ====
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[[Freedom of Choice]],
 +
[[Predictable Consequences]]
  
 
=== Can Modulate ===
 
=== Can Modulate ===
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[[Betting]],
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[[Extended Actions]],
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[[Investments]],
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[[Penalties]],
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[[Resources]],
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[[Rewards]],
 +
[[Risk/Reward]],
 +
[[Scores]],
 +
[[Sets]],
 +
[[Value of Effort]],
 +
[[Vulnerabilities]]
  
 
=== Can Be Instantiated By ===
 
=== Can Be Instantiated By ===
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[[Repeat Combos]]
  
 
=== Can Be Modulated By ===
 
=== Can Be Modulated By ===
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[[Action Caps]],
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[[Event Thresholds]],
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[[Resource Caps]],
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[[Time Limits]]
  
 
=== Possible Closure Effects ===
 
=== Possible Closure Effects ===
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-
  
 
=== Potentially Conflicting With ===
 
=== Potentially Conflicting With ===
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[[Discontinuous Progression]],
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[[Geometric Progression]]
  
 
== History ==
 
== 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''<ref name="Bjork & Holopainen 2004"/>.
+
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''<ref name="Bjork & Holopainen 2004"/>.
  
 
== References ==
 
== References ==
 
<references>
 
<references>
 
<ref name="Bjork & Holopainen 2004">Björk, S. & Holopainen, J. (2004) ''Patterns in Game Design''. Charles River Media. ISBN1-58450-354-8.</ref>
 
<ref name="Bjork & Holopainen 2004">Björk, S. & Holopainen, J. (2004) ''Patterns in Game Design''. Charles River Media. ISBN1-58450-354-8.</ref>
 +
<ref name="wiki">Wikipedia [http://en.wikipedia.org/wiki/Arithmetic_progression entry] for arithmetic progression.</ref>
 
</references>
 
</references>
  
 
== Acknowledgements ==
 
== Acknowledgements ==
 
Jonas Linderoth
 
Jonas Linderoth

Latest revision as of 08:56, 4 August 2022

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.

See wikipedia[1] for more information on arithmetic progression.

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. Repeat Combos is a specific example of how the pattern can be created by allowing the same type of goal to be reached several times with a linear relation between the Rewards given for each goal.

The actual choices consist of deciding what efforts should be related to what effects. The efforts most often are uses of Resources, but these do not have to be concrete Resources but can also be Budgeted Action Points or time invested in Extended Actions. The number of pieces of Sets collected is another possible effort that can be related to Arithmetic Progression. The effects can be either Rewards or Penalties, or both, but affecting Scores or Vulnerabilities is another possibility. The relation needs to be based solely on one unit of whatever the effort consists of, for example adding a value 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; even if these uses of Resource Caps (or Action Caps) and Event Thresholds can be seen as a form of Discontinuous Progression regard how the Investments can be made it does not change the fact that the changes on effects are arithmetic. 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 (although this can negatively affect players' Freedom of Choice). It should be pointed out that when the type of Investment involved can be done many separate times in the game (as compared to only once), the use of Resource Caps and Time Limits may functionally become the same for players.

Since the consequences of Arithmetic Progression are more intuitive than other types of progression, they are often used in Betting situations, especially when players bet Resources against each other.

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

Betting, Extended Actions, Investments, Penalties, Resources, Rewards, Risk/Reward, Scores, Sets, Value of Effort, Vulnerabilities

Can Be Instantiated By

Repeat Combos

Can Be Modulated By

Action Caps, Event Thresholds, Resource Caps, Time Limits

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[2].

References

  1. Wikipedia entry for arithmetic progression.
  2. Björk, S. & Holopainen, J. (2004) Patterns in Game Design. Charles River Media. ISBN1-58450-354-8.

Acknowledgements

Jonas Linderoth