Geometric Progression

Relations where each change in effort results in the effect being multiplied by a fixed value.

Geometric Progression occurs in games when the growth of effects are not linear but grows by depending on the current strengths of the effects and constant factor, called the common ratio. For factors larger than 1, Geometric Progression makes each new effort have a greater effect than the previous one and can thus discourages players to split resources into several smaller investments in favor of one large investment as the combined rewards of two lesser investments are always smaller than the reward of the larger investment using the same amount of resources. Factors less than 1 have the opposite effect and encourage players to spread resources.

See wikipedia for more information on geometric progression.

Examples

The point reward in Tetris for removing more than one row at once increases in a geometric fashion.

Exchanging collected cards for victory points in Bohnanza follows a Geometric Progression, e.g. some types of cards give 2 points for a pair but 4 points for three cards.

The first levels for buying skills in the roleplaying system GURPS has a Geometric Progression that encourages players to diversify their skill sets.

Using the pattern

Drawing Stacks can be used to create Geometric Progression since the increase for drawing a specific Card increases for each card drawn, and this can be used to create implicit Time Limits (Pandemic and Thunderstone uses this together with Stack Seeding to guarantee that certain cards appear semi-regularly).

Positive Feedback Loops Negative Feedback Loops

Investments

Value of Effort Higher-Level Closures as Gameplay Progresses

Extended Actions Randomness Drawing Stacks Combos

Unlike Arithmetic Rewards for Investments, the functions used forGeometric Rewards for Investments to determine the relationship between the Resources and Rewards of Investments are not linear. Thereby, these types of Investments are incompatible with both Arithmetic Rewards for Investments and Diminishing Returns. Using Geometric Rewards for Investments together with increasing the Risk/Reward factor gives the players more interesting choices, by increasing the uncertainties for getting the Reward. This can be used as a sort of a player perceived Balancing Effect where the players who are lagging behind in the progress have a chance to reach the leading players but with the drawback of increased risks. Of course, the leading players can also increase the lead in a similar fashion unless some other kind of Balancing Effect is introduced, for example, by not allowing the leading players to make these kinds of Investments.

Geometric Rewards for Investments instantiates Hovering Closure, especially when used together with Collecting. Compared to Arithmetic Rewards for Investments players are more likely to have strong commitments to subgoals with Geometric Rewards for Investments, and this may be used to increase Tension. Geometric Rewards for Investments also forces the players to plan the Timing of the Investments more carefully than with Arithmetic Rewards for Investments.

Consequences

Rewards Penalties

Geometric Rewards for Investments give the players an incentive to focus their Resources or attention to certain activities, for example Collecting more Resources of the same kind. This can also be used as an incentive for the players to do Trading with other players or other actions that have the effect of Transfer of Control events.

The design choices with Geometric Rewards for Investment are mainly similar to Investments in general. The main differences, however, is the increased incitement to choose an artificial maximum amount that can be invested or to create an abrupt cutoff point where further Investments have Diminishing Returns. The main reason for the increased possibility for these design choices lie in the fact that Geometric Rewards for Investment gives Rewards that grow exponentially and create problems in Player Balance.

Although Investments are often made by committing Resources, Extended Actions and Combos are actions that can merit Geometric Rewards for Investments.

Quite obviously, Geometric Progression is not applicable together with either Arithmetic or Discontinuous Progression.

Relations

Potentially Conflicting With

Arithmetic Progression, Discontinuous Progression

History

A renamed and updated version of the pattern Geometric Rewards for Investments that was part of the original collection in the book Patterns in Game Design.

Acknowledgements

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