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Cookie Clicker

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Abstract

Cookie Clicker is a popular online incremental game where the goal of the game is to generate as many cookies as possible. In the game you start with an initial cookie generation rate, and you can use cookies as currency to purchase various items that increase your cookie generation rate. In this paper, we analyze strategies for playing Cookie Clicker optimally. While simple to state, the game gives rise to interesting analysis involving ideas from NP-hardness, approximation algorithms, and dynamic programming.

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Notes

  1. https://github.com/kaixiao/Cookie-Clicker.

  2. M must be large enough so that the effect of \(\frac{y_2}{y_1}\) not being an integer is irrelevant in the long run.

  3. In the final analysis, we compare the time needed by the optimal algorithm starting from a worse state than the greedy one, so the greedy solution actually takes less time in Phase 2.

References

  1. Demaine, E.D., Langerman, S.: Optimizing a 2D function satisfying unimodality properties. In: Proceedings of the 13th Annual European Symposium on Algorithms, volume 3669 of Lecture Notes in Computer Science, pp. 887–898. Mallorca, Spain (2005)

  2. Garey, M., Johnson, D.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman, New York (1979)

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  3. Wang, X.Z.J., Luh, P.B., Wang, J.: An optimization-based algorithm for job shop scheduling. Proc. SADHANA 22, 241–256 (1997)

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  4. Wikipedia. Incremental game. https://en.wikipedia.org/wiki/Incremental_game. Accessed 9 Sept 2019

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Acknowledgements

The authors would like to acknowledge the support of CREST, JST, Grant No. JPMJCR1402 and KAKENHI, JSPS, Grant No. 15K11985.

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Author notes

  1. Mikhail Rudoy

    Present address: Google, Menlo Park, USA

Authors and Affiliations

  1. CSAIL, Massachusetts Institute of Technology, Cambridge, USA

    Erik D. Demaine, Jayson Lynch, Mikhail Rudoy & Kai Xiao

  2. University of Electro-Communications, Chofu, Japan

    Hiro Ito

  3. F.R.S.-FNRS, Université Libre de Bruxelles, Brussels, Belgium

    Stefan Langerman

Authors
  1. Erik D. Demaine
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  2. Hiro Ito
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  3. Stefan Langerman
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  4. Jayson Lynch
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  5. Mikhail Rudoy
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  6. Kai Xiao
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Corresponding author

Correspondence to Kai Xiao.

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Demaine, E.D., Ito, H., Langerman, S. et al. Cookie Clicker. Graphs and Combinatorics 36, 269–302 (2020). https://doi.org/10.1007/s00373-019-02093-4

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  • DOI: https://doi.org/10.1007/s00373-019-02093-4

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