Games with guaranteed scores and waiting moves

Abstract

Combinatorial scoring games, with the property ‘extra pass moves for a player will do him no harm’, are characterized. The characterization involves an order embedding of Conway’s normal play games, and we call our class the universe of Guaranteed scoring games. Also, we give a theorem for comparing guaranteed games with scores (numbers) which extends Ettinger’s work on Dicot scoring games.

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Notes

  1. 1.

    The first world championships, at TRUe games May 2014, were played on a \(8\times 8\) board with the middle \(2\times 2\) square empty. The authors placed 4th, 11th and 2nd respectively, Paul Ottaway placed 1st and Svenja Huntemann 3rd.

  2. 2.

    see http://en.wikipedia.org/wiki/Game_of_the_Amazons.

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Correspondence to Carlos P. Santos.

Additional information

U. Larsson: Supported by the Killam Trust. C. P. Santos: This work was partially funded by Fundação para a Ciência e a Tecnologia through the project UID/MAT/04721/2013.

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Larsson, U., Nowakowski, R.J. & Santos, C.P. Games with guaranteed scores and waiting moves. Int J Game Theory 47, 653–671 (2018). https://doi.org/10.1007/s00182-017-0590-x

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Keywords

  • Combinatorial game
  • Normal play
  • Scoring play
  • Waiting move