Catch-Up: A Game in Which the Lead Alternates


Aaron IsaksenTandon School of Engineering, New York University
Mehmet Ismail, Department of Economics, Maastricht University
Steven J. Brams, Department of Politics, New York University
Andy NealenTandon School of Engineering, New York University


Catch-Up is a two-player game in which the players' scores remain close throughout the game, making the eventual winner — if there is one — hard to predict.  Because neither player can build up an insurmountable lead, its play creates tension and drama, even between players of different skill.  We show how the game is played, demonstrate that its simple rules lead to complex game dynamics, analyze some of its most important properties, and discuss possible extensions.


Isaksen, A., Ismail, M., Brams, S. J., Nealen, A. "Catch-Up: A Game In Which the Lead Alternates". Game and Puzzle Design Journal. Vol. 1, no.2, 2015. [PDF]

Rules and Demonstration

Catch-Up starts with a set of numbers S.  These are the numbers at the bottom of the screen. Two players, P1 and P2, begin with scores of zero.  P1 starts by removing a number by clicking on it.  The number will be added to P1's score. The players then take turns removing one or more numbers, one by one, until the acting player’s score equals or exceeds the opponent's previous score.  When this is no longer possible, the acting player receives any remaining numbers.  The player with the higher score wins; the game is drawn if scores are tied. You can change the number of pieces to start with by using the "Less Pieces" and "More Pieces" button.  You can start a new game by pressing "Restart Game".

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