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Hackenbush

Hackenbush

Hackenbush is a game in combinatorial game theory played on a finite graph with colored edges and designated ground vertices. Player Left can delete any bLue edge, player Right can delete any Red edge, and either player can delete Green edges. After a deletion, every connected component disconnected from the ground is also removed. Under normal play, a player who has no legal move loses (Lo 2013, p. 1).

A finite red-blue hackenbush figure has a surreal number as its game value. Allowing Green edges gives more general Conway game values, which need not be numbers. A few values are indicated above.

See also

Conway Game, Domineering, Game Theory, Surreal Number

Portions of this entry contributed by Ed Pegg, Jr. (author's link)

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References

Berlekamp, E. R.; Conway, J. H.; and Guy, R. K. Winning Ways for Your Mathematical Plays. Wellesley, MA: A K Peters, 2004.Conway, J. H. On Numbers and Games. Wellesley, MA: A K Peters, 2000.Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 283-284, 1996.Gonshor, H. An Introduction to Surreal Numbers. Cambridge, England: Cambridge University Press, 1986.Knuth, D. Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. Reading, MA: Addison-Wesley, 1974. https://cs.stanford.edu/~knuth/sn.html.Lo, I. Y. "Misère Hackenbush Flowers." 7 Jan 2013. https://arxiv.org/abs/1212.5937.Schleicher, D. and Stoll, M. "An Introduction to Conway's Games and Numbers." Mosc. Math. J. 6, 359-388, 2006. https://doi.org/10.17323/1609-4514-2006-6-2-359-388.Sloane, N. J. A. Sequence A065401 in "The On-Line Encyclopedia of Integer Sequences."

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Hackenbush

Cite this as:

Weisstein, Eric W., with contributions by Ed Pegg, Jr.. "Hackenbush." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Hackenbush.html

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