## Involve: A Journal of Mathematics

• Involve
• Volume 9, Number 2 (2016), 249-264.

### A variation on the game Set

#### Abstract

Set is a very popular card game with strong mathematical structure. In this paper, we describe “anti-Set”, a variation on Set in which we reverse the objective of the game by trying to avoid drawing “sets”. In anti-Set, two players take turns selecting cards from the Set deck into their hands. The first player to hold a set loses the game.

By examining the geometric structure behind Set, we determine a winning strategy for the first player. We extend this winning strategy to all nontrivial affine geometries over $F3$, of which Set is only one example. Thus we find a winning strategy for an infinite class of games and prove this winning strategy in geometric terms. We also describe a strategy for the second player which allows her to lengthen the game. This strategy demonstrates a connection between strategies in anti-Set and maximal caps in affine geometries.

#### Article information

Source
Involve, Volume 9, Number 2 (2016), 249-264.

Dates
Revised: 29 January 2015
Accepted: 6 February 2015
First available in Project Euclid: 22 November 2017

https://projecteuclid.org/euclid.involve/1511370998

Digital Object Identifier
doi:10.2140/involve.2016.9.249

Mathematical Reviews number (MathSciNet)
MR3470729

Zentralblatt MATH identifier
1336.05091

#### Citation

Clark, David; Fisk, George; Goren, Nurullah. A variation on the game Set. Involve 9 (2016), no. 2, 249--264. doi:10.2140/involve.2016.9.249. https://projecteuclid.org/euclid.involve/1511370998

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