id: 06458031
dt: j
an: 2015e.00913
au: Rowlett, Peter
ti: Developing strategic and mathematical thinking via game play: programming
to investigate a risky strategy for Quarto.
so: Math. Enthus. 12, No. 1-3, 55-61 (2015).
py: 2015
pu: Information Age Publishing (IAP), Charlotte, NC; University of Montana,
Department of Mathematical Sciences, Missoula, MT
la: EN
cc: M90 K50 M40 K90 P50
ut: risk; board games; mathematical thinking; game strategy; risk strategy;
computer programming
ci:
li: http://www.math.umt.edu/tmme/vol12no1thru3/07_Rowlett.pdf
ab: Summary: The Maths Arcade is an extracurricular club for undergraduate
students to play and analyse strategy board games, aimed at building a
mathematical community of staff and students as well as improving
strategic and mathematical thinking. This educational initiative, used
at several universities in the U.K., will be described. Quarto is an
impartial game played at the Maths Arcade, in that there is one set of
common pieces used by both players, and one where stalemates are a
common outcome. While some students play without apparent direction
until a winning opportunity appears, others adopt a more risky strategy
of building the board towards a winning position, which could allow
either player to win. Whether building towards a win is a sensible
strategy, when the other player could equally well benefit, is a topic
of debate at the Maths Arcade. Intending to suggest a possible student
project, this article will describe a method to represent Quarto as an
array of binary numbers, making the game suitable for programming in
Python. Then, one strategy is programmed to play at random unless a
winning move becomes available, while another is programmed to work
towards a winning position. These are calibrated by playing against a
completely random strategy and against themselves, then they are played
against each other. The more risky strategy is found to win over the
more naive player in around two thirds of one million games. Some
limitations and possible areas of development are discussed.
rv: