### Abstract

In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a; b) pairs for polyiamonds and polyominoes up to size four.

Original language | English (US) |
---|---|

Pages (from-to) | 147-172 |

Number of pages | 26 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 16 |

Issue number | 3 |

State | Published - 2014 |

### Fingerprint

### Keywords

- Biased achievement games
- Priority strategy

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Discrete Mathematics and Theoretical Computer Science*,

*16*(3), 147-172.

**Biased weak polyform achievement games.** / Norris, Ian; Sieben, Nandor.

Research output: Contribution to journal › Article

*Discrete Mathematics and Theoretical Computer Science*, vol. 16, no. 3, pp. 147-172.

}

TY - JOUR

T1 - Biased weak polyform achievement games

AU - Norris, Ian

AU - Sieben, Nandor

PY - 2014

Y1 - 2014

N2 - In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a; b) pairs for polyiamonds and polyominoes up to size four.

AB - In a biased weak (a; b) polyform achievement game, the maker and the breaker alternately mark a; b previously unmarked cells on an infinite board, respectively. The maker's goal is to mark a set of cells congruent to a polyform. The breaker tries to prevent the maker from achieving this goal. A winning maker strategy for the (a; b) game can be built from winning strategies for games involving fewer marks for the maker and the breaker. A new type of breaker strategy called the priority strategy is introduced. The winners are determined for all (a; b) pairs for polyiamonds and polyominoes up to size four.

KW - Biased achievement games

KW - Priority strategy

UR - http://www.scopus.com/inward/record.url?scp=84940338909&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940338909&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 147

EP - 172

JO - Discrete Mathematics and Theoretical Computer Science

JF - Discrete Mathematics and Theoretical Computer Science

SN - 1365-8050

IS - 3

ER -