10 citations · 28 across the 31 of their papers we have counts for
35 papers
Cyclic impartial games with carry-on moves
Tomoaki Abuku, Alda Carvalho, Urban Larsson +3
In an impartial combinatorial game, both players have the same options in the game and all its subpositions. The classical Sprague-Grundy Theory was developed for short impartial g…
Misère Cricket Pitch
Richard J. Nowakowski, Ethan J. Saunders
Misère games in general have little algebraic structure, but if the games under consideration have properties then some algebraic structure re-appears. In 2023, the class of Blocki…
Simple Chopsticks: Playing with any number of hands and fingers
Antoine Dailly, Valentin Gledel, Richard J. Nowakowski +1
Chopsticks is a game played by two players where they start with one finger raised on each hand. On their turn, each player moves by pointing an attacking hand at one of their oppo…
Affine Normal Play
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of…
A complete solution for the partisan chocolate game
Tomoaki Abuku, Hikaru Manabe, Richard J. Nowakowski +2
The class of Poset Take-Away games includes many interesting and difficult games. Playing on an -dimensional positive quadrant (the origin being the bottom of the poset) gives r…
Indecomposable combinatorial games
Michael Fisher, Neil A. McKay, Rebecca Milley +2
In Combinatorial Game Theory, short game forms are defined recursively over all the positions the two players are allowed to move to. A form is decomposable if it can be expressed…
A complete solution for a nontrivial ruleset with entailing moves
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
Combinatorial Game Theory typically studies sequential rulesets with perfect information where two players alternate moves. There are rulesets with {\em entailing moves} that break…
Infinitely many absolute universes
U. Larsson, R. J. Nowakowski, C. P. Santos
Absolute combinatorial game theory was recently developed as a unifying tool for constructive/local game comparison (Larsson et al. 2018). The theory concerns {\em parental univers…
Æquitas: Two-Player Counterfeit Coin Games
Kyle Burke, Tanya Khovanova, Joshua Lee +3
We discuss games involving a counterfeit coin. Given one counterfeit coin among a number of otherwise identical coins, two players with full knowledge of the fake coin take turns w…
The game of Flipping Coins
Anthony Bonato, Melissa A. Huggan, Richard J. Nowakowski
We consider Flipping Coins, a partizan version of the impartial game Turning Turtles, played on lines of coins. We show the values of this game are numbers, and these are found by…
Impartial games with entailing moves
Urban Larsson, Richard J. Nowakowski, Carlos P. Santos
Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke compar…
A Note on Numbers
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski +1
When are all positions of a game numbers? We show that two properties are necessary and sufficient. These properties are consequences of that, in a number, it is not an advantage t…
Partizan Subtraction Games
Eric Duchêne, Marc Heinrich, Richard J. Nowakowski +1
Partizan subtraction games are combinatorial games where two players, say Left and Right, alternately remove a number n of tokens from a heap of tokens, with (resp. $n…
Ordinal Sums, Clockwise Hackenbush, and Domino Shave
Alda Carvalho, Melissa A. Huggan, Richard J. Nowakowski +1
We present two rulesets, Domino Shave and Clockwise Hackenbush. The first is somehow natural and, as special cases, includes Stirling Shave and Hetyei's Bernoulli game. Clockwise H…
Complete Graphs and Polyominoes
Todd Mullen, Richard Nowakowski, Danielle Cox
In the chip-firing variant, Diffusion, chips flow from places of high concentration to places of low concentration (or equivalently, from the rich to the poor). We explore this mod…
Counting Path Configurations in Parallel Diffusion
Todd Mullen, Richard Nowakowski, Danielle Cox
Parallel Diffusion is a variant of Chip-Firing introduced in 2018 by Duffy et al. In Parallel Diffusion, chips move from places of high concentration to places of low concentration…
Atomic weights and the combinatorial game of Bipass
Urban Larsson, Richard J. Nowakowski
We define an all-small ruleset, Bipass, within the framework of normal-play combinatorial games. A game is played on finite strips of black and white stones. Stones of different co…
Cops and an Insightful Robber
Melissa A. Huggan, Richard J. Nowakowski
The 'Cheating Robot' version of Cops and Robbers is played on a finite, simple, connected graph. The players move in the same time period. However, before moving, the robot observe…
Cheating Robot Games: A model for insider information
Melissa A. Huggan, Richard J. Nowakowski
Combinatorial games are two-player games of pure strategy where the players, usually called Left and Right, move alternately. In this paper, we introduce Cheating Robot games. Thes…
Invertible Elements of the Misere Dicotic Universe
Michael Fisher, Richard Nowakowski, Carlos Pereira Dos Santos
We present a characterization of the invertible elements of the misere dicotic universe.
Diffusion: Quiescence and Perturbation
Danielle Cox, Todd Mullen, Richard Nowakowski
Originally proposed by Duffy et al., Diffusion is a variant of chip-firing in which chips from flow from places of high concentration to places of low concentration. In the variant…
Bounding Game Temperature Using Confusion Intervals
Svenja Huntemann, Richard J. Nowakowski, Carlos Pereira dos Santos
For combinatorial games, temperature is a measure of the volatility, that is, by how much the advantage can change. Typically, the temperature has been measured for individual posi…
The Spread of Voting Attitudes in Social Networks
Jordan Barrett, Christopher Duffy, Richard Nowakowski
The Shapley-Shubik power index is a measure of each voters power in the passage or failure of a vote. We extend this measure to graphs and consider a discrete-time process in which…
Simultaneous Combinatorial Game Theory
Melissa Huggan, Richard J. Nowakowski, Paul Ottaway
Combinatorial game theory (CGT), as introduced by Berlekamp, Conway and Guy, involves two players who move alternately in a perfect information, zero-sum game, and there are no cha…