Tagged Questions

Combinatorial game theory (abbreviated CGT) is the subfield of combinatorics (not traditional game theory) which deals with games of perfect information such as Nim and Go. It includes topics such as the Sprague-Grundy theorem and is tangentially related to the Surreal Numbers.

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The Ring Game on $K[x,y,z]$

I recently read about the Ring Game on MathOverflow, and have been trying to determine winning strategies for each player on various rings. The game has two players and begins with a commutative ...
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Analyzing a class of vertex-deletion games

As part of the discussion on this question (Permutation Game Redux), a simple vertex-deletion game was proposed. The game is very simple. Disconnect. Players alternately remove vertices from a ...
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“Infinito”, a combinatorial game with infinite width game-tree

I recently designed a combinatorial game (sequential game of perfect information) with an infinite branching factor, that is it has a game-tree of infinite width. I'm wondering how is it possible to ...
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NIM with multiple winning final positions

I've been looking at a variant of NIM. You can skip this bit where I'll describe NIM as usually described: There's a starting position with some number of piles of counters and two players ...
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Has this subset-sum game been studied?

Consider the following game: two players, Yolanda (who always goes first) and Zachary, take turns selecting (not yet chosen) numbers between $1$ and $9$. The first player who can make three of their ...
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Game, stealing edges in a graph.

I was inventing a problem for a math contest, I was really pleased with it, but then I found a mistake in my solution and have not been able to solve it. It is as follows: Alice and Bob play a game. ...
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Chat Noir solvable?

There is a relatively simple flash game that I enjoy playing -- http://www.gamedesign.jp/flash/chatnoir/chatnoir.html is one version of it, though I've found many -- and it centers around trying to ...
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Conway's Game OF Life maximum periods on a set x by x game board.

I have taken interest in Conway's Game of Life and want to know if you guys can help me with a mathematical problem :) That is what this website is for right? You need to be familiar with the rules ...
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Create the most 'stressful' tennis game ever!

Some games, such as tennis, use a complicated points system (point, game, set, match; with deuces and tie-breaks) for what would otherwise be an extremely simple and monotonous game. The main reason, ...
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Prime number building game

Players $A$ and $B$ choose digits $(0, \dots , 9)$ turn by turn and build number by concatenating the digit they chose to the end of the number. Player $A$ starts by picking the first (one-digit) ...
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What is the highest possible score in 2048 hard?

There is a variant of the popular game 2048, called 2048 hard or 2048 impossible, which automatically places each new tile in the hardest possible location. Is this variation possible to solve, and if ...
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The point-open game and $\omega$-covers

Let $X$ be a topological space. The point-open game $G_{po}(X)$ is defined as folows. It is played by two players ONE and TWO. In the n'th step $(n \in \omega)$, ONE choose a finite subset $F$ of $X$, ...
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What is the optimal strategy for this 2 player game?

Let some finite array of integers is given initially. There is a number k which is initially '0'. In a move, a player will select a number from the array arr[i] and change k to gcd(k,arr[i]). Also, ...
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The name of a game from the 2013 Putnam

Does the following game from the 2013 Putnam have an official name? Based on my searches, it seems to have been created just for the exam. Let $n\geq 1$ be an odd integer. Alice and Bob play the ...
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Stable Marriage Problem

I would just like clarification for the following problem: Suppose $M_1$ and $M_2$ are two stable matchings between n men and n women, and we allow each woman to choose between the man she is paired ...
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What are the chances of shooting the moon in Hearts?

I'm posting this again here from boardgames.SE because it was suggested there that this is the more appropriate question to ask it. So, that said, here's my question: given a fair shuffle, that all ...
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Unavoidable structure of this kind of function:$Z\rightarrow N$.

Suppose that $f$:$Z\rightarrow N$ is a surjection and $|f^{-1}(n)|=2$ for every $n\in N$. I found that there is $n\in Z$ such that $f(n)$, $f(n+1)$, $f(n+4)$, and $f(n+5)$ differ from each other. "...
Proof that $12$ in a row tic-tac-toe is a tie game?
How can be it proved that tic-tac-toe on an infinite grid (winning with $12$ in a row, a column or a diagonal) can always end in a tie (with optimal strategies of both players)? There is a hint: to ...