Tagged Questions
1
vote
0answers
29 views
Any known strategies for toads and frogs?
Are there any heuristic strategic for playing Toads and Frogs known? I reckon the optimal playthrough may be hard to achieve due to the game being NP-hard but at least something that regularly ...
23
votes
3answers
436 views
Three against the devil: a combinatorial game
A team of three sinners plays a game against the devil. They confer on strategy beforehand; then they go into three separate rooms, and there is no more communication between them. The play in each ...
0
votes
0answers
27 views
Applications of Scoring Play Combinatorial Game Theory
I'm currently looking into economic applications of scoring play combinatorial game theory. Details of the theory can be found in this paper.
http://arxiv.org/abs/1202.4653
A friend of mine ...
3
votes
0answers
51 views
Terminology questions about a game where one may “save his progress” at the cost of a turn.
The game is for $p$ players who each start at square $1$. Each turn, a player can either roll an $m$-sided dice or place a marker on his current square. If he rolls $x\in\{2,\ldots, m\}$, he ...
3
votes
2answers
93 views
probable squares in a square cake
There is a probability density function defined on the square [0,1]x[0,1].
The pdf is finite, i.e., the cumulative density is positive only for pieces with positive area.
Now Alice and Bob play a ...
4
votes
0answers
61 views
Linear Independence Game
Suppose you have a set $X$ of vectors in $\mathbb{F}_2^n$, with $|X| \ge n+1$, and consider the following game. On their turn, each player (2 player game) chooses from $X$ one vector and sets it aside ...
3
votes
0answers
148 views
“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 ...
5
votes
2answers
120 views
Nim addition- binary addition without carrying
A nim addition table is essentially created by putting, in any cell, the smallest number not to the left of the cell and not above that cell in its column. However, I know for a fact that nim addition ...
3
votes
0answers
183 views
Calculating the Shapley value in a weighted voting game.
Given a special case of WVG (Weighted Voting Game) of $a$ 1s and $b$ 2s and a quota q, $ [q:1,1,1,1..1,2,2,..2] $. I need help with calculating the Shapley value of a player with a weight of $2$ and a ...
0
votes
1answer
122 views
Nim Variant (Restricted removal)
Alice and Bob play the following game : There are $N$ piles of stones with $S_i$ stones in the $i$th pile. Piles are numbered from 1 to $N$. Alice and Bob play alternately, with Alice starting. In a ...
2
votes
1answer
186 views
Nim Variant (reducing by divisors)
Alice and Bob play the following game. They choose a number $N$ to play with. The rules are as follows:
Alice plays first, and the two players alternate.
In his/her turn, a player can subtract from ...
4
votes
3answers
125 views
Consider a card game-parity
Consider a card game where the deck consists of 63 distinct cards. The deck is created in the following manner: each card consists of some number of symbols, where no two symbols are the same. There ...
2
votes
2answers
633 views
Winning strategy for a matchstick game
There are $N$ matchsticks at the table. Two players play the game.
Rules:
(i) A player in his or her turn can pick $a$ or $b$ match sticks.
(ii) The player who picks the last matchstick loses the ...
5
votes
1answer
128 views
Stone games again
Two players are playing a stone-picking game.
There are some piles of stones. The number of stones in each pile is given.
Every player takes action in turns as following rules:
The one in his turn ...
2
votes
1answer
74 views
Name for a certain “product game”
Let $G,H$ be two (combinatorial impartial) games. Consider the following new game $P$: The positions are the pairs of positions of $G$ and $H$. A move in $P$ is a move in $G$, or a move in $H$, or a ...
5
votes
1answer
153 views
Motivation for the Sprague-Grundy theorem
The Sprague-Grundy theorem states that every impartial combinatorial game under the normal play convention is equivalent to a (unique) nimber.
What does the equivalence relation thus defined tells us ...
0
votes
1answer
269 views
Simple Nim game with equal-sized piles.
Consider the standard Nim game, i.e. you can take as many coins as you want from a single pile, you should take at least one coin and you can't take coins from two or more different piles at the same ...
2
votes
1answer
77 views
the name of a game
I saw a two-player game described the other day and I was just wondering if it had an official name. The game is played as follows: You start with an $m \times n$ grid, and on each node of the grid ...
7
votes
1answer
334 views
Irreversible chess [closed]
Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
2
votes
1answer
318 views
A checkerboard problem
If $mn$ squares out of a $2m\times n$ white checkerboard are colored black, and a move consists of interchanging the color on any two squares who share a side, how many moves at maximum can it take to ...
17
votes
1answer
812 views
Number of moves to solve a flood-it/sock-dye game
[ Question based on the sock dye game ]
[ Update: It appears that this game is better known as "Flood it" and is NP-hard. Also, "the number of moves required to flood the whole board is $\Omega(n)$ ...
