# Questions tagged [combinatorial-game-theory]

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.

669 questions
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### Perudo Game - probability of succes for my call

I'm making a computer program that should play as a bot against other student's bots as ICT project at school. The game is Perudo. In this part of the program I want to know what's the probability of ...
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### Card Guessing Game Probabilities

Suppose we have a card game in which, for a standard deck of 52 cards, one card of each suit is selected at random and pulled out of the deck. The remaining 48 cards are shuffled together, and laid ...
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### How many moves will it take to turn $100$ coins to the heads side up? [on hold]

You have 100 coins on the table, all tails up. One move is turning any 93 coins over.How many moves will it take to get all the coins on heads? It's question that I found in mathematical "olimpics" ...
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### Is there a reasonable one hour summary of Game Theory?

In his Topology and Geometry course on Youtube (http://www.youtube.com/watch?v=QzfZS3iopR0&t=10m7s), Tadashi Tokieda claims he can teach all of game theory in an hour. He seemed very sincere and ...
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### A game relevant to moving a stone.

There is a straight line of $10000$ cells connected together . It contains $n$ stones at coordinates $p_i(1\le p_i\le 10000,i=\overline{1,n})$. A and B plays a game as follow: 2 players take turns ...
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### A game relevant to sum and sequences.

We have a set of k positive integers $a_i$ and $x$ coins. A and B take turns picking up the coins so that the last picker is the winner. Each turn, one person can only pick up a positive number of ...
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### Winning strategy using prime divisors. NIM varient.

In this game, two people take turns removing sticks from a pile that begins with x sticks. The person who takes the last stick wins. A person removes either one stick or p sticks, where p is a prime, ...
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### The Connect Infinity game

Recently Joel David Hamkins posted an entry on the Connect Infinity game. Connect-$\omega$ is Connect Four but played on an $\omega\times n$ grid ($n$ finite)! The above shows $n=6$. The difference ...
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### A game based on cutting rectangles from paper

You are given a piece of paper that consists of $w \times h$ squares. You can cut the sheet in a vertical or horizontal axis at the positions with integer coordinates so that the paper becomes two ...
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### Wythoffs Game -Game Theory

Suppose in the Wythoff’s game there are 40 matches in the first pile and 20 in the second pile and it is your turn to play. How would you play? Please assist in how to complete this problem.
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### Shapley value is efficient

The question seems trivial: I must show that the Shapley value distributes the full value of the grand coalition among the players. In other words, if the Shapley value of player $i$ is defined to be ...
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### Game on a number line

Define a game on a number line as follows: at the beginning, there are (possibly) some tokens at some negative integers on the number line. Each integer can hold any number of tokens. At each step, ...
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### Who has the winning strategy? [closed]

A $48 \times 29$ rectangle is divided into unit squares. Two players take turns to colour these squares black, as follows. At each turn, a player chooses a number of uncoloured squares that themselves ...
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### Game of Nim Sum Challenge Problem

Suppose in the game of Nim there are 72 chips in the first pile, 60 chips in the second pile, and 100 chips in the third pile and it is your turn to play. How would you play? Following the below ...
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### Winning strategy in a number theory game

Two people play a game, lets call them A and B. There are $n$ stones on a table and players start to remove them. They can remove $p-1$ stones at once where $p$ is a prime number. Whoever takes the ...
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### A question about something in Conway's “On Numbers and Games”

In the book mentioned in the title, which deals with (among other things), Conway's "surreal numbers", there is a small section (pp. 37-38) where the "gaps" in the surreal number line are discussed. ...
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### Integral of a function defined in the set of Surreal Numbers

Given ${\{C}\}\$ the set of all the $Surreal\ numbers$, is it possible to define the integral: $$\int_a^b{dxf(x)}$$where $$a\in{\{C}\},b\in{\{C}\},x\in{\{C}\}$$ Thanks
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### Optimal moves for maximizing perimeter? [closed]

Herman and Alex play a game on a $5 \times 5$ board. On his turn, a player can claim any open square as his territory. Once all the squares are claimed, the winner is the player whose territory has ...
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### Game where all positions specify the entire game history

I'm looking for an example of a game where, just by looking at the current game state, you can tell uniquely the entire game history. Are there any games with these properties? I'm looking for a ...
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### Game on a Graph

Assume a game on a Graph $G$ with two players called Alice and Bob. They alternate their moves and Alice always begins. In the beginning Alice puts a coin on arbitrarily vertex of the Graph. In ...
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### Alice and Bob take turns to remove numbers from a list

Alice and Bob play the following game. In the beginning there is list of numbers $$\{0, 1, 2,\dotsc, 1024\}.$$ Alice starts, and removes 512 numbers of her choice. Bob continues and removes 256 ...
Consider a $3 \times 3$ Tic-Tac-Toe board with opposite sides identified in opposite orientation. We play Tic-Tac-Toe in the Real Projective Plane. More precisely, consider a $3 \times 3$ Tic-Tac-Toe ...