16
votes
2answers
276 views

The expected outcome of a random game of chess?

Imagine a game of chess where both players generate a list of legal moves and pick one uniformly at random. Q: What is the expected outcome for white? 1 point for black checkmated, 0.5 for a ...
2
votes
1answer
51 views

Reverse Hex board game winning strategy

I just wanted to know the winning strategy to this question: In a reverse Hex board game I know it means where the player who first forms a path between his/her edges loses. Find a winning ...
4
votes
1answer
59 views

A game problem- double or increment by 1

Its a two player game. Initially $P=1$, and there is some fixed integer $Q>1$. A valid move consists of either increasing $P$ by $1$ or doubling it iff on doing so $P$ does NOT exceed $Q$.The ...
3
votes
1answer
69 views

For which chess boards do solutions exist for this generalised Knight's Tour problem?

We know from a theorem by Schwenk that for any (m x n) chess board with $m \leq n$ it is always possible to create a knight's tour unless one or more of these three conditions are met: m and n are ...
6
votes
3answers
227 views

Why are the surreals considered “recreational” mathematics?

One of my college math professors once remarked to me that it was interesting that John Conway's two "biggest" contributions to math were both recreational: the Game of Life and the Surreals. No one, ...
-1
votes
1answer
110 views

A Nim game variant: Odd number [closed]

Consider the variant of Nim where the allowed moves are the removals of an odd number of stones from a heap. Who's the winner and what is the winning strategy in normal play (player unable to move ...
7
votes
2answers
225 views

A Nim-like game with conditions and strategies

The game: Given $S = \{ a_1,..., a_n \}$ of positive integers ($n \ge 2$). The game is played by two people. At each of their turns, the player chooses two different non-zero numbers and subtracts ...
4
votes
1answer
77 views

Analysis of “Dungeon Raid”

The computer game Dungeon Raid is quite complicated, but for our purposes we can consider the following simplified version. The player has a current health $\def\hcur{h}\hcur$ and a maximum health ...
0
votes
1answer
89 views

Lattice Squares; Basic Interesting Facts and Problems

I'm going to write an article in an educational magazine for middle school students, about the game Square It. The purpose of the game is to make lattice squares: I want to introduce the game, and ...
5
votes
2answers
192 views

A puzzle on game theory

Bob and Alice are playing a game. They will start with an integer $n$. Alice goes first, in each turn, a player can choose an integer between 1 and 13 and that number is to be subtracted from $n$. ...
2
votes
1answer
110 views

A game involving points in the integer plane - who wins?

I am running a workshop on puzzles and problem solving over the weekend and thought that it might be a good idea to get people engaged by phrasing some interesting mathematical results in terms of ...
4
votes
2answers
316 views

Why does the strategy-stealing argument for tic-tac-toe work?

On the Wikipedia page for strategy-stealing arguments, there is an example of such an argument applied to tic-tac-toe: A strategy-stealing argument for tic-tac-toe goes like this: suppose that the ...
1
vote
1answer
144 views

Winning single-pile, variable limits Nim [duplicate]

Possible Duplicate: Winning strategy for a matchstick game The rules of this variant of Nim are as follows: Starting at zero, each player counts up between 1-N numbers. The person that ...
6
votes
2answers
995 views

How many turns can a chess game take at maximum?

The shortest number of moves that a game of chess can have is 2, as far as I know: White moves pawn from f2 to f3, black moves ...
2
votes
2answers
2k 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 ...
14
votes
3answers
4k views

Average Scrabble graph structure: diameter?

Tonight a game of Scrabble ended in what I consider a very unusual graph structure, unlike this generic web image, which seems more typical: ...
3
votes
0answers
493 views

How many different chess-board situations can occur?

If you play a standard chess game on a normal $8 \cdot 8$ chess board with the usual rules: How many different "board representations" can exist? Upper bound: Well, you have 16+16 = 32 chess pieces ...
23
votes
3answers
1k views

Guaranteed Checkmate with Rooks in High-Dimensional Chess

Given an infinite (in all directions), $n$-dimensional chess board $\mathbb Z^n$, and a black king. What is the minimum number of white rooks necessary that can guarantee a checkmate in a finite ...
6
votes
1answer
669 views

Math and Logic of Infinite Chess

Hello could you help me in this... Two players (White and Black) are playing on an infinite chess board (extending infinitely in all directions). First, White places a certain number of queens (and ...
2
votes
2answers
530 views

expected number of guesses in game of mastermind

Sequence X consists of N pegs each randomly assigned on of M colours. One each go, the player places N coloured pegs in a line. If they exactly match sequence X, the game terminates. Otherwise, the ...
8
votes
0answers
466 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 ...