4
votes
1answer
37 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
0answers
90 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
13
votes
3answers
735 views

The Best Strategy and Highest Possible Score for the “Threes!” Game.

[There's still the strategy to go . . . ] Here's my description of the game: There's a $4\times 4$ grid with some random, numbered cards on. The numbers are either one, two, or multiples of three. ...
1
vote
0answers
35 views

On a certain type of card game

Suppose two players are playing a card game, which is described as follow. Each player is allowed to construct their own decks of exactly $n$ cards with an additional repeatable card, where each ...
5
votes
2answers
102 views

Can you incentivise competitors to handicap accurately, and also try to win?

A problem I ran into for real. A group of friends of widely differing abilities wants to hold a handicap cycling race, so that if everyone does about as well as expected, there would be a perfect dead ...
0
votes
0answers
41 views

Waiting Time For Computer Cluster

There are $n$ computers. Computer users stay on their computers for a certain amount of time, $t$, throughout the day. Computer users come and go. How long will I have to wait, min/max, for a computer ...
0
votes
1answer
116 views

Game theory question

In a game where we have a normal 52 card deck. Two cards are delt out at a time, if both are red, then I keep the two cards. If both are black, you keep the two cards. If its one of each, then it gets ...
-1
votes
1answer
94 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 ...
9
votes
2answers
192 views

Optimal Strategy for Bar Dice

This game is played in bars in Wisconsin, USA, but I'm sure variations are played many places around the world. The game has practical value, since once mathematicians figure out the best strategy, ...
1
vote
1answer
128 views

You are Johnny Depp 3!

An extension of this question. As @Jared stated in his answer the solution is: we assume that the head pirate chooses between multiple possible proposals that maximize his profit by rewarding ...
6
votes
2answers
298 views

You are Johnny Depp 2!

An extension of this question repeated below. A band of 9 pirates have just finished their latest conquest - looting, killing and sinking a ship. The loot amounts to 1000 gold coins. ...
6
votes
2answers
221 views

How to solve this puzzle?

There are $N$ consecutive doors. Two players 'B' and 'J' plays a game. Both take turns alternately, and in each turn a player can open any one door. They define a block of 3 consecutive open doors as ...
5
votes
3answers
215 views

How to formally model the “hesitation” in the hat-guessing puzzle?

Hua Luogeng (in Chinese, εŽη½—εΊš) took a hat-guessing puzzle as an illustration in a booklet focusing on mathematical induction. The following description is a literal translation from Chinese. ...
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 ...
6
votes
1answer
464 views

Game theory problem: Poker with bluffing

Hope someone can help me with this one. The problem I am talking about can be found in the book titled "Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction" by ...
1
vote
1answer
106 views

Winning strategy

Is there a winning strategy for player one or two in the following scenario: The game begins with the number 2012. In one turn, a player can subtract from the current number any natural number less ...
6
votes
1answer
995 views

Number Game: 31 - Winning Strategy?

My Maths teacher taught us how to play a game called 31 on Friday. Not once did my Maths teacher lose. I want to know why. I'll explain the game... 31 is a game between two people. Let's say you've ...
0
votes
2answers
209 views

Given a victory condition and a set strategy, what are the chances of winning on a given turn in a game of Magic: The Gathering?

Tl;DR: You have winning cards. To win, you must be able to play those cards, and have them in your hand. Your hand is randomly drawn. When might you win? How could find the answer to this (very ...
6
votes
1answer
410 views

Soccer and Probability

MOTIVATION: I will quote Wikipedia's article on a soccer goalkeeper for the motivation: Some goalkeepers have even scored goals. This most commonly occurs where a goalkeeper has rushed up to the ...
8
votes
0answers
369 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 ...
13
votes
1answer
1k views

Is chess Turing-complete?

Is there a set of rules that translates any program into a configuration of finite pieces on an infinite board, such that if black and white plays only legal moves, the game ends in finite time iff ...