The Stack Overflow podcast is back! Listen to an interview with our new CEO.

# Questions tagged [game-theory]

Puzzles that involve strategic decision making, usually involving either competitive or cooperative choices between a number of participants.

59 questions
Filter by
Sorted by
Tagged with
3k views

### Time to call the bluff [closed]

You are located outside of two rooms which have a door between them. Each room has one or more computers whose total power is unknown, so they cannot be reliably used as proof-of-work to compare times,...
353 views

### Chess Massacre Variants-Play Find The Fastest Way?

I have thought up several variations of massacre chess. Massacre chess is a game where almost every single move is a capture. The idea here is that only the chosen type of piece can capture. It ...
270 views

### Reverse dots and boxes – Guess the last move

Alice and Bob are playing a game of reverse dots and boxes. The players take turns adding one horizontal or vertical line of size 1 in one free spot on the grid (marked with light gray lines ...
649 views

### Reverse dots and… cubes? - Snowflake edition

A Reverse dots-and-boxes puzzle inspired by @jafe Albert and Robinson are playing a game of reverse dots and boxes. The players take turns adding one plane in one free spot on the grid (...
697 views

### Reverse dots and boxes, swastika edition

Alistair and Roberta are playing a game of reverse dots and boxes. The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light gray lines in ...
686 views

### Reverse dots and boxes

Alice and Bob are playing a game of reverse dots and boxes. The rules are simple: The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light ...
243 views

### Tactical Domino Placement Game

Alice and Bob take turns to place regular dominoes into a $7\times8$ board. The first player who cannot go loses. Is there a winning strategy for either player? Note that in this version the pips on ...
315 views

### Paper, pencil and a bunch of bars

An entry for the Fortnightly Topic Challenge #40. Alice and Bob are two rational players who are playing a simple pencil-and-paper game. In the beginning, there are fifteen small vertical bars on ...
281 views

### No point shuffling, just pick your cards

Alice and Bob are playing a card game with the following rules: Alice selects two piles of 3 cards from a standard 52-card deck and places the piles in front of her, face up. Bob can see these ...
290 views

### Birthday girl's casino game

My daughter's birthday is coming up. Here's a fun party game we can play to celebrate. (Bring your wallet!) I have a pair of 6-sided dice, and a standard deck of 52 cards. You place your ...
129 views

### You versus Computer - Who will be the Winner?

You sit down to play a “new” game of chess. In this game only one Knight is on the regular 8x8 chessboard. Only regular legal moves of Knight are allowed. Game begins with computer going first to ...
554 views

### Racetrack designers, assemble!

Note: Turns out the intended answer to this doesn't work after all (see comments to Sconibulus's answer). The rules have been changed slightly after the fact to ensure there can be valid answers (see ...
538 views

### 2019 gold coins to share

You and your friend has found in total 2019 gold coins in a treasure hunt. Since your friend found the place to dig up, he deserves a bit more gold than you so you offer a game to share the coins to ...
350 views

### Four-in-a-line Puzzle

Disclaimer: This is an open-problem, I don't have a complete solution for this puzzle yet. We are playing a $2$-player game: you as a challenger and me as a judge. Initially, there is an empty ...
2k views

### What is the optimal strategy for the Dictionary Game?

In the Dictionary Game, players take turns saying English words. The first player starts by choosing any word, which splits the dictionary in two parts. The next player chooses a part and picks a word ...
262 views

### 100 prisoners' names in boxes, against smart warden

My question, which I do not know the answer to, concerns the classic 100 prisoners and 100 boxes puzzle, summarized below. The solution to this assumes the names are placed in boxes randomly, and gets ...
414 views

### Games and Puzzles

Four teams take part in a week-long tournament in which every team plays every other team twice, and each team plays one game per day. The diagram below on the left shows the final scoreboard, part of ...
618 views

### Should I kill all of my elves?

I've been playing a simplified variant of The Great Elf Game for a few days now and I'm struggling to identify an optimal strategy. Rules: You start with 12 elves. Each elf is sent to gather a tree ...
5k views

### Rock, Paper, Scissors and Trump

Alicia and Robert are two high-stakes gamblers who are playing a match of rock-paper-scissors. Each winning throw is worth 10 €, paid by the other player. These players have deep pockets, so matches ...
88 views

### A game of n players [duplicate]

There are n players. Each player has to choose an integer. The winner is the one with the lowest integer that has not already been chosen by another player. What is the optimal strategy? e.g....
983 views

### Single-pile Nim with Three Players

Three perfectly rational logicians (Alice, Bob and a Quetzalcoatlus) are playing a game. (Charlie couldn't make it, so he asked the Quetzalcoatlus to fill in for him.) The rules are very simple: ...
655 views

### Strategy in Coloring a 4x4 empty grid and the one who completes any 2x2 area of the grid is the loser

Alice and Bob are playing the following game: They have a 4x4 empty grid and take turns coloring one square each, starting with Alice. Assume that both players will colour the squares in with the same ...
265 views

### Given an $8×8$ square and a set, which contains the pentominoes and four $1×1$ squares

I have a game. Given an $8 × 8$ square and a set, which contains the pentominoes and four $1 × 1$ squares. Players alternately pick one item from the set. Then players (starting with the player ...
116 views

### Solve american eagle statistics game [closed]

If you are one of 100 people playing American Eagle, a game where one person starts alone and has to tackle someone as people run past in order to "recruit" more tacklers for the next run across, and ...
232 views

361 views

### Dollar Auction with Perfect Logicians

The dollar auction is a famous game that shows how seemingly logical choices can end up with very illogical results. Wikipedia says the best strategy is not to play, which is probably true in most ...
798 views

### Winning strategy in a calendar game

Consider a two-player game. The players move in turns to pick either a month or a day. The winner is the player who picks the date December 31 ($12/31$). The following rules apply: The game starts ...
538 views

### 'Companion Planting' Logic Puzzle - Is there an elegant solution?

Problem: You're a vegetable gardener planning to plant out seedlings in a new garden bed, however your farmer's almanac has outlined a system of rules about what plants can and cannot be placed next ...
649 views

### Higher or lower?

The game “Higher or Lower” is a simple one in which playing cards are drawn randomly from a deck, and the player has to guess whether each subsequent card will be higher or lower in value than the ...
405 views

### What is best strategy to multiple turn prisoners dilemma, when your opponents actions are hidden?

Best strategy for multiple turn prisoners dilemma is called tit for tat you start with cooperation and then repeat your opponents answer from previous turn. Is ...
481 views

### It's a Vote! Everybody Out!

There is a country ruled by a ruthless Emperor. He has a plan to make people miserable by ridding himself of the most popular members of the population. Every month, each person in the ...
171 views

### Another Unconventional Dice Blackjack game - is Nash equilibrium here?

This question is similar to This Dice Blackjack game - is there Nash equilibrium?, but the game rules are completely different. This Dice Blackjack is game for two. It is also played with fair six-...
397 views

### This Dice Blackjack game - is there Nash equilibrium?

This dice Blackjack is game for two - bettor and dealer. It is played with fair six-sided dice. Bettor: Bettor starts the game. Bettor can roll dice as many times he/she desires while the sum of ...
172 views

### Turn based Number game

You and a friend take turns saying positive integers greater than one. You can't say a number that is a multiple of previous numbers or a sum of multiples of previous numbers. For example, if A says 3 ...
668 views

### Pirate Puzzle Double Twist

Five pirates, fresh from their first bout of pillaging, return to their island base to celebrate and divide up the treasure. While this was their first time working together, the start of what they ...
167 views

### Coins in a row, without the usual restriction

I had been asked the following question: n coins are placed on a line such that they touch each other. A move consists in taking either one coin, or two adjacent (touching) coins. Solve the standard ...
273 views

### Five coins on a 15x15 board

[Note: this puzzle is derived from a coding contest question at HackerRank. The question is no longer in active use there. It was originally posted with content copied-and-pasted directly from there, ...
480 views

### Coin Splitting Game [closed]

There are 8 coins to be divided between A and B. A first makes an offer of how to divide the 8 coins between them. If B refuses A’s offer, then now it is B’s turn to make the offer, but this time 4 ...
5k views

### Will a greedy algorithm solve Tatham's Flood?

I was just investigating some of the puzzles on Simon Tatham's website, and came across Flood, in which we start with an $n\times n$ grid of cells each of which is filled with one of $k$ predetermined ...
593 views

### Optimal running-time tic-tac-toe algorithm

A perfect tic-tac-toe AI/algorithm would ideally never lose, but only win or draw, 100% of the time. Imagine that you play against once such algorithm, and it calculates the next move to make. Is ...
159 views

### Which player wins in this takeaway game?

Two players A and B play a game where they take turns removing 1,4, or 5 coins from a pile of n coins, A moving first. The player who takes the last coin wins. Who wins when: n=18, n=41, n=56? This ...
504 views

### Frugality 101: How to Replace Your Police Force with Cardboard Cutouts

In the far away land of Frugalia - a land where the conservation of money has been elevated to the status of any of Newton's laws - a conundrum is being had. There has been an upsurge in citizens ...
716 views

### Reverse Puzzling 3

This is a continuation of Reverse Puzzling 2 "Okay George, let's try this one. Pretty simple." I gave George the puzzle. He picked up his marker and quickly sketched out the following. "Well... I ...
271 views

### Who Wins At Horsie-Push?

Allan, Brian, and Charlie had a chess set and an afternoon with nothing to do. A chess tournament was suggested but to three towering intellects such as these, regular chess is a frivolous, juvenile ...
4k views

### Who shall come to the tea party?

All of your stuffed animals are assembled, anxiously waiting to learn who will be be invited as the Guest of Honor to your next tea party. This is to be an exclusive party, after all, as there is ...