# Questions tagged [game-theory]

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

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675 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 ...
360 views

### Playing the Square Chess

On an ordinary chess board (8x8) without any pieces on it as a starting position, two players will alternately place a pawn on any square (unoccupied) so that the first player that form a square (...
444 views

### Three Cowboys, 11 bullets

While seeing a previous question not very well explained, a variant has emerged. I guess it wasn't intended by the OP but I find the variant even more interesting than the original one. Let me ...
502 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 population has ...
154 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 ...
207 views

### Simple game of dice - what is the optimal strategy?

The game is pretty simple, whoever reaches 50 first wins, but there are a few important details: 2 players, one die. Players take turns. Rolled values are simply added up If you roll a 6, however, ...
244 views

### Achieve the best outcome by a tactical statement

This puzzle is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which bargaining power is gained, paradoxically, by burning bridges and removing options for oneself. Here it ...
511 views

### Question about 1 on 1 on 1

Warning: Most of my posts are riddles disguised as something else. For those who have enjoyed my contribution and are expecting more, DO NOT try to guess that the answer is a tugboat, geese, or the ...
1k views

### In a Guess The Color game, what's the optimal strategy?

Here's a one-player card game: We begin with a shuffled card deck The player try to guess the color of the card at the top (black or red) If the player guess right, he can keep the card. Else the ...
178 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 ...
258 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 ...
395 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 ...
319 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 ...
175 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 ...
128 views

### How to effectively hide an earth rebooter thingy [The Good Place Season 4 spoilers]

This puzzle is unsolved. I don't know if there is a solution or how to solve it. I'm also not sure what type of puzzle this would be, so if anyone wants to correct the tags, feel free. Imagine you ...
675 views

### How to generalise Partition of the pie for N envy people?

There is well known task: How to divide a pie between two people, so each will think that he got equal or more that the other one? It has the following solution: I know that it is possible to ...
509 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 ...
172 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 ...
686 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 ...
468 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 ...
139 views

### playing “Coins on a table” against a distracted friend [duplicate]

This puzzle is a follow-up of Coins on a table (warning: the link contains the answer to the original question). You are playing a game against your friend Alice: first Alice places one coin on a ...
355 views

### The Buzzer Game [closed]

Two players, A and B, are each given air horns. Also present is a device which will at some random point produce a noise. If the device produces a noise before either player, they die. If both players ...
430 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 ...
197 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-...
120 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 ...
285 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, ...
99 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....
152 views

### How many cheating husbands? [duplicate]

There is a matriarchal town which believes that a prophetic stranger will tell the wives whether any of the husbands are cheating. The stranger will only say yes if there are any and no if there are ...