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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9
votes
12answers
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,...
10
votes
1answer
265 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 ...
12
votes
1answer
647 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 (...
8
votes
2answers
685 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 ...
14
votes
2answers
674 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 ...
4
votes
1answer
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 ...
8
votes
1answer
276 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 ...
10
votes
1answer
287 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 ...
5
votes
1answer
127 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 ...
11
votes
2answers
534 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 ...
14
votes
4answers
553 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 ...
8
votes
3answers
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 ...
5
votes
5answers
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 ...
4
votes
2answers
256 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 ...
4
votes
1answer
350 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 ...
5
votes
3answers
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 ...
0
votes
1answer
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....
9
votes
1answer
307 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 ...
43
votes
4answers
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 ...
1
vote
2answers
653 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 ...
7
votes
6answers
964 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: ...
7
votes
1answer
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 ...
1
vote
0answers
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 ...
7
votes
1answer
230 views

Domino Tiling Game

Two players are presented an $n\times n$ grid. They take turns placing a piece on the board until no more moves are possible. The last player able to make a move is the winner. The pieces are $2\times ...
6
votes
1answer
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 ...
23
votes
3answers
2k views

Angels & Demons (Open question)

This puzzle was given to me by a friend of mine, who in turn heard it from someone else who neglected to provide the answer. The text of the puzzle as it was given to my friend is below: Angels ...
8
votes
5answers
407 views

Two person game, choosing an integer between 1 and 30?

Suppose two players are playing a game. The first player chose an integer, n st. $n \in \left\{ 1,\ldots ,30\right\}$. The second player picks a different one. After that, a random integer x st. $x \...
11
votes
3answers
358 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 ...
12
votes
2answers
754 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 ...
5
votes
1answer
430 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 ...
7
votes
4answers
644 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 ...
1
vote
1answer
402 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 ...
5
votes
2answers
474 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 ...
1
vote
1answer
168 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-...
0
votes
3answers
384 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 ...
4
votes
1answer
171 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 ...
9
votes
1answer
662 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 ...
2
votes
1answer
166 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 ...
0
votes
1answer
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, ...
-4
votes
2answers
584 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 ...
31
votes
6answers
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 ...
2
votes
5answers
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 ...
3
votes
2answers
158 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 ...
14
votes
5answers
502 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 ...
7
votes
4answers
534 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 ...
9
votes
1answer
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 ...
8
votes
1answer
713 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 ...
4
votes
3answers
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 ...
1
vote
7answers
350 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 ...
6
votes
2answers
749 views

The Fanatic Fever(twist on the 5 pirates puzzle)

While raiding a tropical island, 6 pirates have an incredibly unlucky day. While they scoured the island in search of treasure, one of them was infected with the Fanatic Fever, a disease which hits ...