Questions tagged [game-theory]
Puzzles that involve strategic decision making, usually involving either competitive or cooperative choices between a number of participants.
87
questions
-2
votes
1answer
242 views
The Box of Tic-Tacs
You were kidnapped and had no way of escape. The kidnapper opens the lights, and in front of you is an opened box of Tic-Tacs. He claims that he ate from 0-5 Tic-Tacs, (with 60 from the newly-bought ...
7
votes
2answers
304 views
Can the fugitive escape?
A fugitive is surrounded by N police officers, with the nearest one at distance 1 away. The fugitive and the officers move alternatively.
In a fugitive move, the fugitive can travel no more than a ...
4
votes
1answer
199 views
Winning strategy in game
Context: I played this game at one point (and lost) and now I'm wondering whether it was possible to win or not.
We have a hexagonal board like this:
I'm defining the following terms:
Each hexagon ...
12
votes
3answers
753 views
Outmaneuver your opponents in the duel
A, B and C are in a three way duel. Starting with A, they rotate in the order of A-B-C, each firing one shot at a time. They stand close to one another, so that each can kill one of the others or ...
1
vote
1answer
153 views
Variation of 100 prisoners [duplicate]
There are 100 prisoners, each prisoner is given a number between 1 and 100 without knowing which number, the number can repeat and not all of the numbers must be given.
Each prisoner in his turn can ...
17
votes
1answer
536 views
Lap Theory Optimal Betting Game
Three prisoners are seated at a table. Each of them has a mobile phone on their lap, and they are not allowed to look at anyone else’s phone (and obviously no other form of communication is allowed).
...
9
votes
2answers
397 views
Three way duel, which guns to choose?
Alice, Bob and Carole are involved in a game of three way duel. They take turns to shoot in the order of Alice-Bob-Carole-Alice-... until only one surviver is left standing. The rule is very simple: ...
11
votes
4answers
746 views
A packing game!
Amy and Ben are playing a game which is suggested by a genie. Amy first chooses $a,b,c\in\mathbb{R}^+$. Then a empty cuboid box with internal measurements $a+b,b+c,c+a$, and infinite supply of cuboid ...
16
votes
2answers
663 views
Topological Nim
You and your friend's new favorite game is "topological nim": You take your favorite compact metric space $X$ and a radius $r$. Each player removes an open disk of radius $r$ from the space ...
8
votes
2answers
520 views
Buzzword Bingo Boss Battle!
Two bosses of different companies take turns delivering long speeches. Every speech much “claim” at least one unused square by uttering the corresponding buzzword(s) in the table below. Victory is ...
6
votes
2answers
381 views
A game of 101 stones—win at (not quite) all costs
In the land of Humilia, a tournament game is played between two players with 101 stones in a pot between them. On each turn, a player may take up to five stones from the pot (and must take at least ...
7
votes
3answers
545 views
The 15 Pebbles Game
This is a game for 2 players - Each player uses a different coloured marker or pencil, there are 15 pebbles in total.
Players take turns to colour 1, 2 or 3 pebbles (player chooses how many). When all ...
10
votes
3answers
338 views
Find a good strategy to survive the multiplayer duel
Alice is involved in a duel with $N$ other opponents. She can choose a gun for herself with any hit probability as she wishes. She also prepares guns for her opponents, whose hit probabilities she can ...
5
votes
3answers
384 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 (...
9
votes
2answers
241 views
A knight chased by four knights
This is a follow up to A knight chased by three knights
Two players are playing a variant of chess on a 11x11 grid. The first player controls a white knight that starts in the centre square. The ...
11
votes
3answers
752 views
A knight chased by three knights
Two players are playing a variant of chess on a 8x8 grid. The first player controls a white knight that starts in the top-left corner. The second player controls three black knights that start in the ...
5
votes
2answers
236 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, ...
27
votes
5answers
6k views
Shortest game of Monopoly
This video claims that the fastest game of monopoly involves 4 turns and 9 rolls of the dice. I am wondering if this is actually the shortest game or can we do better in theory? What is the ...
5
votes
2answers
330 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 ...
7
votes
1answer
237 views
The sadistic chieftain and the lethal truel game
In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind.
"I'll ...
10
votes
2answers
288 views
Add a divisor! A game
Let $k$ be a positive integer. Amy and Ben are playing a game, with the number $1$ written on the whiteboard initially. Amy and Ben do the following in order, starting with Amy:
Suppose the number on ...
8
votes
5answers
548 views
Which gun is Alice's best choice?
Alice, Bob and Charles are involved in a deadly three way duel game.
Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
8
votes
3answers
360 views
Rock, Paper, Scissors, Anti-Rock
Alice and Bob are both well-known perfect logicians who have the ability to internally randomize and often pass their time by playing rock-paper-scissors. One day, tired of the usual RPS game, Alice ...
6
votes
1answer
505 views
Playing blindfolded 2048
Suppose you are playing many 2048 games, all blindfolded. As usual you can press left, right, down, or up to move the tiles. When there are no more moves the game terminates and you are told your ...
1
vote
3answers
149 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 ...
10
votes
1answer
420 views
Is Oh Tetris Oh! always a draw?
Alice and Bob were playing Oh-Tetris-Oh!, when they decided that every game must be a draw (played intelligently).
Can you prove this?
(Oh yes, the rules: A $10\times10$ grid, you can pick any ...
3
votes
2answers
146 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 ...
6
votes
1answer
337 views
Russian Roulette (Redux!)
You are challenged to a game of Russian roulette with a six-chamber revolver, but you and your opponent are allowed to change the outcome of the game in different ways. Here's how the game will ...
8
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
342 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
693 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
776 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
763 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
268 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
332 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
341 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
166 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
649 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
594 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
434 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
373 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 ...
5
votes
1answer
459 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
797 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
102 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
368 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 ...
46
votes
4answers
6k 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
718 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 ...
8
votes
6answers
1k 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
273 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 ...
