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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Which parent should you start playing against?
Let $k < n$, $k$ even, $n$ odd. Mary is to play $n$ chess games against her parents, alternating between her father and mother. To receive her allowance she must win $k$ games in a row. Given the ...
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votes
1
answer
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Pursuit-evasion game [closed]
A criminal has been spotted along a straight single-filed road of length $L$ at position $P$, measured from the left endpoint of the road! Two police officers arrive to the road at positions $A$ and $...
- 21
1
vote
5
answers
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A question from Bob to Bob
Set-up:
John and Bob are playing a game that goes like this:
Bob is alone in a completely opaque, featureless room.
Bob chooses a question, though some types of questions are off-limits, which will ...
- 312
4
votes
1
answer
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Don't let 'em die!
There is an 8x8 array of sleeping humans with ten feet between adjacent humans, with sides in the four cardinal directions. A hero and a villain start ten feet west of the northwest human. The hero ...
- 803
16
votes
1
answer
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Game of the glasses on the windowsill
The windowsill above the sink is where my wife and I place our dirty wine glasses. And while both of us love each other, neither of us love loading the dishwasher. As a result, these dirty glasses ...
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2
votes
0
answers
145
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Trippples - optimisation [closed]
Trippples
Introduction
Tripples (BGG) is a board game from the 1970s.
It is played on an 8x8 grid, and each tile on that grid (except the corner starting tiles, and four blank tiles) contain three ...
- 1,015
7
votes
4
answers
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How will the wolf catch the sheep in minimum time?
A wolf is trying to catch two sheep. At time $0$ the wolf's at $(0,0)$ and the sheep are at $(1,0)$. All animals move continuously in real time and react instantaneously according to each other's ...
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Alternative solutions to a Michael Rabin puzzle
I first heard the puzzle below around 1990 while working at Carnegie Mellon University; the puzzle was attributed to Michael Rabin. After solving it, I realized that alternative solutions are ...
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1
answer
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Toroidal tic-tac-toe
Part of the Monthly Topic Challenge #10: Möbius Strips, Klein Bottles, and other unusual topological surfaces
Warm-up for topological thinking. You are playing tic-tac-toe with the usual 3x3 grid,...
- 1,691
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votes
6
answers
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Can you stop copy Alice?
At time 0, Alice and you both move freely at speed 1 on the plane.
As each hour passes, all copies of Alice will subdivide into 2, each moving at half the speed of the parent. So if left alone, at ...
- 6,354
8
votes
1
answer
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Stickered Dice Game
You and your friend play a game.
To begin with, each of you has an unlabelled die. On the table laid in front of you are 12 stickers labelled 1-12.
The first player chooses one of the stickers and ...
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0
votes
1
answer
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I ask you to find a game, then a place in the game and finally make a screenshot
Clues to find the game:
I drive a lot.
Everything I eat tends to poison me.
Passion neon.
Do you like kombucha?
Clue for location in the game:
boys, boys, boys (I’m looking for a good time)
Clue ...
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9
votes
2
answers
459
views
Moving tokens game
I've been thinking about the following two player game played on a 3x3 grid:
Red goes first and players alternate in taking turns.
Red moves tokens horizontally right.
Blue moves tokens vertically ...
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3
votes
2
answers
246
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Directed Graphs from numbers
Bob and Alice play a game. Bob sends a sequence of positive numbers to Alice and using that information she forms a directed graph.
For each number in the sequence, she splits it into two non-empty ...
- 2,694
3
votes
1
answer
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Trapping the Adventurer: the Value of a Gambling Game
An Adventurer is standing on the first of eight sequential platforms, ready to advance. But a Booby-trapper is positioning a trap to catch them in a game played over several rounds.
Each round, the ...
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3
answers
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Beyond earth and countries fighting for land
Consider 2 countries, A,B that have discovered a new planet, the size of Earth.
They have decided to split the planet into regions of minimum area $10^3 m^2$ and maximum area $10^5 m^2$, with borders ...
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votes
2
answers
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Who is most likely to win all the chips?
Alice, Bob and Charlie each have 5 chips. Starting from Alice, they take turns to act in the order of Alice, Bob and Charlie. The $n$-th person to act must take a total of $n$ chips from their ...
- 6,354
7
votes
2
answers
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views
What number should the first person announce?
Five people each announce a number in turn. The number must be an integer in the range from $1$ to $100$, and different from the ones already announced by others. The winner (or winners) of the game ...
- 6,354
26
votes
9
answers
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N prisoners locked in cells
N prisoners are locked in N separate cells, numbered 1 to N. The warden visits each cell in order with a bowl. Each prisoner can decide whether to put a single coin in the bowl, depending on its ...
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2
votes
1
answer
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Hitting twice with different choices
This game of two players has public parameters an integer $n\ge2$, and a probability $p$ with $1/n<p\le1$. E.g. $n=4$, $p=1/3$.
In the first phase of a game, a player secretly decides $n$ ...
- 383
5
votes
2
answers
671
views
The Median Game - For Money
Inspired by this interesting puzzle which was quickly solved.
Five friends play a simple game with the following rules:
Players play consecutively one after the other.
Each player must call out a ...
- 7,378
11
votes
1
answer
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The median game
Five friends play a simple game with the following rules:
Players play consecutively one after the other.
Each player must call out a whole number between 1 and 10 (inclusive), such that it hasn't ...
- 33.2k
0
votes
5
answers
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Two wrongs can make a right
Can you construct two single-player games A and B, such that:
Every time you play game A you are guaranteed to lose.
Every time you play game B you are guaranteed to lose.
Every time you alternate ...
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1
vote
2
answers
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Pokemon battle puzzle: Chansey vs Wobbuffet
This is a 1v1 battle between two pokemons: Chansey vs Wobbuffet.
Your task is to analyze the battle and predict its outcome.
Information about the battle:
The battle takes place in Generation III.
...
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3
votes
2
answers
464
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Three-player Nim
Suppose I'm forced to enter the game of nim with two players who are perfectly logical people. The rules is simple:
We play a set number of rounds.
In every round, a random number of marbles (between ...
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votes
2
answers
527
views
Catch the angel in less than 7 units of time
The devil has trapped the angel in a regular hexagram of firewalls. The perimeter of the hexagram is 12.
The devil
starts at the apex of the hexagram.
can move at speed $1$ to leave a trajectory of ...
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18
votes
4
answers
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How long can you survive at the devil's playground?
The devil has trapped you in his playground.
The devil knows that you can't cross over the burning boundary of his circle, so he allows you to choose a position within the circle before he starts to ...
- 6,354
8
votes
0
answers
352
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A Glutton and a Split Check
N, T, A, B are arbitrary constants in this problem. I have only definitively solved the N=1 subproblem, so, if the general problem cannot be solved, I will be satisfied to mark as accepted a solution ...
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1
answer
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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 ...
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7
votes
2
answers
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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 ...
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4
votes
1
answer
235
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 ...
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12
votes
3
answers
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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 ...
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1
vote
1
answer
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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 ...
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18
votes
1
answer
635
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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).
...
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9
votes
2
answers
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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: ...
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12
votes
4
answers
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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 ...
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16
votes
2
answers
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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 ...
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10
votes
2
answers
661
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 ...
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9
votes
3
answers
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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 ...
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8
votes
3
answers
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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 ...
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votes
3
answers
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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 ...
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5
votes
3
answers
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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 (...
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9
votes
2
answers
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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 ...
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12
votes
3
answers
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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 ...
- 33.2k
6
votes
2
answers
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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, ...
user69519
26
votes
5
answers
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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 ...
- 33.2k
5
votes
2
answers
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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 ...
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6
votes
1
answer
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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 ...
- 6,354
10
votes
2
answers
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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 ...
- 5,560
8
votes
5
answers
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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 ...
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