Questions tagged [game-theory]
Puzzles that involve strategic decision making, usually involving either competitive or cooperative choices between a number of participants.
128 questions
0
votes
1
answer
148
views
Game of discs inside a square [duplicate]
A 3*3 square is given. Two players alternate in placing discs of 1 unit diameter inside the square. A disc can be placed if it doesn't overlap another disc or the edge of the square, it can however ...
- 37.6k
34
votes
1
answer
2k
views
Can you win this territory game while going second?
Rules
Alice and Bob take turns claiming territories on a map with a finite number of territories. After their first turn, a player may only claim a territory if it borders one they already own. If a ...
- 19.1k
10
votes
2
answers
535
views
Connect 3 on different board sizes
Two players, White and Black, sit down to play a few rounds of Connect 3 on a rectangular board of any size. White plays first. Assuming both players play perfectly:
What will be the outcome of this ...
- 6,579
4
votes
4
answers
541
views
Revealing the least helpful of three numbers
(This is a follow-up to Guessing whether the revealed number is higher.)
They're at it again. This time Andrew is secretly shown three real numbers, all independently, randomly, uniformly chosen from ...
- 2,170
9
votes
2
answers
1k
views
Guessing whether the revealed number is higher
Consider the following game:
Two real numbers are independently, randomly, uniformly chosen from the interval [0, 1].
Andrew is secretly shown the two numbers. He must choose one of the numbers and ...
- 2,170
13
votes
4
answers
3k
views
How fast can you win this (very stupid) game?
You and I get together to play the following (dumb) game:
Two positive integers N and K are fixed from the outset.
We both start the game with N coins and proceed to play some number of rounds like ...
- 6,579
14
votes
2
answers
1k
views
The Ultimate Battle of two players
The Ultimate Battle is a turn-based two-player game.
Player $i$ (1 or 2) has three stats: initial hit point $P_i$, attack $A_i$, and heal $H_i$. The values can differ between players. All values are ...
- 17.1k
1
vote
1
answer
278
views
Pirate's Game with a twist!
I recently encountered the Pirate's Game and I found the solution for the malevolent pirates where the strict majority is needed for the highest ranking pirate's survival. Rules:
We have $P$ pirates ...
- 11
1
vote
1
answer
193
views
How long will it take for the horse to be captured?
Source: https://open.kattis.com/problems/ambush
Problem: When Farmer Oskar doesn’t watch his cows closely enough, they tend to wander off into the forest to hunt for horse spies. To catch an enemy ...
- 103
-1
votes
3
answers
242
views
Another Another 6 tries to guess a number between 1-100 [closed]
Inspired by Another 6 tries to guess a number between 1-100, what is the most efficient strategy of questions requiring yes/no answers to guess the number $k$, if $k$ is formed in the following way?
...
- 127
6
votes
1
answer
787
views
Guarantee a win in choosing numbers from extremes of a row of numbers
2n random numbers are laid in a row. We take turns to take a number. Each time, one can choose from the number on the tail or the head of the sequence/row. The one with the bigger summation wins the ...
- 346
5
votes
6
answers
3k
views
Rock-Paper-Scissors but rock scores double
Suppose two perfect game theorists play rock paper scissors. Scoring is slightly different:
2 points when beating scissors with rock
1 point when beating rock with paper
1 point when beating paper ...
28
votes
4
answers
6k
views
Can you beat random?
It is known that one cannot beat a truly random player in Rock Paper Scissors.
Here you will play a variant of the game. In this variant you are not allowed to play the same shape twice in a row. So ...
- 37.6k
20
votes
8
answers
3k
views
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 ...
- 8,115
2
votes
1
answer
195
views
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 $...
- 39
1
vote
5
answers
598
views
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 ...
- 322
4
votes
1
answer
745
views
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 ...
- 1,623
19
votes
1
answer
614
views
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 ...
- 2,419
2
votes
0
answers
155
views
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 ...
- 1,023
7
votes
4
answers
416
views
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 ...
- 6,976
10
votes
3
answers
1k
views
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 ...
- 621
10
votes
1
answer
751
views
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,...
- 2,264
17
votes
6
answers
1k
views
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 ...
- 6,976
8
votes
1
answer
452
views
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 ...
- 317
0
votes
1
answer
290
views
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 ...
- 27
9
votes
2
answers
509
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 ...
- 37.6k
3
votes
2
answers
262
views
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 ...
- 2,693
3
votes
1
answer
192
views
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 ...
- 199
7
votes
3
answers
1k
views
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 ...
- 189
14
votes
2
answers
705
views
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 ...
- 6,976
9
votes
2
answers
913
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 ...
- 6,976
26
votes
9
answers
3k
views
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 ...
- 6,976
2
votes
1
answer
177
views
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
688
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 ...
- 8,600
11
votes
1
answer
671
views
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 ...
- 37.6k
0
votes
5
answers
533
views
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 ...
- 37.6k
0
votes
2
answers
407
views
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.
...
- 7,455
4
votes
2
answers
560
views
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 ...
- 41
4
votes
2
answers
538
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 ...
- 6,976
19
votes
4
answers
1k
views
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 ...
- 6,976
9
votes
0
answers
372
views
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 ...
- 2,419
-1
votes
1
answer
292
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 ...
- 31
7
votes
2
answers
384
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 ...
- 6,976
4
votes
1
answer
252
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 ...
- 143
13
votes
3
answers
914
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 ...
- 6,976
2
votes
1
answer
279
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 ...
- 21
18
votes
1
answer
691
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).
...
- 7,862
9
votes
2
answers
636
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: ...
- 6,976
12
votes
4
answers
801
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 ...
- 6,334
17
votes
2
answers
741
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 ...
- 2,419