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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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 ...
• 2,790
531 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 ...
• 2,036
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 ...
• 2,036
2k 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 ...
• 2,790
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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 ...
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1 vote
264 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 ...
1 vote
192 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
221 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
773 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 ...
• 336
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 ...
• 278
5k 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 ...
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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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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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