Mastering Nim Game Strategy: Optimal Tactics and Winning Chances for 3 Players

  • Thread starter Thread starter unscientific
  • Start date Start date
AI Thread Summary
In a 3-pile, 3-player Nim game, Player 1 can adopt a strategy focused on maintaining a non-zero nim sum to control the game. If Player 1 and Player 2 cooperate to eliminate Player 3, Player 1 has a better chance of winning if they can manipulate the nim sums effectively during the game. The optimal approach involves Player 1 ensuring that they leave a zero nim sum for Player 2 after their turn, thereby limiting Player 2's options. Strategies may include careful calculation of moves and anticipating Player 2's responses to maintain an advantage. Understanding these dynamics is crucial for mastering the game and increasing winning chances.
unscientific
Messages
1,728
Reaction score
13
Good day guys.

Q1: I was wondering if there is any optimal strategy for Player 1 in a 3-pile 3 player nim game?

Q2: If Player 1 and Player 2 cooperates and finishes of Player 3, who stands a higher chance of winning? Player 1 and Player 2? And Why?

Q3: Is there a strategy when Player 1 and Player 2 cooperate for Player 1 to win most of the time and why?
 
Mathematics news on Phys.org
What have you tried so far? Where are you stuck?
 
We have no ideas..we only know the optimal strategy for a 2 plaer nim..where player 1 will win when the game starts with a nim sum of non-zero and ends his turn with a nim sum of zero.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

A A game of seemingly mutually independent events
Replies
7
Views
2K
Help finding winning strategies in the following tile game?
Replies
2
Views
2K
How Can You Calculate Winning Probabilities in a Game with T's, D's, and I's?
Replies
3
Views
3K
Optimizing Your Chances in a Game of Paper, Scissor, Rock: A Strategic Approach
Replies
3
Views
2K
What Are the Optimal Strategies for Player 1 in Kuhn Poker?
Replies
1
Views
4K
What is the perfect strategy for each player in this 2 by 4 array game?
Replies
1
Views
706
Help understanding proof that a winning strategy exists for Chomp
Replies
2
Views
4K
Game Theory: Nim - Winning Strategy for 5 & 1000 Stones
Replies
16
Views
4K
Chances of player A winning a chess tournament?
Replies
12
Views
3K
Winning Strategy for Player 1 in the 10x20 Lattice Game
Replies
9
Views
3K

Hot Threads

Recent Insights

Back
Top