## What type of game is Nim?

Nim is a mathematical game of strategy in which two players take turns removing (or “nimming”) objects from distinct heaps or piles. On each turn, a player must remove at least one object, and may remove any number of objects provided they all come from the same heap or pile.

### What is Nim sum in game of Nim?

Nim-Sum : The cumulative XOR value of the number of coins/stones in each piles/heaps at any point of the game is called Nim-Sum at that point. “If both A and B play optimally (i.e- they don’t make any mistakes), then the player starting first is guaranteed to win if the Nim-Sum at the beginning of the game is non-zero.

How do you win a NIM game in Python?

In Python, XOR is denoted by ^ operator. In normal play, the winning strategy is to finish every move with a nim-sum of 0. This is always possible if the nim-sum is not zero before the move. If the nim-sum is zero, then the next player will lose if the other player does not make a mistake.

How do you beat Nim in Python?

To win at Nim-game, always make a move, whenever possible, that leaves a configuration with a ZERO “Nim sum”, that is with ZERO unpaired multiple(s) of 4, 2 or 1. Otherwise, your opponent has the advantage, and you have to depend on his/her committing an error in order to win.

## Does it matter who goes first in Nim?

If the Nim sum of coins in the heaps at the start of the game is equal to 0, then player B has a winning strategy. Whatever player A does on the first move will result in a non-zero Nim sum when it’s B’s turn.

### How do you always win Fibonacci Nim?

In a winning position, it is always a winning move to remove all the coins (if this is allowed) or otherwise to remove a number of coins equal to the smallest Fibonacci number in the Zeckendorf representation.

How do you win Nim everytime?

How do you always win at Nim?

## Is there a winning strategy for Nim?

This shows that if the Nim sum of coins in the heaps at the start of the game is not 0, then player A has a winning strategy. The strategy is to always make a move that reduces the next Nim sum to 0.

### Is it impossible to win the game Fibonacci Nim?

The Fibonacci numbers feature heavily in its analysis; in particular, the first player can win if and only if the starting number of coins is not a Fibonacci number. A complete strategy is known for best play in games with a single pile of counters, but not for variants of the game with multiple piles.

Can you win Nim If you go second?

Editor’s notice: The second player can always win, that makes Nim a distinctly ‘impartial game’. The traditional Nim-game (aka Marienbad-game) consists of four rows of 1, 3, 5 and 7 matchsticks (or any other objects). Two players take any number of matchsticks from one row alternately.

How to play Nim-game with array?

A Player can choose any of element from array and remove it. If the bitwise XOR of all remaining elements equals 0 after removal of selected element, then that player loses. This problem is variation of nim-game. Note: Each player play game alternately. Find out winner if both of the players play optimally. Alice starts the game first.

## How to solve variation of Nim-game?

You are given an array A [] of n-elements. There are two players Alice and Bob. A Player can choose any of element from array and remove it. If the bitwise XOR of all remaining elements equals 0 after removal of selected element, then that player loses. This problem is variation of nim-game. Note: Each player play game alternately.

### What is Dr Nim Stack Exchange?

beginner – Dr. Nim game in Java – Code Review Stack Exchange This video should explain how the game works, but in simple form, it’s a game where you enter a number between 1 and 3, This number is than removed from 12, in doing so the computer will then pick a Stack Exchange Network

What algorithm does the AI use to lose so fast?

The game is played “Misere” (last one that has to pick a stick loses). The AI is supposed to be using the Minimax algorithm, but it’s making moves that make it lose faster and I can’t figure out why.