Nim

This is a classical 2 players game called Nim. There are N rows with Ni sticks in each row. By turns, each player takes as much sticks as they want from a single row. The player that takes the last stick wins.

This is a 0 sum game with perfect information.

Goal

The goal of this game is to take the last stick.

Score

The player that takes the last stick: - 1
The player that cannot take a stick: - -1

Import

from IArena.games.Nim import NimPosition
from IArena.games.Nim import NimMovement
from IArena.games.Nim import NimRules

Movement

A movement is represented by 2 int representing the number of the row and the number of sticks:

line_index - int - 0 <= line_index < N - Index of the line to remove sticks
remove - int - 0 < remove < Ni - Number of sticks to remove from the line (must be less than the number of sticks in the line)

movement = NimMovement(
  line_index=2,
  remove=1)
# Remove 1 stick from the 3rd line

Position

A position is represented by a list of int describing each row:

# position : NimPosition
len(position)      # Number of rows
position[0]        # Number of sticks in the first row

lines = position.get_lines()  # Get the list of int
len(lines)         # Number of rows
lines[0]           # Number of sticks in the first row

Note

This class has every other method from IPosition, for example next_player.

Rules

The NimRules inherits from IGameRules and implements the rules of the game.

Constructor

Can receive 1 argument:

original_lines - List[int] - The amount of sticks in the first position - Default: [1,3,5,7]

# Start default game [1,3,5,7]
rules = NimRules()

# Start game with 3 rows of 5 sticks
rules = NimRules(
  original_lines=[5,5,5])

Score

The score is calculated by the NimRules class. The player that takes the last stick wins, so the score is 1 for the winner and -1 for the loser.