How do you always win Misere Nim?

Winning positions The practical strategy to win at the game of Nim is for a player to get the other into one of the following positions, and every successive turn afterwards they should be able to make one of the smaller positions. Only the last move changes between misere and normal play. * Only valid for normal play.

How do you beat Nim 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 to come up with an algorithm for misere Nim?

Thought I might share some observations that helped me come up with an algorithm. If anyone sees a mistake in my reasoning, or has an easier way to think through this problem, I’d be happy to hear about it. If player 1 starts with an xor value of zero, player 1 loses unless the piles are: [1,1], [1,1,1,1], etc.

When does player 1 lose in misere Nim?

If player 1 starts with an xor value of zero, player 1 loses unless the piles are: [1,1], [1,1,1,1], etc. If player 1 starts with an xor value other than zero, player 1 wins unless the piles are: [1], [1,1,1], etc. 1) The last losing position of every game will have exactly one stone and one active pile.

What is the goal of the game of Nim?

Nim is a mathematical game of strategy in which two players take turns removing objects from distinct heaps. 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. The goal of the game is to be the player who removes the last object.

How many objects can you remove in Nim?

Instead of removing arbitrarily many objects, a player can only remove 1 or 2 or or k at a time. This game is commonly played in practice with only one heap (for instance with k = 3 in the game Thai 21 on Survivor: Thailand, where it appeared as an Immunity Challenge) .