Nim Game Strategies
Nim is a combinatorial game that has different ways to play it. In the following paragraphs you will learn about the strategies we figured out for one, two and three pile nim. Nim is a game that is played with any number of objects which can be coins, stones, sticks, or anything on hand. The players take turns at taking away a number of game pieces and the person to take away the last piece wins.
The first variation of Nim we would like to talk about is one pile nim. In one pile nim you can only take one or two pieces at a time. This type of game in game theory is called a partial game. In partial games it matters if a player goes first or second. If both players play perfectly in Nim, the first player will always win. In one pile Nim the strategy to win is to divide the number of pieces by 3. After dividing the pieces into groups of three you should have the last group with only one or two pieces. You should take the one or two pieces that are in the group. For this explanation we will start with a pile of thirteen objects, and each player can remove only one or two objects per turn. Since each player can take only one or two objects, the first player wants to keep the pile in a multiple of three. In a pile of thirteen pieces the first player would choose to take one away, making a pile of twelve. If the second player took one on his turn, the first player would take two, to keep the number of pieces in the pile a multiple of three. Or, if the second player were to take two the first would take one. By continuing this pattern it will decrease from twelve to nine to three. When the pieces get down to three you can tell that the winner is player one, because if player two takes one piece player one can take the remaining two pieces and win. If player two were to take two pieces, then player one can take the last one and win.
3 Pile Strategies
Cause of uneven number