Nim Strategy Game - How to Win Every Time!

An old pub trick that I like to show off from time to time is the mastery of a version of the ancient game known as Nim. The game has been played for centuries and is thought to have originated in China. There are many variations, but the general principle is that two players take turns removing objects (often stones or sticks) from one or many rows/heaps. You can remove as many stones as you want from any given group, and the player who removes the final stone is the loser in default game play (known as 'misère'). In other versions of the game known as 'normal play', the player who removes the final stone is the winner.

One of the very first computer games was built by Westinghouse and was capable of playing Nim. It was called Nimatron and debuted at the 1940 World's Fair in New York. It may seem to be part guessing and part strategy, but in reality it is possible to calculate your way to victory. There is even a binary mathematical proof for how to determine the best move at any given point in the game. It is possible to always win some versions of the game if you go first and make all the right moves. The real challenge is letting your opponent go first, yet somehow still winning. I'll teach you how!

I prefer a version of Nim that involves three rows and 15 stones – we'll call it 7-5-3, correlating to the initial number of stones in each row. With this version, it is possible to consistently win by learning a few simple strategies. Using some basic pattern recognition, you too can master this game effortlessly and beat anyone who is unfamiliar with the logic.

To become a 7-5-3 expert without calculating the best move in binary code, you only need to memorize a few “winning configurations”. Once you know these arrangements and recognize how to remove the right number of stones to get there, you can only lose if you make a mistake.

Carefully at Three

Keep all three rows active until you have a winning configuration

Only remove a single stone for first couple moves. There are several winning configurations that are desirable with stones in all three rows that will be discussed below. The sooner that you move the game into a winning configuration, the sooner you can start smiling at the expense of your opponent! Once the game is configured to win with three rows, use the remaining rules.

Dueling Duals

With two rows in play, make both rows have the same number of stones

The easiest winning configurations occur whenever the game is reduced to just two rows, either by you or your opponent. When two rows have the same number of stones, this is a winning configuration. No matter how many stones your opponent removes, you can do the same and maintain the winning configuration until only one stone remains.

Lonely One

Only reduce the game to one row when that row has just one stone in it.

Since the object of default game play is to make your opponent remove the last stone, you are destined to lose if you reduce the game to one row but leave more than one stone. All you or your opponent needs to do is remove every remaining stone except one.

Three-row Winning Configurations

This is a complete list of winning configurations. If you are able to put the game into one of these states and maintain the winning configuration with each move, you are guaranteed victory!

Remove one stone at first

Maintain winning by using these

• The starting configuration is a winner if played perfectly
• Removing one from any row is a winning first move!
• Removing one from each row is a winning configuration

Two-row Winning Configurations

A 2-row winning configuration is just as good as a 3-row and generally must be used to win the game. Sometimes your opponent might unknowingly provide an opportunity for you to steal a 2-row Dueling Duals configuration, so watch closely!



Remember, you can remove as many as you want from a row in a turn. For example, if the game state is 7-3-3, just remove all 7 from the row to make it 0-3-3!

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Configurations to Avoid

Avoid leaving the game in a state that can easily be turned into a winning configuration by your opponent. A few common states to avoid are :

• 4-3-2
• 5-4-2
• 1-2-1
• 2-2-1
• 6-4-1
• 4-2-1

Additional Strategic Tips

It is sometimes easier to reach a winning configuration by letting your opponent go first, assuming they are unaware of the logic. If you win so many times that your opponent thinks the game is rigged, reluctantly agree to go first. Now it is impossible for you to lose! However, you must follow the exact path of right moves until you have a winning configuration.

Regardless of who goes first, in the beginning you should only remove one stone. If your opponent goes first, do this until your opponent makes a mistake. This technique leaves you more opportunities to find a winning configuration. As soon as you see the opportunity to move into one of the above winning configurations, take it!

If your opponent goes first and manages to guess the first few winning configurations, do not panic! If they are not familiar with the game, doing something sudden and unexpected like removing all of the stones from one row in one smooth sweep can surprise and confuse your opponent into making a mistake. The more rapidly that you take your turn, the more pressure it puts on your opponent to react quickly. Rushed thinking tends to make people more likely to make foolish mistakes! It can also help to smile and laugh as if you know that you have already won, even if this is not yet true! Intimidation is a powerful distraction!

Take the last stone and you lose the throne!

With practice, you too can become a NIM CHAMP! Source

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