This simple game is a famous math puzzle! It belongs to a family of "Impartial Games," where the available moves depend only on the state of the game, not on which player is moving. Because of this, the game can be "solved," and there's a secret to finding the perfect move every time.
The secret is to stop seeing rows and start seeing groups of pins. The goal of a winning strategy is to always make a move that leaves the board in a state where the remaining groups can be perfectly paired up. A board like this is called a balanced position.
Let's look at an example from the middle of a game. Notice how we've identified four groups of pins:
| Game Board View | Mental View (The Groups) |
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A group of 3 A group of 5 A group of 3 A group of 3 |
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Can we make identical pairs from these four groups? We can pair up two of the 3s, but we're left with another 3 and a 5. They don't match! This is an unbalanced board, which means there is a winning move to be made.
The perfect move is to remove 2 pins from the middle of the 5-pin group. This turns that group of 5 into a group of 3. Here is the result:
The new groups are:
Now we have four groups of 3! We can make two perfect pairs. The board is now balanced. Any move your opponent makes will have to break one of these pairs, and you will always be able to find a move to balance the board again, leading you to victory.
This "pairing" method is a fun way to understand the real math behind the game, called the Nim-sum, which uses binary numbers. To learn more, we recommend the official Wikipedia page.