Two children sit across from one another.

Between them are four small piles of stones.

One child reaches forward and removes two stones from a pile of five.

The other pauses.

Their eyes move slowly from pile to pile.

They are not simply choosing stones.

They are thinking.

This is Nim, a classic mathematical strategy game, likely connected to the ancient Chinese game jiǎn-shízi (捡石子), meaning “picking up stones.” Despite its simple rules, Nim has challenged players for centuries because success depends not on luck, but on careful observation, logical reasoning and strategic thinking.

For this version of the game, arrange 16 identical objects into four piles: 1, 3, 5 and 7. The objects themselves don’t matter—they could be stones, pencils, counters, bottle caps, paper clips, hair clips or anything else you have available.

Two players take turns. On each turn, a player must remove one or more objects from a single pile only. Players continue alternating turns until all the objects have been removed. Before starting, agree which version you will play. In the version we use most often, the player who is forced to take the last remaining object loses, encouraging players to think several moves ahead rather than focusing only on the next turn.

Before you read any further, why not try it yourself?

Find 16 identical objects, arrange them into the four piles, invite someone to play a few rounds with you and simply notice what happens.

At first, your moves may feel completely random.

Then, almost without realising it, you’ll probably begin asking yourself questions like:

“What pattern am I starting to notice?”

“If I make this move, what choices will my opponent have?”

“Can I predict what might happen two or three turns from now?”

The game hasn’t changed.

Your thinking has.

That is exactly why Nim is such a powerful game for developing critical thinking.

Unlike games that rely mainly on speed or chance, Nim rewards careful observation and thoughtful decision-making. Every move changes the possibilities that follow. Children quickly discover that making good decisions isn’t about guessing—it’s about looking for patterns, testing ideas and learning from the results.

One way to deepen this learning is by introducing a simple Pattern Lab Cycle alongside the game. Encourage children to become young investigators.

They begin by observing the game and noticing patterns.

Next, they form a hypothesis, predicting what might happen if they make a particular move.

They then test that idea during the next round.

Afterwards, they record the outcome, asking themselves whether their prediction was supported or challenged.

Finally, they revise their thinking before trying again.

Rather than seeing mistakes as failures, children begin to see them as valuable information that helps them improve their next strategy.

Another simple addition is to encourage Move Explanation. Before or after each turn, invite players to briefly explain their thinking.

“I removed two stones from this pile because…”

Making reasoning visible helps children become more aware of their own thinking while also allowing classmates to learn from different strategies.

After several rounds, pairs or small groups can take part in a quick Theory Swap. Invite them to share one pattern they noticed, one strategy they tested, what happened and what they would try differently next time. These conversations often become just as valuable as the game itself because they encourage children to reflect, justify their ideas and appreciate different ways of thinking.

Perhaps that is the greatest strength of Nim.

The learning is not hidden in the stones.

It is hidden in the thinking the stones invite.

And perhaps that’s one of the greatest gifts games can offer our classrooms. Behind what looks like simple play, children are developing habits of mind that will serve them far beyond the game itself—observing carefully, thinking critically, learning from evidence and having the confidence to change their thinking when new information appears.