How to win at mancala: the opening, free turns and captures

Mancala looks like a game of luck. You scoop up a handful of stones, drop them one by one around the board, and see where they land. It feels like rolling dice with extra steps.

It isn't. Mancala has no hidden information and no randomness at all. Every outcome is decided by counting, and the counting is simple enough that a few rules of thumb put you ahead of almost anyone who plays by feel. To find out which rules actually matter, we played thousands of games between bots of different strength, using the same rules engine as the mancala game in Duelo.

The rules, in one paragraph

We use the most common modern rules: six pits per side, four stones in each, and a store at each end, 48 stones in total. On your turn you pick up every stone in one of your pits and sow them one at a time anticlockwise, skipping your opponent's store. If your last stone lands in your own store, you move again. If it lands in an empty pit on your side and the pit opposite has stones, you capture both into your store. When either side runs out of stones, each player banks whatever is left on their own side, and the bigger store wins.

Throughout this article, pits are numbered 1 to 6 from your left, so pit 6 is the one next to your store.

How we tested it

We used three bots. One plays random legal moves. A greedy one takes whichever move gains the most right now, including any free turns it can chain. A strong one searches eight moves ahead with standard game-tree search. We ran 400 games for each pairing of the first two, 200 games for each pairing with the strong bot, and 100 strong-against-strong games for each of the six possible openings.

Lesson 1: counting beats instinct, almost every time

The greedy bot does nothing clever. It never thinks about your reply. It just counts what each move gives it right now. Against random play, it won 99.3% of games moving first and 97.8% moving second, by an average of 25 stones.

That is the most useful number in this article. Most of the skill in mancala is simply noticing the free turns and captures that are on the board this turn. Players who sow by feel are giving all of that away.

Lesson 2: the opening that wins, and the one that loses

At the start, every pit holds four stones. A pit gives you a free turn when its stone count equals its distance to your store. Pit 3 is four steps from the store and holds four stones, so it is the only opening move that lands exactly in your store.

Here is how each opening did when the strong bot played itself:

Start with pit 3, take the free turn, and keep going. After pit 3, pit 6 holds five stones; sowing it puts one in your store and hands only four to the other side, and the search found that sequence strong. The other four openings all end your turn immediately and give your opponent stones and choices. Pit 5 is the worst of them in our tests: the strong bot never found a way back from it.

A caveat: an eight-move search is very good, but it isn't perfect play. Treat the table as "what strong players should do", not as a proof.

Lesson 3: chase free turns before stones

The rule for a free turn is worth memorising: pit 6 needs 1 stone, pit 5 needs 2, pit 4 needs 3, and so on up to pit 1, which needs 6. Before every move, scan your six pits for an exact match. If you have more than one, play the one nearest your store first. Taking it rarely disturbs the others, while playing a farther pit first drops a stone into the nearer one and breaks its count.

Strong players live on this. In the strong-against-strong games, there were 16 free turns per game on average. A free turn is a whole extra move, and in a game of about 40 moves, that adds up fast.

Lesson 4: the capture is a loaded gun, on both sides

The capture rule decides close games. In our strong games there were about six captures per game, moving 15 stones in total. That's nearly a third of the board changing hands by one rule.

• Attack: an empty pit on your side, opposite a full pit on theirs, is a threat. Look for a move whose last stone lands in it.
• Defend: look at your opponent's empty pits and ask what sits opposite them. A pile of eight stones facing an empty pit is an invitation. Either move that pile or make sure nothing of theirs can land in that empty pit.
• Don't feed the gun: a big sow that wraps around the board drops stones into your opponent's empty pits, which can quietly disarm your own captures and arm theirs.

Lesson 5: in the endgame, stones on your side are yours

When one side runs dry, the other player banks everything still on their side. So late in the game, stones on your side are not idle. They are points you collect if your opponent runs out first. If you are ahead, it can pay to keep stones at home and let the other side empty. If you are behind, you want to keep the game going and keep sowing onto their side. The strong bot gives a small bonus to stones on its own side for exactly this reason.

Lesson 6: going first is worth more the better you are

With two random players, moving first did nothing: 46% against 47%, with the rest drawn. With two greedy players, the first mover won 73%. With two strong players, the first mover won 96% and never lost. A first move is a tempo, and a tempo is only valuable if you know how to use it.

So if you're the weaker player, ask to go first, and then open with pit 3. We looked at the same question across other games, with real results, in does going first give you an advantage.

The whole thing on one card

1. Open with pit 3 for the free turn, then consider pit 6.
2. Every turn, look for a pit whose stone count equals its distance to your store. Play the nearest one first.
3. Look for an empty pit of yours facing a full pit of theirs.
4. Check theirs before you move: what do their empty pits face?
5. Late on, count the stones on each side, not just the stores.

That's it. The game still has plenty of depth past these five points, but they are what separate a player who counts from one who scoops and hopes. In our tests, that gap was worth 25 stones a game.