Kingdomino Layout: Building a 5 by 5 That Scores

Most discards in Kingdomino are not bad luck. They come from a layout that boxed itself in three rounds earlier. A good kingdom is planned like a garden: big beds in the open, paths left clear, and no corner you cannot reach. This lesson covers the shape of the kingdom, from the castle to the last square.

The floating frame

The rule is that your kingdom must fit in a 5 by 5 square. It does not say where. At the start, your castle could end up anywhere in that square, and you narrow it down with every domino.

• After your first placement going east, you know the frame extends at least one square east of the castle.
• Once you are five wide, the left and right edges are fixed. Nothing more can go past either side.
• Once you are five tall, the top and bottom are fixed too, and every empty square inside the frame is a space you must fill.

Fixing an edge early is not bad. It is a decision. Make it on purpose, when it helps a territory, not by accident.

Where should the castle end up?

Two forces pull in opposite directions:

• Center castle. The Middle Kingdom variant pays 10 points for it. The castle is also wild, so in the center it touches up to four different territories and gives each of them a safe place to start.
• Edge or corner castle. Leaves a larger open area on one side for one big territory, which lesson 4 says is where the points are.

Without the Middle Kingdom bonus, many strong players let the castle drift toward an edge or corner and build their biggest territory across the open space. With the bonus in play, 10 points is a lot in a game where winning scores often sit in the 40s and 50s, so plan for the center from the first domino.

The one square no domino can fill

A domino covers two neighboring squares. So an empty space that is a single square surrounded on all sides can never be filled. Watch for it every time you place: a domino that leaves a 1 by 1 pocket inside your frame has cost you a square for the rest of the game.

A bigger version of the same trap: any closed-off empty area with an odd number of squares cannot be filled completely. A 3-square pocket can take one domino at most, and one square stays empty.

The checkerboard check

Here is a neat bit of math that decides whether a full 5 by 5 is even possible.

Color the 25 squares like a checkerboard, with the corners dark. That gives 13 dark squares and 12 light ones. Every domino covers one dark and one light square, because its two halves are side by side. Twelve dominoes cover 12 dark and 12 light. So the castle must sit on a dark square, or the kingdom cannot be completed.

The light squares, where the castle must not end up, are easy to name. There are twelve:

• On the edges: the two squares beside each corner, eight in all.
• In the middle: the four squares directly above, below, left, and right of the center.

Every other square, including the corners, the center, and the middle of each edge, is dark and fine. If your castle ends up on a light square, at least one space in your kingdom will stay empty no matter how well you place.

You do not need to do this every game. Do it once, at home, with the castle on each square of a 5 by 5 drawing, and you will feel it afterward.

Keep lanes open

A territory needs room to grow. Some layout habits that keep it:

• Grow your biggest territory toward open space, not toward the frame’s edge.
• Keep the castle’s sides useful. The castle accepts any terrain, so an open side next to it is a safety valve for an awkward domino.
• Build in strips late. Near the end, the empty squares should form rows or pairs that a domino can fill, not scattered single holes.
• Mind the second half of each domino. The square you are not matching still lands somewhere. Put it where it starts something useful, or where it will not block a territory.

Harmony: the full 5 by 5

The Harmony variant pays 5 points for a complete kingdom with no discards. Even when you are not playing it, a full kingdom matters: every empty square is a square that could have scored.

Plan for it like this:

1. Fix the frame by the midgame. Around the sixth of twelve rounds, know your edges.
2. Count the empty squares in pairs. If an empty area cannot split into pairs of neighbors, fix that while you still have choices.
3. In the last two rounds, take fit over value. A domino that completes the frame is worth its squares plus the 5-point bonus. A richer domino that has to be discarded is worth nothing.

The middle of the game

By round six or seven, a strong kingdom usually has one large territory with crowns, one or two mid-size ones, and a clear plan for every empty square. If yours has five small territories and three holes, that is the thing to fix. The next lesson looks outward, at the other kingdoms at the table.