Sumitohexagonal pushing game

Goal of the game

Push six opposing marbles off the board. The first player to do it wins.

You never capture: you push. A marble only leaves the board when it is pushed beyond the edge.

The board and the marbles

• A hexagonal board of radius 4, that is 61 cells, with six directions of movement.
• Fourteen marbles per player, set up facing each other at the start.
• No cell is special: only the edge matters, since that is where marbles go out.

The two ways to move

• In-line move — one, two or three marbles in a line move one cell forward along the axis of their line. It is the only move that can push.
• Broadside move — two or three marbles in a line shift sideways, each onto a free neighbouring cell. Quick for regrouping, but it pushes nothing.
• You never move more than three marbles at once, and they must be adjacent and in a line.

Pushing

• Pushing requires strict numerical superiority along the axis: two against one, three against one, or three against two.
• Two against two, or three against three: impossible. The move is refused.
• The cell right behind the pushed marbles must be free, or off the board.
• If it is off the board, the opposing marble goes out — one point for you.
• One of your own marbles behind the ones you push blocks the manoeuvre: you cannot push your own marbles.

The centre strategy

• Stay in the centre. A marble on the edge can no longer back away: it is one push from going out. The centre is the only safe place.
• Stay grouped. A compact mass of marbles cannot be pushed — it takes superiority along the axis, and a dense group denies it everywhere.
• Isolate, then push. The game is about separating one or two opposing marbles from the rest, then driving them to the edge with three.
• The broadside move is your best defence. It rebuilds a wall in a single action, whereas in-line moves stretch you out.
• Do not chase an early knock-out: a player who attacks early gets stretched, and a stretched group gets pushed in turn.

The mistakes that cost the most

• Sending lone marbles forward. An isolated marble is a gift: it can push nothing and gets pushed by two.
• Lining your own marbles along the edge. Every marble against the edge is a point given away.
• Attacking in too long a column. Three marbles in a line push well, but they only cover one axis: an opposing broadside move goes around them.
• Forgetting to count knock-outs. With five marbles lost, every change of position must be weighed as a risk of defeat.

Controls

Keyboard and mouse

• Click to select one to three marbles in a line, then click a direction.
• Illegal moves are refused: the superiority rule is applied for you.
• The count of marbles knocked out is shown on each side.

Touch screen

• Tap your marbles to select them, then swipe in the direction you want.
• The possible directions appear around the selection.
• With two players, pass the device after each move.

Frequently asked questions

How many marbles do you need to push out to win?

Six. Each player starts with fourteen marbles; the game ends as soon as one has pushed six off the board.

Can you push with equal numbers?

No. You must be strictly more numerous along the axis: two against one, three against one or three against two. Two against two is blocked.

How many marbles can you move at once?

Three at most, and they must be adjacent and in a line.

What is the difference between an in-line and a broadside move?

In line, the marbles move along their own axis and can push. Broadside, they shift sideways: more flexible, but no push is possible.

Why should you stay in the centre?

Because a marble on the edge has no space left behind it: a single successful push sends it out. The centre gives depth in every direction.

More classics, free as well

• Yams — five dice, thirteen combinations, three rolls
• Air hockey — same screen, two paddles, a real physics puck
• Backgammon — twenty-four points, two dice, the oldest race in the world