Strands & the China Labyrinth - a natural merger
Strands is an abstract strategy game that was invented by Nick Bentley in 2022. Below you see a hexhex board of 91 cells that, for the purpose of playing the game, has been overlaid with a distribution of numbers, whereby lower ones are situated in or around the centre while higher ones are towards or on the edge.

The number 4 is missing in this particular layout, but that's not a requirement, it just testifies to the concept's arbitrariness. Many different number layouts are possible.

A tradeoff
Nick made an earlier placement game named Catchup, the goal of which is to have the largest group in the final position. A group is a maximal set of connected stones. If the players' largest groups are equal in size, they're left out of contention and the next largest groups are compared, and so on, cascading down to an inevitable decision because the board has an odd number of cells.

In this context he envisioned a placement protocol that at its heart has a dilemma between placing a few strong stones and placing more but weaker stones. Here's the placement protocol:

  • To start, Black covers any space marked “2”.
  • From then on, starting with White, the players take turns. On your turn, cover up to X empty spaces marked “X”. For example, you could cover any 3 empty spaces marked “3”.

The game ends when the board is full and the player with largest group, cascading down in case of equality, wins. Characteristically for connection games, placing pieces near the centre of the board is stronger but placing near the edges allows you to place more pieces. The key is navigating this tradeoff.

My take on Strands
Nick Bentley is a major protagonist of simple rule sets, absolute decisiveness, and maximised accessibility and marketability. In that sense, Strands only falls short on over the board play because of the variable distribution of numbers. Note also that you can leave out certain numbers, like the 4 in the above example, but not the number 2, or the game can't start.

The arbitrariness of the layout doesn't have to bother anyone in actual play, but it bothers me in a conceptual sense. Whatever the layout, you have to adapt the distribution to low numbers in and around the center and high numbers along the edge. Of course the players face the same conditions, but the balance of the game would in my opinion be severely affected by a totally random distribution, even more so in the absence of a pie rule. For balance, you have to distribute the numbers in a suitable manner, but what exactly is 'suitable'?

I disagree with the inventor on calling Strands a game of deep strategy. In fact, its strategy is already flashing in neon lights: managing the trade-off between fewer but stronger placements and more but weaker ones. Its tactics may be considered 'deep' under the caveat that there's only placement, so tactics tend to be of the kind of accumulating positional advantages acquired by connecting, cutting and blocking. All worthy of deep consideration, but not exactly rocket science.

A natural habitat for the Strands placement protocol
It was sometime after Strands' publication that I realised the link between the placement protocol and transcendental solutions of the China Labyrinth, an intriguing tile puzzle worthy of consideration for its own sake.


More specifically, I realised that the 63 cells of the big group of any two-groups transcendental solution would make a natural habitat for the Strands placement protocol. In transcendental solutions a beam always borders on an adjacent cell, or neighbour, while a blank edge never borders on anything. Beams, neighbours and adjacencies can thus be used interchangeably and the beams necessary to find a solution can be removed in the finished result without any loss of information, as the above diagrams show.

Long ago Ed van Zon made a program that generates transcendental solutions for I Ching Connexion, so adapting it for the envisioned game merely meant it should generate two-groups solutions, ignoring the single blank and displaying only the 63-cells group as the board. Some properties of the China Labyrinth as a playing area are:

  • The six edges of a cell, starting with the top-left edge and going clockwise, are assigned values 2^5 to 2^0 (that is: 32, 16, 8, 4, 2 and 1). A beam (1) means the corresponding value counts, a blank edge (0) means it does not. The number of a cell is the sum of its beam-values. Thus is assigned the digital number 101011, which is the numerical value 43. If a stone is placed on it, then the notation gives only a cell's numerical value, not its position because its place within the board varies.
  • A natural division of cells in the Strands manner, with fewer neighbours scattered along the periphery and more densely packed ones in central areas in every possible board. Here are a few examples.

The applet generates new boards with different shapes ad infinitum, always with the same 63 cells and the same structure. Note that these boards will always have two holes in them. In the China Labyrinth the number of holes always equals the number of groups.