Numbridge — Strategy

Notation

You have read the rules: the field, the bag, the hand, the three kinds of turn. What follows is about something else — about what a choice of move is made of. But first let us agree on how to name cells, or any talk about particular places turns into waving hands about.

Counting cells

Rows are counted from the top down, starting at one. Columns run left to right, also from one. A cell is named by its row and column: r3c5 is the fifth cell of the third row. The record of a game labels its cells the same way, so the notation in this booklet and the notation in the archive are one and the same.

row 1  r1c1 r1c2 r1c3 r1c4
row 2    r2c1 r2c2 r2c3 r2c4
row 3      r3c1 r3c2 r3c3 r3c4
row 4        r4c1 r4c2 r4c3 r4c4

Every next row is shifted half a cell to the right — that is how they lie on the board. That is why a column slants: r1c2, r2c2, r3c2, r4c2 stand one below another, but each one slightly further right. Keep that in mind when you read a column off the screen: to the eye it drifts sideways.

How to read the record of a game

A live table shows no list of moves: the board gives you your hand, the number of your opponent's tiles, the bag, the mistake counter — and a brief red mark on a cell when somebody has just missed. The written record appears afterwards, in the archive, and that is where a game is studied.

A move is written as a number, a cell and a sign. There are no words in the record, only glyphs, and here they all are:

14. r3c5 ← 7       a seven placed, the cell taken
15. r6c2 ← 4 ✗     a miss: the four did not fit, the turn burned
16. r1c7 ⊕ 3       a given claimed, a three discarded in payment
17. r1c7 ⊕ 3+5     a claim at a price of two tiles: a three and a five paid
18. r1c7 ⊕         a claim with an empty hand — free
19. r2c4 ⟳         the first stone taken (the pie rule)
20. ⇄              the whole hand exchanged
21. —              the turn passed: time out, or nothing to play

Since there is no list of moves during play, you have to remember for yourself: in which cell your opponent missed and with which digit, whether they exchanged their hand. The red mark is short-lived, but knowing "this cell is not a seven" stays useful to the end of the game. In the archive, clicking a line shows the position at that moment — a good place to check yourself afterwards.

Neighbours

A cell has six neighbours, and in this notation they look like this:

row 2      r2c2 r2c3
row 3    r3c1 r3c2 r3c3
row 4      r4c1 r4c2

The neighbours of r3c2 are r3c1 and r3c3 in the same row, r2c2 and r2c3 above, r4c1 and r4c2 below. Remember the shift: above you get the same and the next column number, below the previous and the same. Nearly all the geometry of Bridges and connection grows out of that.

Words used further on

• Chain — your cells running one after another through neighbourhood.
• Path — the shortest road from one of your sides to the other across empty and own cells. Its length is how many cells you still have to take.
• Cut — a cell that, once taken, breaks the opponent's shortest path.
• Bridge link — a pair of your cells that do not touch each other but share two empty neighbours. A single move cannot break that link.
• Contested block (Domains) — a block where neither player holds five cells yet.

Sides are named by colour, as on the board: blue connects top and bottom, red connects the left side and the right.