Why every system groups
Psychologists use the word subitizing for the ability to see a small quantity without counting it. The term dates to a 1949 study by Kaufman and colleagues, and the reliable range tops out around four. A row of nine loose strokes forces a recount; two closed groups and four strays do not. Every serious tally system is a workaround for that limit.
The four contenders
Five-bar gate
Four vertical strokes, a fifth drawn across them. Standard in the UK, Ireland, the United States, Australia and much of Europe. Strength: the diagonal is visually loud, so groups read instantly. Weakness: a sloppy diagonal can cover only three strokes and nobody notices.
正 (zhèng)
The Chinese character meaning "correct" or "upright" has exactly five strokes, written in a fixed order. Used in mainland China, Taiwan, Japan (where it is read sei) and Korea. Strength: the stroke order is taught in school, so a half-finished character tells you exactly where the count stands. Weakness: unfamiliar to readers outside East Asia, and harder to write fast with chalk on a rough board.
Square and diagonal
Four sides of a box, then a diagonal for five. Common in France, Spain, Portugal and across Latin America. Strength: a closed shape is hard to misread. Weakness: the corners tempt writers to start the next group inside the old one when space runs short.
Dot-and-line
Four dots at the corners count one to four; four connecting lines take it to eight; two diagonals make ten. Associated with forestry timber tallies and North American field work. Strength: ten per cell, which halves the paper needed. Weakness: a learning curve, and a missed dot is invisible until reconciliation.
Scoreboard
Scores are the desk's editorial ratings out of 5, based on the trade-offs above. They are judgements, not results of a controlled trial.
| System | Main regions | Per cell | Readability | Density | Error resistance | Total |
|---|---|---|---|---|---|---|
| Five-bar gate | UK, US, Australia, Europe | 5 | 5 | 3 | 3 | 11 |
| 正 | China, Taiwan, Japan, Korea | 5 | 4 | 3 | 5 | 12 |
| Square and diagonal | France, Spain, Latin America | 5 | 4 | 3 | 4 | 11 |
| Dot-and-line | Forestry, field surveys | 10 | 3 | 5 | 3 | 11 |
| Plain strokes | Universal | 1 | 1 | 2 | 1 | 4 |
Pick by job
- Counting in front of witnesses: 正 or the five-bar gate. Both are easy for an audience to verify group by group.
- High counts on a small sheet: dot-and-line. Ten per cell beats five per cell.
- Mixed-language teams: the five-bar gate. It is the most widely recognised outside East Asia.
- Error-sensitive audits: any closed shape, plus a running subtotal written beside every fourth group.
One rule across all systems
Write a numeric subtotal at the end of every row. Every system above fails the same way — a stroke missed or doubled — and a subtotal limits the damage to one row. Counters in the field apply exactly that rule, as the next ledger shows.