Five In A Row

    Calculi means "stones" (or "pebbles" or "counters") in Latin. Stones were used for counting before the abacus was introduced, hence the word 'calculate'. The Latin term ludus calculorum means "the game of stones", but the references are general and unclear. To be sure, there is no evidence that there was a specific game called Ludus Calculorum. The term Ludus Calculorum seems to have been applied to board games in general, including Latrunculi.

    Murray, in The History of Board Games other than Chess, says, "The Romans used ludus calculorum for any board-game played with calculi, "pebbles' or 'counters', and specifically ludus latrunculorum or latrunculi for their war-game played with latrunculi, 'soldiers'." Seeing that Ludus Calculorum was the general term for board games, it is difficult to escape the implication that there were Roman board games other than latrunculi that were played with calculi or stones. It is entirely possible that the familiar game of 'Five in a Row' was played on the same boards as Latrunculi. In fact, there is some suggestion that the Ancient Greeks played this game (see below), which, if true, surely means that the Romans played it also. This game is so simple, being basically an extension of Terni Lapilli, that children could spontaneously invent it even today, and it was played in China along with Wei Chi (Go) and possibly as early as 2000-3000 BCE. If the Romans played a version of Five-in-a-Row on Latrunculi boards it would have been referred to by the general name Ludus Calculorum. The absence of evidence, as they say, is not evidence of absence, and therefore the name Ludus Calculorum name has been adopted here to describe the ancient and delightful game of Five-in-a-Row.

    The Japanese call this game Go-moku (five stones). Curiously, there is also a Roman game called "Five Stones" or pentelitha where pente=five and litha=stones, but Pentelitha has been referred to by many as a game played with tali (astragali or knucklebones) as discussed on the Tali webpage. Presumably the "stones" refer to the astragali, although this seems odd -- perhaps "pentetali" would have been the more natural name. The actual evidence for the name pentelitha is not known and if anyone has a clue which ancient reference forms the basis it would be worth re-examining for the possibility that it might be a misnomer and perhaps actually refers to the game of Five-in-a-Row.

    The board below shows the three types of winning arrangements as they might appear on an 8x8 Petteia board. Obviously the cramped conditions would result in a draw most of the time, depending on the rules. Play would be easier on a larger Latrunculi board of 12x8 or even 10x11.

    Many versions of Five-in-a-Row exist around the world, including the Chinese Wuziqi (which also means "five stones") or Wutzu, the Korean Omok, Japanese Kakugo (from 100 AD), Japanese Renju (a rather sophisticated version with extended rules), Rendzu, Nanju, Goseki, G-bang, Russian XO, Czech and Slovak Piskvorsky, Swedish Luffarschack (or Luffarshack), Ristinolla, and Caro, among others. Pente is a modern version, as is Connect5 but all the latter Renju-type games have additional rules and variations, some including capture moves. Alexander Nosovsky and Andrek Sokolosky, authors of "Renju for Beginners" states that archeological evidence exists that "...this game was independently created in Antic (Ancient) Greece and pre-Columbian America." See From the History and Geography of Renju. If indeed it existed in Greece then almost surely it existed in Rome. It seems evident that the basic form of Five-in-a-Row was developed independently by people all over the world, and some suggest it is even played on other planets (see Rules and History of Renju).


     This game requires more stones than Latrunculi, but can be played on boards of any size -- the larger the better. Go-moku is played typically on Go boards that are 19x19. Some large bags of stones have been found, which include roundels (gambling chips) as well as glass latro (glass soldier-stones).

    The traditional rules of Five in a Row, are as follows:
    1. Black plays first.
    2. First person to line up five stones in a row orthogonally or diagonally wins.
    3. It is illegal to make a "double open-ended three" unless one is forced to do so.
    4. If the board becomes filled, the game is a draw.

    A double open-ended three, or three in a row simultaneously in two directions, is banned because it is too easy to win, and occurs frequently. This rule makes for a much more interesting game, and leads to the strategy in which one tries to make a double "three and a four," which is like a double open-ended three, except that one line is made of four in a row. The photo below shows the game played on a 12x8 Latrunculi board, which works much better than an 8x8 board. In this game black, whose move it is, is on the verge of winning.

    Women as well as men played board games, although the references are almost nil. Pliny, in his letters makes mention of Ummidia Quadratilla, the grandmother of one of his friends, who lived to be eighty and played lusu calculorum (where lusu = ludus = games), although exactly what 'games of stones' she played is not clear, and may be one or more of latrunculi, tabula, five-in-a-row, or other board games. Pliny writes:

      Audivi ipsam, cum mihi commendaret nepotis sui studia, solere se ut feminam in illo otio sexus laxare animum lusu calculorum, solere spectare pantomimos sous; sed, cum factura esset alterutrum, semper se nepoti suo praecepisse, abiret studeretque; quod mihi non amore eius magis facere quam reverentia videbatur.

    The above passage reads in translation as follows:

      I once heard her say, when she was commending her grandson's oratorical studies to my care, that it was her habit, being a woman and as such debarred from active life, to amuse herself with playing at lusu calculorum, and to look on the mimicry of her pantomimes; but that before engaging in either diversion, she constantly sent away her grandson to his studies; a custom, I imagine, which she observed as much out of a certain reverence, as affection, to the youth.

    Here is part of an epigram from Martial:

      A taverner, and a butcher and a bath, a barber, and a game board with stones, and a few books... warrant these to me, Rufus, even at Butunti, and keep to yourself Nero's warm baths."