Think of this game as a predecessor of Connect Four 🙂
~As taught by La Signora Onorata Giata Alberti at the Academy of Performing Arts, Gleann Abhann~
Calculi, or “Five in a Row” is a Roman game played on the same board as Latrunculi. Each player has 33 pieces, in opposite colors.
The traditional rules of Calculi, or “Five in a Row,” are as follows:
1. Black plays first.
2. First person to line up five stones in a row orthogonally (straight across or straight up and down) 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.
As researched by Wally J. Kowalski from Able One Education Network
La Bella Donna 
Why would you need 33 stones each for 64 squares? Wouldn’t it make more sense to have 32 stones each? My first thought was that Latrunculi was sometimes played on a larger board, but then 33 pieces would not be enough.