What's the Latin word for the person at cena who decided whether more or less water was added to the wine to keep the party going steadily?
The Latin term for this is magister bibendi or arbiter bibendi, or "master of drinking." Here's some context:
After a roll of the dice, a magister bibendi was chosen. By appointing a certain ratio of water to wine to be mixed in the cups, this so-called "master of the drinking" then decided the strength of the wine to be drunk. (Latin for Dummies)
Drinking at the cena was moderate, but it was frequently followed by a drinking bout called cōmissatio. One of the guests was chosen magister or arbiter bibendi, and his function was to decide the respective proportions of wine and water.
Horace mentions the latter option in Odes, 2.7:
curatve myrto? quem Venus arbitrum
dicet bibendi? non ego sanius
bacchabor Edonis: recepto
dulce mihi furere est amico.
Who’ll throw high Venus at dice and so become
the master of drink? I’ll rage as insanely
as any Thracian: It’s sweet to me
to revel when a friend is home again. (translation source)