Brill's New Pauly mentions tesserae (as well as talus) - see http://www.perseus.tufts.edu/hopper/morph?l=tesserae&la=la#lexicon "a die for playing, numbered on all the six sides"
Suetonius quotes a letter written by Augustus that says
"Inter cenam lusimus geronticos et heri et hodie; talis enim iactatis, ut quisque canem aut senionem miserat, in singulos talos singulos denarios in medium conferebat, quos tollebat universos, qui Venerem iecerat."
"We gambled like old men during the meal both yesterday and to-day; for when the dice were thrown; whoever turned up the ‘dog’ or the six, put a denarius in the pool for each one of the dice, and the whole was taken by anyone who threw the 'Venus'" (transl. by ?).
Martial writes the following:
non mea magnanimo depugnat tessera talo,
senio nec nostrum cum cane quassat ebur:
haec mihi charta nuces, haec est mihi charta fritillus:
alea nec damnum nec facit ista lucrum.
("My dice do not contend with highhearted knucklebones, nor do sice and ace shake my ivory. This paper is my nuts, this paper my dice box; such gambling brings neither loss nor gain." - translated by D.R. Shackleton Bailey)
"Hac mihi bis seno numeratur tessera puncto"
Also, I've been able to find at least one example of the plural for alea (in the Loeb Classical Library):
"aut pugnaciter aleis certant, turpi sono fragosis naribus introrsum reducto spiritu concrepantes" (Ammianus Marcellinus)
"or they quarrel with one another in their games at dice, making a disgusting sound by drawing back the breath into their resounding nostrils"(translated by J.C. Rolfe)
For further details, see "Literate games: Roman society and the game of alea" by Nicholas Purcell (Purcell 1995).
We should also consult the TLL. The entry you need is https://www.degruyter.com/view/TLL/1-0-07/1_0_07_alea_v2007.xml (no access from home)
Incidentally, this is what Klaus Bartels writes in Brill's New Pauly (in the entry "dicta"):
"Caesar's “Alea iacta est(o)”, regularly misconstrued as "the die is cast", is more correctly translated as: "the die is (or is to be) thrown". This phrase, a verse of Menander's that was already proverbial, does not refer to the decision made by the fall of the die, but the decision for the boldness of casting it in the first place."