The singular of dice—a plural noun referring to the small cubes used in games of chance—is die. Because the irregular plural is more common than the singular, many writers forget to use the singular at all—for example:
If the dice is rolled and there is a choice, what do we need to consider? [Irish Times]
The way the dice is loaded, as things stand, the company takes on interest bearing loans and in turn advances interest free loans to its 100% owned subsidiaries. [Equity Master]
The singular die is exemplified in Julius Caesar’s the die is cast (not the dye is cast or the die is caste)—though, of course, he said it in Latin. Here are a few contemporary examples:
Provided with a bucket, bean bags, stick horses, a large die, three rings, three discs, three hats and plastic Easter eggs, each group of four kids came up with a game. [Grand Island Independent (article now offline)]
A die will be rolled in front of the audience and the result will determine which half of the dance goes first and which score, costumes and lighting will be used. [The Detroit News (article now offline)]
Players take turns rolling the die and then drop whatever piece the die chooses. [Chip Chick]
If dice is treated as singular often enough, we may simply have to accept that the word has changed. But, for now, careful writers still keep dice and die separate.