I'd always thought it refered to the gambling cube or some fascimile thereof for the reaons you and others have cited. Interesting allusion for me. I've always thought that the emphasis was part "fait accompli" the done deed. He's done his part, flung die by crossing the rubicon - but the die has not yet settled, that is, he didn't at the time not know the outcome of his roll, his gamble. (Never knew it came down to us from Plutarch.)

k