2. An explanation that something did not occur.
In either instance, "no dice" is used to indicate that there is no chance or probability of the event happening. Dice represents the likelyhood of whatever item taking place (by the roll of the die), and not having dice means that there is not even a slim chance.
Boy: Will you go out with me?
Girl: No dice. (No chance in hell.)
"I was hoping that I would run into her at the park, but no dice." (She was not at the park, therefore there was never any possibility.)
1: Not going to happen
2: Not allowed to try
3: Not being given the go-ahead
4: Not allowed to use your throw in Backgammon (and possibly other games)
Example of antonym: "green light"
1b: No dice
2a: May I try to beat your highscore?
2b: No dice
3a: Permission to follow?
3b: No dice
4: No dice, it landed on the tip.