Definition
An unacceptable alternative.
An unfavorable result.
Origins
A term used in the game craps when the dice land off the table, invalidating the throw.
How People Actually Use It
1. A rejection or refusal. 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.
"1. Boy: Will you go out with me? Girl: No dice. (No chance in hell.) 2. "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.)"
Source: Urban Dictionary