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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.)
no dice by Chika January 8, 2007
no luck, plans fell through, not going to happen
no dice by Anonymous October 1, 2003
Can mean
1)don't agree
2)not happening
1) Hey man you wanna go smash that mailbox? No Dice
2)Hey, party at your house tonite. No Dice
no dice by j/a June 29, 2003
An outright refusal, denial or rebuttal; essentially, shorthand for 'no fucking way'.
Joe: Hey Johnboy, can I borrow a cigarette?
Johnboy: No dice!
No dice by The-Observatory.net September 19, 2004

No dice, homeslice. 

no·dice·home·slice
-ghetto

1. not a chance
2. bad luck
3. rejection
4. disagreement
A) an' i said to myself, i finna' swag into my room. so i do, an' bam, there be jello errawhere. oh lawd, we family, help a brotha clean this shit.

B) no dice, homeslice. i got caps to bust and blow to snort.
Asking for something and not receiving it.
Hey ma I want some cookies?
No Dice!
Dis ain't ova
no dice by bronson September 8, 2003