no dice (US)
exclamation (informal)

- a rejection or refusal

- something that people say when they cannot or do not want to do something

Cambridge Dictionary

---
ORIGIN

NO DICE is a US phrase and originated there in the early 20th century. Gambling with dice was illegal in many states and so gamblers went to some pains to hide the dice when challenged by the police. Courts would sometimes throw out cases if the dice weren't offered in evidence.

There are several court records where gamblers were alleged to have swallowed dice to avoid arrest.

Dice have been used since before recorded history, and it is uncertain where they originated. The oldest known dice were excavated as part of a backgammon-like game set at the Burnt City, an archeological site in south-eastern Iran, estimated to be from between 2800–2500 BC.

"No way" is a common synonym for no dice.

"A no go" or a "no-no" is something which is strictly forbidden

"no soap" alludes to the phrase it won't wash, meaning “it won't find acceptance.”

The contrarian phrase is "Where there's a will, there's a way!"