No dice is an expression used mainly as an exclamation and can have a several meanings depending on the context. Mostly, they all signify a negation of some sort e.g. no way, no such luck, impossible etc. It is originally American and dates in this sense from the 1920s. Its date of origin is not the issue nor that it derives from gambling dice, but there are two theories about the origin. The first is that it derives from an illegitimate throw of the dice e.g. the dice not lying perfectly flat. This was called ‘no dice’ and the dice were thrown again. The other is that it derives from legal sources. Dice gambling was illegal in many US states and when cases were brought before judges, the actual dice constituted important evidence. If they could not be produced as evidence, judges would say, ‘no dice, no conviction’. The first explanation seems the more likely, but there were recorded instances of the latter.