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The phrase "the die is cast" indicates that a decision has been made or a set of circumstances sent into motion which can no longer be stopped. If the die has been cast, there is generally nothing that can be done other than to let the situation play out. The phrase can be interpreted literally to refer to the roll, or casting, of a die, or to the process of pouring liquidized metal into a mold.
Idioms are figures of speech which do not simply convey their literal interpretation. For example, to "kill two birds with one stone" doesn't literally involve the killing of birds with a stone, but the accomplishment of two goals with one action. Idioms exist in many languages across different cultures, and they can be difficult to interpret cross-culturally. "The die is cast" is an idiom which is said to have origins in the Roman Empire.
Historically, it is believed that Julius Caesar first uttered the phrase "the die is now cast," but an exact account of the instance is hard to pin down. The story is that in around the year 49 BC, Julius Caesar was ordered to relinquish command of his army at the request of the Roman senate, and he received this order when he was at the river Rubicon. Caesar decided to ignore the order and march his army over the Rubicon and into Italy, which was a crime in itself. As he rebelliously marched the army over the river, both ignoring the command and flouting the law, he declared that "the die is now cast," knowing that nothing could now prevent war.
The phrase "the die is cast" can be literally translated as "the die has been thrown, and whatever number comes up, will come up." The outcome of a single die roll is decided once it has left the hand of the roller, and the onlookers have to wait and see what happens. Alternatively, the die is cast could refer to the process of casting metal into a mold, otherwise known as a die. This explanation is likely to have arisen later, but essentially has the same meaning: once the die is cast, the metallic form cannot be altered.