Which of the following sentences is more correct or more preferred?
As context, the sentence will be followed by
At any time, you may stop throwing dice and finish your attempt. Your attempt must end once all eight dice have been thrown.
In that context I'd use “...after another”, as it suggests a sequence of throws. By contrast, the “...after the other” form suggests (to me) exactly two throws, rather than some number from one to eight throws. A useful comparison of terms similar to consecutive in macmillandictionary says that “one after another” indicates little time between things, which I think is sometimes true but not always. For example, the “one after another” entry at dictionary.cambridge.org says “many, in a series” and makes no mention of rate.
The form “One X after another” refers to a series of X's; as in, eg, One Monster After Another, or in Arnold Toynbee's comment about “the dogma that History is just 'one damned thing after another....'”.
