Some shows use an extended running time to challenge the audience and its perceptions. Pulling viewers into a trance state and testing their endurance is the ultimate artistic gambit.

Then there are the shows that are long simply because they have a lot to tell.

Such is the case with “Counting and Cracking,” which fills its three and a half hours with an absorbing tale of family ties and national strife, from Sri Lanka to Australia, across almost five decades. When the first of two intermissions arrived, I had barely recovered from a head-spinning plot twist. And the production, which is at N.Y.U. Skirball in partnership with the Public Theater, had more in store. It’s that kind of good yarn.

Written by S. Shakthidharan, who drew from his own family history and is also credited with associate direction, “Counting and Cracking” starts in 2004 Sydney. The show opens with Radha (Nadie Kammallaweera) briskly instructing her son, the 21-year-old Siddhartha (Shiv Palekar), to disperse his grandmother’s ashes in the Georges River, and then immerse himself in the water, as required by tradition.

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“In Tamil we don’t say goodbye,” Radha tells Siddhartha. “Only, I will go and come back.”

As the show progresses, we gradually realize what these words really mean to her, and to her family and community. In 1983, when she was pregnant and living in her home country of Sri Lanka, Radha was told that her husband, Thirru (Antonythasan Jesuthasan), had been killed in the budding civil war between the minority Tamil and the majority Sinhala. She fled the violence and settled in Australia, where she gave birth to a child who would grow up largely unaware of his heritage.

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At a steady clip, Shakthidharan and the director Eamon Flack (also credited with associate writing) hopscotch between Sydney and Sri Lanka, from the 1950s — when the South Asian nation was still known as Ceylon — to the 1980s and 2000s and back again. Even the language is in constant movement as the 16 actors juggle English, Sinhala and Tamil, providing instant translation when necessary.

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