It's not likely to be a coincidence, if that's the implication of your question! Virgil has a well-known acrostic in his Georgics in the terminal characters of four lines, spelling out O-T-I-A. He was followed by Horace in his Satires, who employed the same acrostic in the first characters of four lines.
Otium was an important word for upper-class Romans with good educations: it signified for them the kind of dignified leisure that they praised most highly; managing (perhaps directing is a better word for it) the cultivation of their country estates, maintaining personal libraries, collecting statuary, frescoes and fine furniture, playing host to the convivium, and, of course; reading and writing Greek and Latin literature.
Ask someone on the street to describe poetry, and the first thing they're likely to say is that 'it rhymes'. But poetry in the ancient world did not rhyme; like Milton and Shakespeare, they wrote in strictly metered blank verse. Also like Shakespeare, they continued to avail themselves of many other literary devices to ornament their work: Alliteration, assonance, dissonance, cacophony, chiasmus, asyndeton, onomatopoeia, metonymy, synecdoche--and probably a hundred others that I never even learned the names of!
There is a bawdy epigram in the Greek Anthology whereby the epigrammatist, a noted παίδἐραστής, observes that: (spoiler...)
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The numerical value of the letters in πρωκτὸς (anus) and χρυσὸς (gold) is the same. I once found this out reckoning up casually.
Perhaps not the most helpful example of wordplay I could furnish, but certainly one I won't soon forget...