Praise be to the OED -
"In phrases sortes Virgilianae, Homericae, Biblicae: divination, or the seeking of guidance, by chance selection of a passage in Virgil, Homer, or the Bible. Also ellipt. and transf.
a1586 SIDNEY Apol. Poet. (1595) sig. B4, Whereupon grew the worde of Sortes Virgilianæ, when by suddaine opening Virgils booke, they lighted vpon any verse of hys making. 1646 T. BROWNE Pseud. Ep. V. xxi. 272 The first an imitation of sortes Homericæ, or Virgilianæ, drawing determinations from verses casually occurring. 1700 J. WELWOOD Memoirs 100 Lord Falkland, to divert the king, would have his Majesty make a trial of his fortune by the Sortes Virgilianæ, which..was an usual kind of augury some ages past. 1740 H. WALPOLE Let. 25 Sept. (1974) XXXVII. 79 In three words I will give you her picture as we drew it in the Sortes VirgilianæInsanam vatem aspicies. I give you my honour, we did not choose it. 1801 M. EDGEWORTH Belinda II. xiii. 25 Several volumes of French plays and novels were lying there, and Clarence Hervey raking up one of them, cried: ‘Come, let us try our fate by the sortes Virgilianæ.’ 1845 G. E. JEWSBURY in A. Ireland Sel. Lett. G. E. Jewsbury to J. Welsh Carlyle (1892) 179, I send it you by way of a ‘sortes’, and the Bible has as much virtuethat wayas Virgil! 1886 D. C. MURRAY Cynic Fortune xv. 183 In the practice of the sortes (which was a favourite occupation of his) [he] was elevated or depressed by the text he fell upon. 1897 A. C. BENSON Diary June in D. Newsome On Edge of Paradise (1980) ii. 63, I took a Sortes Biblicae before refusing. 1947 H. NICOLSON Diary 11 Dec. (1968) 118, I consult sortes Biblicas. My Bible opens at Ezekiel XL 22. 1969 G. GREENE Travels with my Aunt I. xvi. 170 The Sortes Virgilianaea game my mother considered a little blasphemous unless it was played with the Bible. 1975 V. CANNING Kingsford Mark vi. 105 He acknowledged the encouragement of the sortes. All the omens were right."
In The Star Factory, Ciaran Carson advocates the sortes Ashberyae (although without my inelegant cod-Latin). Paul Muldoon I rather suspect of having committed, perhaps even more than once, the sortes OEDae. When in the direst of straits I have considered a sortes Unhemmedae. (Actually, that's not true.)