Green’s Dictionary of Slang

Thommo’s n.

also Thomo’s, Tommo’s
[‘Australia’s most notorious two-up school was, and still is, known as Tommo’s. It was conducted by a man known as Joe Thomas and, in spite of hundreds of raids over the years, it returned him a fortune. Though known as ‘Tommo’s’ to thousands of gamblers, Thomas was not the owner’s right name' V. Kelly Bogeyman (1956)]

() ‘Thommo's Two-up School, which operated at various locations in Surry Hills, Sydney from the early years of the 20th century until at least 1979, was one of Australia's first major illegal gambling operations’ (Wikipedia).

J. Byrell Liars, Urgers & Coat-Tuggers : .
[Aus]Age (Melbourne) 31 May 4/1: ‘One two-up school, the notorious “Thommos,” has been running for at least 35 years’.
[Aus]D. Hewett Bobbin Up 159: The cockatoos kept watch outside the dirty house in Reservoir Street, where Thomo’s two-up school did a roaring, open trade.
[Aus]F. Hardy Yarns of Billy Borker 82: One night he went to Tommo’s two-up school and won five hundred quid backing the tail.
[Aus]L. Wright Cards, Dice & Pennies 107: The so-called ring at Thommo’s is, in fact, square.
N. Donaher Sylvania Waters Diary 16: The closest we ever came to any trouble was at Thomo’s two-up school in Oxford Street in the city.
J. Byrell Liars, Urgers & Coat-Tuggers 203: [T]he man who once conned his poor Aunty Ada out of her pension money so he could go and play swy at Thommo’s - did something marvellously out of step.