Green’s Dictionary of Slang

tats n.

also tatts
[ety. unknown; ? the rattle of dice as they hit the table]

1. [late 17C+] dice, esp. crooked dice.

2. [20C+] (Aus./N.Z.) teeth [refers to the ivory in dice and teeth].

3. [20C+] (Aus./N.Z.) a set of false teeth [refers to the ivory in dice and teeth].

In compounds

tat-box (n.) (also tatt-box)

[mid–late 19C] a dice-box.

tat-man (n.) (also tatsman, tatt-man)

[late 18C–mid-19C] a professional dice cheat.

tat-monger (n.) (also tattmonger) [-monger sfx]

[late 17C–early 19C] a professional dice-cheat.

tat-shop (n.) [shop n.1 (3)]

[early 19C] (UK Und.) a gambling den.

In phrases

ring the tatts (v.)

(UK Und.) to substitute crooked dice for good ones.

In exclamations

tats and all!

[early 19C] nonsense! rubbish! humbug!