here is the -high end- blackball/english pool aramith tournament balls set ( the favorite ball set ATM in the blackball pool halls here, in France) :
But IMHO the smallest Aramith ball is the -pink- cue/'goal' ball of an Aramith Petanque ball set , in the small version the players balls are 38mm/ 1"1/2 , the -pink- cue ball, used as a 'goal' , is around 1" i believe ( 2 sizes of balls set can be ordered 38mm or 48mm , diameter of the yellow/white/blue/red balls) :
in some french carom clubs , you'll find sometimes an old Petanque set stored in a closet ;-).
the pink Petanque cue balls/'goal' balls are for sure the smallest Aramith balls avaible. in my favorite club the game is played with the smallest size, 38mm for the blue/yellow/white/red , we play the game on a 10' carom table .
Loosers pay drinks & table times, that's the usual rule (gambling being a no-go here , for legal reasons )
No need of a fancy cue, you could win using a broomstick if you're good enough

. that's an odd & funny game ...