I'm actually partial to balanced ternary
For those of us who use a Level 1 system and count on our fingers, binary is a much better choice. With just one hand, discreetly beneath the table, you can count from -16 to +15, leaving the other hand free for playing, drinking, and "giving the 4" to the guy who keeps telling you third base is supposed to play for the whole table.
With values -1,0,1. I'll use 'T' for -1.
For instance, 6 = 1T0 = (1)(3^2)+(-1)(3^1)+(0)(3^0).
What's cool is you can negate a number by simply flipping the 1 and -1s: -6 = T10.
You would implement this with your hand: finger straight = 1, one knuckle bent = 0, two knuckles bent=-1. This requires some dexterity as most people can't bend their pinky without bending their ring finger. Using five fingers, you get 3^5 = 243 possible combinations, far more efficient than binary.