Yes, voltage drop across the transistor as well. Typically 0.7V.
(9 - 3*1.85 - 0.7)/xxmA = Resistance
Think I got distracted & left it off.
Vce @ saturation is typically around 0.7V.
9V battery are typically only good for a couple hundred mAH.
So 18 strings of 3 LEDs, each string drawing 10mA, is 180mAH.
So maybe you'd get 2 hours of life? With LEDs getting dimmer fairly quick I'd imagine.