I've done around 200 maps by myself. I get my daily and buy them whenever they reached below 8k each for piete and boarskin, with an occasional toadskin thrown in.
I've gotten around 7 bluebirds, 6 tonberrys and 2 of the bulb.
That's like 15 / 200. So about 7.5% of the time I got a minion.