My most ever in a competition is 2 Off the yellows in a casual game though I've had 5 in one round.
I've also had an eagle and 3 birdies in one round from the yellows, and 2 Eagles off the whites, both non-competitive rounds though.
I usually give myself at least one really good birdie chance in a round. I don't always take it but even when I get 2 or 3 in a round I quickly cancel them out with a double or treble bogey. I've never struggled to make birdies / eagles. For me a good round is about the doubles I don't make not the birdies I do!
My best has been 3 in one round whilst playing in Spain.
Two on the trot, lipped out (albeit from long range) for the third on the next hole then birdied the one after that.