Use 'not half' when you want to show you're surprised by how much or to what extent something is true. He's not half clever, solving that puzzle so quickly!
Pro Tip 2/3
Understated Approval
'Not half' can hint that you're impressed or approve of something, often in an understated way. Your homemade cake is not half delicious!
Pro Tip 3/3
Intensity Amplifier
'Not half' can amplify a quality to show intensity, similar to 'very' or 'extremely.' It's not half cold today, I should've worn a coat!