Four Pairs, Three Sounds: αι, ει, οι, ου
Greek vowel pairs are NOT diphthongs - each pair spells ONE plain vowel. The big idea is iotacism: over two thousand years several distinct vowels collapsed into a single /i/ sound, and Greek kept every one of the old spellings. So η, ι, υ, ει and οι are ALL pronounced “ee” (εικόνα = i-KÓ-na, οικογένεια = i-ko-YÉ-ni-a) - which is exactly why Greek spelling has to be learned word by word. Next to that, αι is simply “e” as in bed (παιδί = pe-DÍ, και = ke), never “ai”. And ου is the one pair that adds a genuinely separate sound: “oo” as in food (ούζο = OÚ-zo, λουλούδι = lou-LOÚ-di).
The rule
Greek vowel pairs are not diphthongs - each pair spells one plain vowel. The idea behind the apparent mess is iotacism: over two thousand years several distinct vowels collapsed into a single ee sound, and Greek kept every one of the old spellings. So η, ι, υ, ει and οι are all pronounced “ee” (εικόνα, οικογένεια), which is precisely why Greek spelling has to be learnt word by word rather than derived from the sound. Beside that, αι is simply e as in bed (παιδί, και), never “ai”. And ου is the one pair that adds a genuinely separate sound: oo as in food (ούζο, λουλούδι). Four pairs, three sounds - and only ου is new.