No diamond. Is this possible?

Hi all,

I've been mining/crafting on that Robinson Crusoe seed that floated around maybe a month or two ago. It's been really fun but I haven't found much diamond. I've found I think 6 pieces total and i've explored numerous underwater caves.

Last night I finally built a boat and looked for land. Found some with a few different Biomes and also a village but every mine I dug had no diamond. Is it possible there just isn't any in this map? Should I start over?