Unfortunately for Greece with an ongoing civil war, the Greeks could not effectively defend themselves in the Peace Treaty talks following the end of World War II.
From the three areas claimed, Greece only managed to acquire the Dodecanese, a group of islands with an overwhelmingly Greek population that formerly belonged to Italy. And this was out of "luck" since the UK and Turkey had interests in the area.
The other areas claimed were:
Northern Epirus
This area (liberated by Greek forces in 1913,1920, and 1940) was promised to Greece by Britain. Greeks were an significant minority, with 124k people out of 263k, and indigenous to the region.
Many factors were against Greece, including a US promise for the territorial integrity of Albania, a Yugoslav intervention and the fact that (even if initially their government collaborated with the Axis) Albanians helped a lot, compared to their size, in the war against the Nazis.
The Arda Valley
Greece claimed the valley because, according to them, the current border was too weak to defend (and Bulgaria had taken advantage of that many times in the past). According to them, with the border change, Greece would be safe.
Bulgaria (with Soviet, Yugoslav and American support) claimed that losing the tobacco-rich valley (which had a Muslim majority population) would destroy the Bulgarian economy.
Greece was blamed for imperialism, and Bulgaria demanded to be ceded the Greek region of Thrace, something that would "make economic sense". The UK and US opposed this, and a middle solution was found: the borders remained the same.
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