Even though is used to express a fact, something that is real or true.
Even though means ‘despite/in spite of’ the fact’.
It is more emphatic than ‘though’ or although’.

• Even though John is rich, he lives in a small house. – Annak ellenére, hogy John gazdag, egy kis házban él.
  (John is rich, but despite having money he lives in a small house.)

• Even though she likes animals, Mary doesn’t want a dog. – Annak ellenére, hogy szereti az állatokat, Mary nem szeretne kutyát.
  (In spite of the fact that she likes animals, Mary doesn’t want a dog.)

• Even though the building was damaged, business went on as usual. – Annak ellenére, hogy a ház megsérült, folytatódott tovább az üzleti tevékenység.
  (The building was damaged, but despite that business went on as usual.)

• Even though I washed it several times, I couldn’t get rid of the stain. – Annak ellenére, hogy többször is kimostam, nem tudtam kiszedni a foltot.
  (I couldn’t get rid of the stain despite washing it several times.)

Even if – Még akkor is, ha …/ Még akkor sem, ha … 

Even if is used in a supposition or hypothesis.
It refers to an imaginary or unreal situation

• Even if Caroline earned a big salary, she would not buy a fast car. – Akkor se venne magának gyors kocsit Caroline, ha sok pénzt keresne.
  (Caroline doesn’t like fast cars. It is not because of the price that she won’t buy one.)

• Even if I had time and money, I still wouldn’t go on a cruise. – Még akkor se mennél el egy tengeri hajózásra, ha lenne rá időm és pénzem.
  (It’s not because I have no time or no money that I won’t go on a cruise.)

• I have other reasons for not going.)

• I wouldn’t wear that dress even if I got it for free! – Még akkor se venném fel azt a ruhát, ha ingyen adnák! 
  (Imagine getting that dress for nothing. I still wouldn’t wear it!)