Learn Turkish: İşbirliğimiz ve stratejimiz sayesinde odadan çıktık. - Thanks to our cooperation and strategy, we got out of the room.

When a noun already has a personal possessive suffix like -miz (our), the genitive suffix is often dropped before sayesinde in everyday Turkish. Saying stratejimiz sayesinde is much more common and sounds smoother than the strictly grammatical stratejimizin sayesinde.

Since sayesinde is for positive things, what would happen if we used yüzünden in this sentence?

Grammatically it would work, but it would change the tone to placing blame. İşbirliğimiz ve stratejimiz yüzünden odadan çıktık would mean you didn't want to leave the room, and you are blaming your cooperation and strategy for forcing you out. Sayesinde shows that escaping was a positive success.

Where does the ğ in işbirliğimiz come from?

The word for cooperation is işbirliği, which is a compound of iş (work) and birlik (unity). When birlik takes a vowel suffix to form the compound, the k softens to ğ (consonant mutation). It stays softened when you add the possessive suffix -miz (our).

Why does oda (room) take the -dan ending here?

The verb çıkmak (to exit, to go out) is used with the ablative case (-dan/-den) to show the place you are leaving or moving away from. So odadan çıktık literally means we went out from the room.