Probably 3 rounds plus, but I don't really keep track.
One day I started out to just play 9 after work; thought I had a lot of balls in my bag but later found out I didn't. Lost one ball on the first hole, one on the second, and one on the third (all water balls!). Oh, and I was about 5 over after those 3 holes. Really sad start.
Standing on the 4th tee, I realized that I had but one ball left in my bag. Rather than going back to the car to fetch more, I decided to just play until that ball was lost, and then go home. Promptly got a par on the 4th hole and on the 5th.
On the 6th hole (a downhill par 3 with water front right) I lost the shot a tiny bit to the right and wasn't sure if it trickled into the drink or not. I went down there to look and, indeed, the ball was gone, but there was another ball sitting there, so I played on. Ended up with bogey there (up and down).
Played the found ball on 7, 8, and 9 and went one over through those holes. So, 2 over on the last 6 holes after starting 5 over after 3. And the main difference was that I only had one ball!