So what are the odds of rolling three "1"s on d20 in 10 rounds of combat?
The odds of rolling exactly three 1's is:
C(10,3) (1/20)^3 (19/20)^7 = about 1.05%, or about 1 chance in 95.5.
The chance of rolling 3 or more
1's is about 1.15%, or about 1 in 86.9.
Now for a couple stories of my own! I was playing a solo superhero game and the GM says, "Make a Notice check." I roll a 1.
He says, "What the heck. Go ahead and roll again." I roll a 1.
He must have kinda wanted me to notice whatever it was, because he said, "Third time's the charm?" I roll a 1.
1 chance in 8000!
On the other hand, years ago I was playing TORG, which has d20 rolls explode on 10s and 20s. We come across an enemy camp, and my cyberpriest decides to attempt a minor miracle to make their lives harder before we attack. (Miracles in TORG are usually very subtle and unpredictable.)
I roll a 20. Then a 10. Then a 20. Then a 17. (If I'm not mistaken, there's odds of about 1 in 4211 of doing that well or better.)
The GM just glares at me and says, "Fine! A pillar of fire descends from the sky and burns up the entire camp! Satisfied?!"