7th Interportal Tournament of HMM3-OFF: "Earth Magic"

If the chance of an ability triggering is 10%, then the chance of it triggering twice is 1%, and three times is 0.1%.
In other words, by simply repeating the battle, we achieve the result after 1000 attempts.

That's correct, but this is the probability for 3 out of 3 triggers.
If we take our case, we have about 5-6 hits = attempts.
Let's look at the battle process itself. We start the battle and complete the first round. If Death Gaze doesn't trigger in the first round, we immediately exit the battle and try again. This way, we only consider the cases where Death Gaze triggered in the first round. And then, for the remaining 4-5 hits, we need 2 triggers, in any rounds. The probability of this event is quite high, around 6%.