Clarification about the Hell Knight

There's an aspect of this subclass I've only just noticed and I waned to make sure we are all on the same page here.

The first time(s) I read the subclass, I assumed that you could only apply an Advanced Wound when you first inflicted your Infernal Wound, giving you a 17% to do it, so, assuming two Short Rests, only once or twice per Long Rest.

Advanced Wounds:

When you roll your Infernal Wound Die and roll a 6, you can apply one of the following effects.

However, re-reading the subclass... there's a whole slew of things that could trigger an Advanced Wound, including the ongoing damage from Infernal Wound.

Infernal Wound:

Once per turn when you hit a creature with your Hellfire Weapon, you can deal extra Fire damage equal to one roll of your Infernal Wound Die and give the target an infernal wound.
While wounded in this way, the target takes Fire damage equal to one roll of your Infernal Wound Die at the start of each of its turns.

You're rolling your Infernal Wound Die even for that ongoing damage, so it counts, right? And Hellfire Surge would also seem to qualify.

Hellfire Surge:

On a failed save, a target takes Fire damage equal to one roll of your Infernal Wound Die and is burning.

If I read this right, every target affected by your Hellfire Surge could also be affected by an Advanced Wound if you roll a 6 on the Damage Die.

Then, all of these features are affected by Blister of Avernus and Infernal Bargain, which increase their damage (a little) and double the odds of inflicting Infernal Wounds.

Blister of Avernus:

When you roll a 6 on your Infernal Wound Die, you can roll another d6 and add it to the damage.

Infernal Bargain:

When you roll your Infernal Wound Die, you can treat a roll of 1 as a 6.

To honestly evaluate this subclass vs the Battle Master, we should probably try to figure out how likely we are to inflict an Advanced Wound and how likely each of these dice is to explode and trigger an additional effect.

(NOTE: The extra damage from Blister of Avernus does not count as a roll of your Infernal Wound Die. Should it?)