Jiu-jitsu Times: An interesting and controversial question!
The instructor who runs your academy can really vary in terms of age, injury history and competitiveness.
If your head instructor is in their competitive prime and preparing for a competition then they likely want,…NEED for you to roll hard and test them.
They still must exercise caution in the roll, as they teach classes to make their living and need to stay healthy enough to teach 10+ classes per week.
Conversely, an older instructor who may likely be plagued by injuries from a lifetime on the mat may need to roll in a reduced capacity.
The instructor loves bjj and wants to roll like everyone else, but “Father Time” has diminished their capacity to be king of the hill in every class and every roll.
They enjoy rolling for the purpose of exchanging positions on the mat and seeing which techniques the students are using.
For example I have attended some excellent seminars with older jiu-jitsu masters and it would have been inconceiveable (and highly disrespectful) to me for any student to challenge the instructor to a hard roll.
Grandmaster Helio Gracie got on the mat until after the age of 80 and it is difficult to imagine a 22 year old blue belt head hunting the master!
My best suggestion would be to match the energy of the instructor.
Or as one of my instructors (a younger competitor type) said to me “I give back what I get!”
If the instructor is pushing the intensity of the roll, then he likely expects your intensity in return.
If the instructor is more flowing and “keeping it playful” then try to roll in that style. Exchange technique and keep the strength and explosiveness out of that roll.
As an instructor, I am not impressed if a student uses superior athleticism, speed and strength to tap another training partner.
As Rickson Gracie said “You can find strong guys hanging from the trees around here.” It is nothing special and not an indicator of the students technical level.
What DOES impress the instructor is observing the student using TECHNIQUE that was taught in class during the roll.
That reveals that the student is acquiring the SKILLS of jiu-jitsu.
At a seminar, I had the opportunity to roll with a multiple time World Champion in his competitive prime.
I said to myself I could approach the roll in one of two ways:
1) Try to survive as long and as possiblke and give him my best roll (which was going to end with my getting submitted no matter what)!
2) Try to move and exchange positions and have some fun…which was ALSO going to end with my getting submitted!
I decided on the 2nd approach and had a very fun roll where the instructor caught and released several positions allowing the roll to go longer before choking me.
We smiled and bumped fists and I had a great roll.