With exempt tournaments sometimes 3 but usually 4 games, my general feeling is it should be 6 quality games, 6 that are a combination of cupcakes and/or regional, and then 1 wildcard (a decent opponent not likely to require a return road game). Hopefully, the cupcakes fall no higher than the #250 range.
The reasoning is simple. Automatically that's likely 6 wins right off the bat. That means the Gophers have 7 games (if the wildcard ends up being good) to build a non-conference resume (not 4 like they had this year). Win 3 or 4 of those, and most seasons get a 10-3 or better record they'll be in solid shape heading into the conference season. ... much better off than being 11-2 or 12-1 and having played a ton of home cupcakes.
Piggy-backing on BJN"s post, the typical season would be 9-1-3 (home/road/neutral) or 8-2-3, which occasionally would allow for an additional true road test. Using next season as an example, assuming the Gophers will host the ACC, play Oregon, and also play in the Dave Gavitt Tipoff (with the Big East), it might look something like this
Home (9)
1. Puerto Rico Tipoff Opponent/Likely cupcake #1 (exempt)
2. Cupcake #2
3. Cupcake #3
4. Cupcake #4
5. Cupcake #5
6. North Dakota State (regional)
7. ACC Challenge Opponent
8. Oregon (front end of home and home)
9. Belmont (wildcard, strong mid-major)
Road (1)
1. @ Big East opponent (Dave Gavitt Tipoff games vs. Big East)
Neutral/Puerto Rico Tip-Off (3)
3 of: Butler, Miami-Florida, Mississippi State, Missouri State, Temple, Texas Tech, Utah
With this schedule, the 6 presumed quality games would be the 3 in Puerto Rico, the Big East and ACC games, and the Oregon game. At the same time, there's a decent chance that Belmont and NDSU could end up being pretty decent wins, if won.