10 loads total.
1. Put 3 loads in washer. Wait for cycle. 7 loads waiting to start.
2. Move 3 loads to dryer. Put 3 new loads in washer. 4 loads waiting to start.
3. Move 3 loads out of dryer and fold, move 3 loads from washer into dryer, put 3 new loads in washer. 1 load waiting to start.
4. Move 3 loads out of dryer and fold, move 3 loads from washer into dryer, put 1 remaining load in washer. 0 loads waiting to start.
5. Move 3 loads out of dryer and fold, move 1 load from washer to dryer.
6. Move 1 load out of dryer and fold.
Total run time, 5 cycles.
10 loads at laundromat
1. Put 10 loads in 10 washers.
2. Move 10 loads from 10 washers to 10 dryers.
3. Move 10 loads out of dryers and fold.
Total run time, 2 cycles.
Compounding variables are overfilled dryers that may result in clothes not getting entirely dry or a very busy laundromat with limited available capacity. At the laundromat, you begin folding while adding time to any load that needs it. At the home dryer, the entire line cycle is blocked for the additional time needed by each blocking dryer.
Don't get me wrong here, I'm not advocating for letting laundry build up just so you can go do it at a laundromat. The convenience of having it in your home is well worth it - but if for some reason you do have a huge build up it's a great way to buy back your day / weekend if you want to be able to leave the house.