To keep a long story short, the basic objective is to get a Pokemon to survive even when it's using Struggle by Tricking Leftovers onto the Pokemon, putting it to sleep, and using Pain Split as a last resort. Struggle takes away 1/4 of the Pokemon's HP every time it hits; Lefties heals back 1/16 of the Pokemon's HP every turn. That means the Pokemon "loses" 3/16 every turn, technically. By putting the Pokemon to sleep, you give it more time to recover health with Lefties. And finally, if the Pokemon is below 1/4 HP, and you are not confident that it will stay asleep long enough to regain health, you use Pain Split with a high HP Pokemon in order to get the wild Pokemon's HP back to a higher level. It's really incredible.
A lot of RE hunts end early, but a significant number end after many more than 8192, too. Over 10% of MM hunts I've seen have ended in under 10 eggs, which is ridiculously lucky if the odds really are 1/1365.3. It can't hurt to track how long it takes us, and at worst we'll just confirm that the odds really are what we've been told.