1st rule - never violate thirds with total gas. A previous post advocating doing just this. You can arguably get away with this on easy dives where you are staying in the kiddy pool and spend most of the dive in high flow areas. Then again, you can get away with diving 1/2 on most cave dives too. But, it is a bad habit and will eventually bite you.
2nd - thirds is the minimum. Once conditions (syphon, unexplored cave where exit vis will suck, etc.), dive plans (distance, scooter usage), and other factors change beyond idealy easy conditions, thirds really isn't enough since you can expect holdups if any problems are encountered on exit, particularly if there are gas issues. I can't remember the last time I did a gas contrained dive. In Florida, it is deco and in Mexico it is the ridiculous bottom times you start getting. Carrying plenty of gas in a cave is really easy to do. We will often do easy 1.5 to 2 hour dives in mexico on just a single stage with no back gas which provides a huge safety net plus it allows you to simply leave your rig set up for the next dive without changing tanks. I have done days of diving this way. This also allows enough gas for unplanned side excursions, but that gets beyond the scope here.
In most situations, diving a third of a stage is dumb. In an emergency, you don't want a bunch of stages floating around with 1,000 psi in them. You want to use them and then dump them reducing the drag of the team and speeding the exit. (Or, in more minor situations, hand off gear to a less task loaded team member with plenty of gas.) So, you want to breath half the gas in, and half out. Leaving enough for stage swithes, etc.
Exactly what the 1/2+ turn pressure is depends on the cave. The 1/2+ 200 rule was developed for the WKPP. It works perfectly there. The last 150psi of gas in a tank are inaccessible due to depth. At those depths you burn around 200 psi on the drop and pickup. So, a 3400 fill dived at 1/2 + 200 would use 1500 going in, 200 on the switches, 1500 exiting, and you have about 200 left you can't breathe. This generaly rule adds a bit of safety and works well elsewhere in Florida. In Mexico, 1/2 or 1/2 + 100 usually works fine. When breathing stages in ths manner you have to reduce back gas breathed by the amount you breathed the stage past 3rds. For a single tank swim dive that is probably enough given the other constraints noted above are met. But, add the peentration distances of scooters, multiple stages, etc. and then you start needing a much greater reserve which is where the general rule of not touching back gas comes in. Again, in some situations you may breathe a small amount of backgas. But, once the dive logistics get to this level, the better decision is usually to bring another stage.
Gas planning can get more complex, but if you are actually learning anything from this, doing so would be a bad idea. Hypothetical dive in Mexico, three stage dive, two scooters, 1st stage gets dropped at halves or slightly above with scooters at about 90 minutes. Second stage will be used until a predesignated point is reached due to not wanting to impact the cave and this being the only good drop point in the section of cave. This point is a stretch on the second stage. So, you back off halves on the third stage and on exit just grab the second stage and don't switch to it until the third is empty. These types of on the fly adjustments can greatly complicate the dive and are generally only used when absolutely necessary. Back gas in al80s in this example would would be slightly better than thirds. So, if all of the stages where really being used, you may need to consider placing a safety with the scooters. Or, you would probably just barely use the third stage for penetration on this dive and it would be acting mostly as a safety.
