Haha this is why I'm getting my advanced cert to learn more about this. I just like thinking mistakes can happen.
The typical AOW course won't contain much detailed information about precision gas planning and buddy procedures. However, a well motivated and properly experienced instructor will add such elements to the course as additional learning. Be sure to investigate what your potential instructor will actually be teaching you on the course - AOW level courses can be awesome or a complete waste of time, depending absolutely on the instructor you choose.
If you are concerned about OOA emergencies, then your first steps are to investigate proper gas planning and effective buddy procedures.
Proper gas planning includes the following aspects:
1) Knowing your Surface Air Consumption (SAC) so that you can predict your gas use as part of dive planning.
2) Knowing the amount of gas you will consume during an ascent to the surface.
3) Setting a minimum gas reserve that takes account of both divers air consumption requirements, should you be air-sharing.
There are lots of threads and online resources that will help you understand how to perform this precision gas planning. Search for SAC/RMV calculation to understand how to formulate your air consumption figures. Then search for 'Rock Bottom Gas Management' to understand how to set a precise reserve figure for the needs of a buddy team.
Here are my workshop notes for gas management:
Scuba Tech Philippines - Gas Management Workshop
Once you understand the gas planning, management and required reserves, you will need to ensure that your buddy is reliable to provide those reserves should you ever be without a gas supply. Good buddy procedures are taught on every entry-level course, but many instructors neglect to emphasise their importance and/or help the students learn how to apply those skills for real world diving. Go back to basics with this. Conduct comprehensive dive planning as a buddy pair. Conduct effective pre-dive safety checks. Develop and maintain mutual situational awareness during your dives. Communicate often during the course of the dive. Maintain a constant awareness of each-others gas levels. etc etc
Also check out my article on how to dive with insta-buddies, as this can help you ensure good buddy procedures:
How to Dive with 'Insta-Buddies' - Scuba Tech Philippines – News & Articles
For open-water recreational diving, those two steps will ensure that you have the support and gas that you need to reach the surface if your own air supply should fail.
Some divers do enjoy having a pony cylinder as an 'extra' insurance. There are a few specific circumstances where a redundant personal air source can be a safety bonus. For instance;
1) Cold Water Diving. In very cold water, with higher risk of free-flow. Not only can your reg free-flow easier, but air-sharing from a buddy will increase demand on their reg and could cause a secondary free-flow on that reg also. An approporiately size redundant air source guards against this possibility.
2) Deep recreational dives. Whilst a 'rock bottom' reserve and reliable buddy should be sufficient, high gas consumption at depth can easily lead to over-demand beyond your calculations. The combination of increased breathing gas density, narcosis and potentially elevated breathing rates during an incident at depth can enable air consumption beyond your highest reasonable estimations. Likewise, the risk of accidentally exceeding no-decompression limits increases significantly at depth. A small delay at bottom depth can lead to lengthy decompression obligations, especially after multiple deep dives. Most recreational divers won't plan gas reserves to include emergency decompression. An appropriately sized pony cylinder guards against these risks.
3) Overhead environments. Cavern and wreck diving courses place very prudent recommendations about depth/distance penetrations into overhead environments. Recreational divers should still be able to air-share, exit and ascend from a wreck or cavern as per normal. However, the risk of silting/reduced vizibility can jeapordize timely air-sharing. Also, any change to the structure of a wreck (i.e. collapse) or navigational error (get lost/lose guideline) could mean that the buddy team encounter restrictions that make air-sharing difficult. A personal redundant air supply guards against such possibilities.
If you do opt to equip yourself with a pony cylinder, then you should do so intelligently. A pony cylinder can be a 'false comfort' if you have not already conducted the foundations outlined above. This is especially true if you don't equip yourself with an
appropriately sized pony cylinder. You should apply the SAC and Rock Bottom calculations to your choice of cylinder, to ensure that it
actually contains enough reserve air to get you comfortably to the surface.