Training is absolutely essential. It is more important than the gizmos in the FAK. For one thing diagnosis, recognition of the condition, is the first step in rendering aid. If you don't recognize the problem, how are you going to treat it? A good course will provide you with a systematic, relatively thorough process so that you consider all the possibilities.

In many major trauma situations, you will face the decision to more or not to move the victim. This can be very tricky - there is an obvious injury, but also a more subtle injury which can be aggravated by improper handling. You often should delay movement until proper resources are available.

If I should be the victim, I would rather be treated by a trained, knowledgeable person without a FAK than an untrained person with a complete assortment of goodies. Of course, the best situation is training plus good, appropriate gear.
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Geezer in Chief