Either open or concealed weapon can be cared for personal self-defense. Legality of open or concealed care of weapon by civilians is differ from jurisdiction to jurisdiction and you should seek professional advice on it.
Therefore, I won't touch the legal issues, but rather talk about difference in effect of open or concealed care as it applied for self-defense.
Weapon is an item that has two related, but distinct, functions:
The open or concealed care make a difference in using weapon in its second capacity, as negotiation tool.
What I said above is nothing new: the old Colt Six-Shooter that captured American Wild West was called the Peacemaker for a reason.
In case of a Human vs. animal display of weapon (be it a large stick, stone, metal chain, or alike) may deter aggressive animal from attack, if animal already familiar with the effect of use of this weapon.
In case of Human vs. Human - and this is applied to self-defense scenarios that I'm concerned with - display of weapon plays the similar role, but it's not always works straightforward as a determent of aggression. In some cases display of weapon can be seen as an aggression of its own, that requires immediate and forceful reply. It's in a large part depends on the presumption and training of parties involved in the altercation with weapon display.
In the world of military and law-enforcement professionals it's often (and absolutely correctly) emphasized that weapon should not be brandished. Weapon is a dangerous tool and should be handled with great care. Cases of incidental manslaughter or self-inflicting wounds from reckless weapon handling are too numerous to be ignored. In any weapon training class safe handling is the first and the most rigorously controlled subject.
The problem is that when trained weapon professionals facing poorly trained (or not trained at all) armed civilian they tend to apply to that civilian their own rigorous standards. They tend to error on the side of their own safety and sometimes it's resulted in unnecessary violence and bloodshed, that afterwords seems as unjustified and avoidable.
So, purposeful display of weapon should not be used as a rule. As, based on widely spread assumption that if weapon is shown it will be used, it's can trigger violence - the exact opposite result of your intentions.
Open care weapon is a rarity even in the most weapon friendly countries. But in those cases the open care itself is a negotiation factor (remember The Peacemaker).
The concealed care will work the same way as open care if you can be presumed to care concealed weapon based on general expectations.
If you are facing adversary who is displaying his weapon, or even brandish it in a threatening manner, remember that he's not killing you (yet), but negotiating to get the upper hand (I'm addressing it on this page on handgun defense).
And the last-but-not-least: if you found yourself displaying your weapon, be ready to use it and to face the consequences of it. This is absolutely firm rule: NEVER display weapon that you're NOT READY to use. For this reason caring concealed weapon gives you more flexibility in selecting your options in any self-defense scenario you may face.
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