Not sure what you are getting at. Armed robbery is not a property crime.
Armed robbery is typically considered a violent crime, regardless of the weapon used. However, not all armed robberies result in shots fired, stabbings, bludgeonings, etc.
The 2 incidents I mentioned in my previous post involved armed robberies where the suspects were armed with guns,
but they hadn't yet shot anyone while demanding money. The off-duty cops decided to intervene, which is when the suspects started shooting.
I remember being told as a young cop that if I chose to invoke my status off-duty when on-viewing a violent crime, such as an armed robbery, I needed to consider the totality of the circumstances before taking an action which might escalate the nature of the danger inherent in the crime (robbery) and increase the potential risk to the Public.
Specifically, if the robbery suspect(s) hadn't yet shot anyone, and it appeared they might leave without shooting anyone, it reduced the risk to the Public if I allowed them to leave without pulling my weapon and engaging them. Why
start a shooting when one wasn't occurring? I could always act as a trained witness, or even follow the suspect(s) outside to attempt to get a description of any veh (bicycle, or no veh used), and the direction of travel to aid in the attempted apprehension.
In other words, actions can have consequences, and my actions ought to be geared toward helping preserve the Public safety. The safety of innocents was of a higher priority than the loss of someone's money or personal property. We could always attempt to track down the suspect(s) once they'd fled the scene - without them having shot anyone - and taking an unwise action which might cause a shooting to start was both irresponsible and an unnecessary risk to the safety of the victims and bystanders.
It's common sense that any action taken by an off-duty peace officer which involves a drawn weapon and the use of deadly force isn't something to be considered lightly, and especially if that action might increase the risk of injury or death to the innocent Public.
Now, once a suspect has started shooting, or the suspect's actions (threats, manner, etc) gives the off-duty cop a reasonable cause to believe that victims are at an immediate risk of suffering seriously bodily injury or death due to the suspect's violent actions, then the off-duty cop may be forced to choose to take action.
Better be right, though. You can't call bullets back, either yours or those of the suspect(s).