This is one of my favorite cards to play with. It is so deadly! :) It is so much more than just using your influence to fight.
First thing to note is that it allow you to call a dude no matter the situation: meaning you can for example, call a dude at your opponent's home, or call a dude with your booted dude. A good combo i like to use is to pair this with The Spiritual Society outfit, booting one of my dudes to boot a dude with lower influence, and then call him using this, knowing he can't refuse and i'll have the advantage (since i have more influence than him).
One other thing it's quite good at is dealing with big threats. Most of the time, a dude with a tons of bullets won't necessarily have a ton of influence either, making it a potential easy target for a suicide shootout with this. And all his bullet boosting actions won't help him either! :)
Overall a quite underappreciated card, in my opinion.