I just looked this up so I understand a bit better.
When a ball hits the bumper it moves the skirt on the bumper and that actuates a switch connected to the solenoid coil, firing the bumper. The bumper fires independent of the Arduino.
So do the relays that you see control the bumper coil or are they connected to the light or scoring contacts? Can you show a schematic of the connection?
I apologize for the delay in replying but it has also given me a chance to dig deeper and have a deeper understanding.
it seems the term "relay" in pinball machine refers to a 3rd mechanism that is used to control the gameplay mechanically.
In the old machines the mechanism would use a second solenoid which had multiple switches connected to scoring, pop bumpers, lights, etc.
I was confused since a lot of places I've seen used the term without properly explaining it when it comes to pinball machines
this video shows the basic idea
seeing as we live in the digital age I think ill use a micro controller to control the bumpers and other parts of the game, more power efficient and adaptable.
Having a digital controller also adds the benefits of protection in case the pop bumpers skirt gets stuck and risks the solenoid being burnt.