I mostly take one guitar, and one amp to any normal gig. Occasionally if I am in the mood to switch guitars I will bring an extra guitar, just for fun.
I will also bring a backup guitar if we are doing a private event because it looks good on stage, and if I did happen to break a string I could easily switch, but for a regular club gig, I wouldn’t even consider this. Over the years as my picking technique became more refined, I stopped breaking strings, so for me to break a string something has to be really wrong, like a burr in the saddle, or a faulty string.
As for bringing an extra amp, I only bring a backup amp if I just modified or built an amp. If I am playing a brand new guitar amp, a vintage guitar amp that I just bought, or some amp that I just repaired, then I will usually bring a small backup amp, but those are the only situations where I even consider loading an extra amp into the car.
Over thousands of gigs there have only been a few times where I needed a backup, so I believe if you have good gear then the risk of not taking a backup is minimal.