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How do you determine how much power is enough?

I was able to (a) gig with a 100 watt 15” combo amp back in the day, but it was totally unsatisfactory. When I (b) added a 200 watt amp and 4x10 cabinet to that, it got to a point where it was satisfactory. I eventually got to (c) a 350 watt amp into a 4x10, with that feeding into a 550 watt PA amp going into another 4x10.

Note that going from (b) to (c) was not about making things louder. It was all about headroom, about having a signal chain with zero strain points. The good thing is that by doing a little research in the used market, that step only cost me $350. Which, incidentally, step (b) was only $400.
 
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(((This is strictly my ears talking, NO scientific rederick for proof. It's all about how I percieve my sound.)))

I've two, class D, 500 watts at 4 ohms heads.
I've two, class D, 800 watts at 4 ohms heads.

I've gigged many, many times using either wattage in a moderately loud, 5 pcs., outlaw biker country/rock group playing everything from large stage outdoor jobs to local bars, pubs and animal clubs.
I've FOH support 100% of the time.

Yeap, the 500's will get the job done through my gigging cabinet, a 4 ohm Bergantino CN212.

But, (as I said above, this is strictly my ears talking), gigging with one of the 800's into the CN212 cabinet at live band volume, the lows have a more solid feel, bigger, fuller, less strained, the mids and highs feel bigger, clearer.
Both wattage sounds good at low volume, but the 800's retain a clean clarity at all levels.

The 500's are now used for backups or rehearsal amps, the 800's go to the gigs.
 
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If you’re currently rocking an 800+ watt rig, what kinds of gigs would you no longer be able to do, or what kind of musical compromises would you have to accept, if you had to make do with a 500 watt rig?

For me, no compromises. I don't notice a significant difference until power changes by a factor of 4 (6dB). Power ratios of 2:1 don't matter much to me. My early gigging was with amps in the 50-100 watt range. Then I kicked up to a 400W amp and haven't been underpowered since.
 
It can vary depending on which amp we're talking about, but it's really down to cabs more than amps for "volume" IME.

If 500w into a 4x12 or 8x10 can't get you there, might be some other variables at play. I'd struggle to find a situation where 500w in general couldn't do the job.
 
People get hung up on the size of a venue but it really has more to do with the sound reinforcement system. If you match the drums (and this does not mean “overpower”) and you can slot in with the other instruments in volume and frequency then you should be fine.

that’s the band’s job. If they do this right FOH has a good day instead of fixing an amateur stage balance.
 
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For years all my rig was, was 500 watts head into a single 15 inch 8 ohm speaker. And in all that time I've never had to turn the master up higher than halfway. So, that's maybe 125 watts? I upgraded to a Fender Rumble 500 recently, giving me 350 watts into 2x10 speakers, so a little more power and speaker surface. And I can hook my 15 inch up to it to get the full 500 watts. Although I think I never need to that. I've played ballrooms without PA and an outdoor stage with PA, where my old rig was enough for monitoring.
 
Let me add in to say I play in a doom band. Famously/infamously probably the single loudest genre to play. Lol. And I'm in a duo. Just me and a drummer. I do split my signal and run all dirt into essentially a guitar rig.

Relevant here is the 'bass side'a 800w Quilter bassblock I run into a GK Neo 412 [rated max 1200w at 4ohm]. I've never ever ran the Quilter above '400w' [the master volume knob on a bassblock is demarcated by watts versus a 1-10 range] with the gain on 4 [out of 10]. In a doom band. That's loud. With a drummer that hits like a ton of bricks and plays a Ludwig John Bonham set [26" bass drum, big toms]. And its up against the fuzzed out 'guitar' side of my rig [200w quilter, running at 'only' 50w] on a 412 Marshall cab.

And honestly, that cab is overkill but it's too fun not to use it. Lol. could easily 'make do' with a 2x12 or 2x10.

Efficient speakers plus efficient amp equal happy bassist. Get the most efficient cab of a size/config you like and power it with an appropriate head and I think 99 out of 100 times you'll be happy.