What’s the relationship between gain (dB) and power (watts)?

I'm wondering if the question is about the switch values or how it should be set?

IN the end MC’s point is one all should take to heart. Doubling the volume -- all things equal - requires 10X the power.

Don’t mean to be difficult but no, that’s not quite right. Sound volume is how loud we call something we perceive or hear. That’s why I resist measuring and object to people saying they listen at so and so many dB. Instead I prefer to say I listen at a satisfying level, or if I want to get across that it is good and loud I like to say Supertramp Loud.

It sounds goofy but at least it is clear I know the difference between volume level and SPL. Sound pressure level is what we measure with decibels. Literally the pressure difference between the compression and rarefactions of the sound wave.

The difference is that we can say a 10dB increase requires ten times the power. Because both decibels and watts are quantifiable. Volume however is totally unquantifiable. Is 10 dB twice as loud? According to who? Some can barely hear a 2dB change. For others that is a big jump and they want a volume control with finer increments. For others anything past a certain point is simply "too loud".

But your main point is definitely one people will do well to learn. To play even just 3dB louder requires twice the power. 3dB is not that much of a difference. But it requires twice the amp to do it. This more than anything else is why people will do themselves such a big favor to ignore low sensitivity speakers. You can get them. They can be made to work. But the math is stacked against you.

If the amp is rated 300Watt at 8Ω, gain set to 23dB, the amplifier need 3.5Volt input signal in order to output 300Watt at 8Ω,
If the gain set to 29dB, the amplifier need 1.75Volt input to output 300Watt at 8Ω.
Its depends on the max. output voltage of your preamp, set the gain on your power amp accordingly.

@millercarbon - thank you.  I like this:

That is the difference between power and gain. Gain is a multiplier. Power is a ceiling. You cannot get any more power from your amp no matter what gain you set it on.

@timlub - thank you. This is helpful and simple:

With higher gain, it takes less of a turn of the volume knob before you hit the amplifiers full output.
With the lower gain setting, you need to twist it a bit further.

@erik_squires - now this seems relevant to me:

That is, put in 0.1V peak to peak input signal and you should get 2V peak to peak on the output. 

Of course, gain only works so long as you don't exceed the output limits, whose absolute limit in a linear amp is by the power supply rails. So, if your rails are +- 20V, that's your peak output. With 20x gain (around 28 dB) this means your maximum input voltage is 1v peak to peak before clipping.

This is where my technical ignorance seems significant.  Maybe I’d need a textbook to understand this:

Of course, gain only works so long as you don't exceed the output limits, whose absolute limit in a linear amp is by the power supply rails.

My Sanders sound pre has a gain setting I think of 8DB, or close.

   I set it at 3 DB, for a bit of boost, but the McCormack amp does the rest