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

This discussion is getting out of hand as simple DC models are being compared with exotic AC ones. The math is being dumped out of a need for a model of understanding which doesn't match the challenge of the questions. The answer to all of them is... the questions are too difficult to separate into little pieces. The basics are just that, basics. The answers are beyond the understanding of most people because they encounter ideas such as statistics and psychology, which some people think do not "fit" into any discussion of music. However, they do... as well as other areas of mathematics and exotic theory, both electronic and as apparently "simple" as component design (so sorry, that is ALSO extremely math oriented). The bottom line is, most people simply cannot, will not, and don't either believe or know the answers. That means if they are right or wrong. Good luck.

@millercarbon

Gain is a multiplier, power is a ceiling.

a ceiling of what, though?  Current?  Voltage?  

Power.  

Seriously. Helps to think things through. What is power? Current? Voltage?  
Here I'll give you a hint: Watt is power? That's not a typo. 

They're not paying me enough. You could mention that.....