How does gamma adjustment work exactly?

[tofu-dreg]

I have a display that tracks pure power 2.2 gamma quite closely. I want to be able to adjust gamma to simulate the look of 2.6 in mpv for viewing SDR content in a completely dark room as per theatre standard which specifies 2.6, but how can I know what value of the gamma adjustment (the one that ranges from -100 to +100) will adjust for my native 2.2 display to make the video "look" like 2.6? Is there some formula that describes how exactly the units of mpv's gamma adjust work so that I can calculate any correction value assuming current and target (ideal, for simplicity) pure power gamma values?