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Thanks, that's exactly what I am wondering

Is #010101 effectively #FFFFFF or does it actually use less energy the darker it is? With LCDs we know it is the former, but what about OLED displays?

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The brighter the pixels are, the more power they are using. A pixel uses 0 power at 0 brightness, and it goes up from there.

Well, with LCD it does not matter. It always uses the same power. Hence the question.

So you are confirming that the statement is actually wrong. The darker a pixel on OLED, the less power it uses. Right?

I'm not sure. Considering what I know about OLED, I'd assume that #010101 consumes considerably more energy than #000000 since it needs to emit light for that individual diode. The energy efficiency from there will mostly depend on the brightness/size of the display.

But does it use less power than #FFFFFF?

Yes, but it's efficiency scales with the overall brightness of the display. True OLED black will always consume the same amount of power, regardless of brightness.

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