Actually that's what the C stands for in ADC: ADd with Carry.
Yeah, but I thought that only meant that it would set Carry upon overflow (whyever I would think that, and however useful that might be), as opposed to ADD which would only... add. I don't think I've ever seen it explained anywhere what it means to Add
with Carry and that it would do A←A+C+argument.
Look at this page, for example:
http://www.6502.buss.hk/6502-instruction-set/adc
ADC #10 | Perform the ADC operation between $10 (Decimal 16) and the content of the Accumulator
... which does not mention Carry, and as far as I know, the Carry flag is not part of the content of the Accumulator.
Anyway, thanks to you, I know how it works now. So thanks again.