[immibis]

If values are normally distributed, random errors accumulate with the square root of the number of components. Four components in series have 2x the uncertainty over all, etc, but if you divide that double uncertainty by four times the resistance, it's half the percentage uncertainty as before. (I avoid using the word "tolerance" because someone will argue whether it really works this way)

In reality, some manufacturers may measure some components, and the ones within 1% get labeled as 1%, then it may be that when you're buying 5% components that all of them are at least 1% off, and the math goes out the window since it isn't a normal distribution.

[afiori]

I wonder about the effect of different wiring patterns. For example you can can combine N^2 resistors in N parallel strips of N resistors in serie.

I expect that in this case the uncertainty would decrease

[RetroTechie]

In the article's example, I'd prefer 2 resistors in parallel. That way result is less dramatic if 1 resistor were to be knocked off the board / fail.

Eg. 1 resistor slightly above desired value, and a much higher value in parallel to fine-tune the combination. Or ~210% and ~190% of desired value in parallel.

That said: it's been a long time since I used a 10% tolerance resistor. Or where a 1% tolerance part didn't suffice. And 1% tolerance SMT resistors cost almost nothing these days.

[bombela]

This might be why pretty much all LED lightbulbs/fixtures have two resistors in parallel. Used for the driver chip control pin, that sets the current to deliver via some specific resistance value.

It's always a small and a large resistor. The higher this control resistance, and the lower the driving current.

Cut off the high value resistor to increase the resistance a bit. In my experience this often almost halves the driving current, and up to 30% of the light output (yes, I measured).

Not only most modern lights are too brights to start with anyways, this fixes the intentional overdriving of the LEDs for planned obsolescence. The light will last pretty much forever now.

[afiori]

Iterating either of

f(x) = 3/(1/x + 1/110 + 1/90)

g(x) = 1/(1/(3x) + 1/(3110) + 1/(3*90))

Seems to show that 100 is a stable attractor.

So I will postulate without much evidence that if you link N^2 resistors with average resistance h in a way that would theoretically give you a resistor with resistance h you get an error that is O(1/N)