[old_tv_nut]

The important thing about the flyback winding is its self resonance due to distributed capacitance. This depends both on the winding pattern and the insulation material dielectric constant. It is generally important to get this right because this self resonance is used to shape the peak voltage waveform that gets applied to the horizontal output and also the waveform that gets rectified for high voltage supply. The coil resonates with an external capacitor to give the basic half-sine wave flyback pulse, but the self resonance may be, for example, the 3rd harmonic, which produces a flat top or even a dimple in the top of the pulse. This reduces the peak voltage on the horizontal output. Tuning a flyback design is re-iterative work based on modifications from an existing design and requires running the re-designed winding through the potting process to get the final capacitance, and seeing how close you got, then trying again until it's right.

I think it's difficult to re-create a flyback transformer if you don't know the characteristics of the insulation as well as the winding configuration. I'd be interested in hearing if anyone has done it. How critical it is depends on how close to the stress limits of the horizontral output and other components the design is.

The pi winding is specifically used to reduce self-capacitance and increase the self-resonant frequency, compared to other winding patterns.

[above taken from long-ago memory - worth checking with someone else if you can]