Jitter, I do know, and the answer is that it varies, depending on a number of factors, including soil, climate, potato variety, and whether your potato plants were grown vegetatively (from a tuber with ‘eyes’ which are buds that give rise to new plants which are genetically much the same as the parent plant - basically clones), or from actual seeds, which can be found in those pretty, sweet-tasting and highly poisonous berries that sometimes follow the flowers on potato plants. I must emphasise: do not eat the berries, or leave them anywhere that children or pets can get at them. When I say poisonous I mean that potato berries are similar in their effects to the berries of the related Belladonna or deadly nightshade, perhaps with a little less sedation and more gut and liver symptoms, because there is more solanine and solasodine in potato berries.
However, those nasty berries are useful because they contain seeds. The seeds are small, flat and kidney-shaped, rather like those of the related tomato or capsicum. Growing any plant from seeds rather than from cuttings, offshoots or clone buds gives you much more genetic variability among the offspring, especially if the seeds have been fertilised by pollen from a different potato variety. That is how new varieties of potato are developed.
So growing potatoes from actual seeds, rather than from the sprouting tubers that are sold as ‘seed potatoes’ is very much a lottery. You may get something very like the parent, or a wonderful new variety, but most likely the result will not be amazing. Sigh. (Says the person who has been trying for decades to breed another blight-resistant potato.) what you will quite often get is a reversion to the ancestral wild potato, which is tough, hardy, a good groundcover, about as frost resistant as any potato gets, and which produces tubers about the size of a smallish walnut. I eat mine but they are not the most delicious of spuds. I mostly grow them and allow them to flower so as to have pollen for my experiments, because the ancestral potato is resistant to many of the diseases that afflict modern hybrids.
The ones that are sold as ‘certified seed potatoes’ are ones that have been specifically grown in an environment free of the common potato diseases and pests, and/or are resistant to such, so usually safer to grow from, though if a spud sprouts in my cupboard I will usually plant it.
As for the potatoes in forsaken gardens, I have lots of experience with those, including while poking about in old ruins in the Central Victorian Goldfields area, where one of my sons now has a farm, plus abandoned gardens and farms in Gippsland and the Snowies. As I may have mentioned, I lived for some years in Walhalla, a ghost town in the part of Gippsland that runs up into the foothills of the Snowy Mountains, while I helped a mate restore and reopen an old gold mine. Back in the day, Walhalla was quite a big regional town, partly because of the gold rush, partly from timber getting and farming in the surrounding areas. Having the railway also helped. But early to mid last century the railway closed, the easily accessible gold ran out, (still plenty there but hard and dangerous to get - much of the area has terrain you can fall off and underground water very close to the surface), and the place went from a roaring town big enough to have three breweries, more than a dozen pubs, lots of shops, a fancy bandstand and several suburbs to a ghost town with a population of seventeen.
So when I wasn’t down the mine or exploring/prospecting, one of the things I used to do was poke about the gardens of the old abandoned miners’ cottages. I found all manner of fascinating stuff, much of which I transplanted to the gardens of the surviving population in Walhalla itself or in nearby Mormontown and Maidentown, or shared with another mate who was a hermit at Coppermines. I found pæonies, lilies and all manner of other flowers, and took cuttings of old apple, pear and mulberry varieties to graft onto trees in the town. I foraged for vegetables, finding not only many kinds of potatoes but carrots, kale, cucurbits, spinach, parsnips, and transferred roots, tubers or seeds to the gardens of the town. We ate well considering that the nearest shops were 40k/26 miles away. Many of those potatoes were varieties I knew, unchanged and growing from the old days, some were types I had never seen. All good.