The most effecient way is to NOT peel potatoes. Why would you ever want to peel them? Potato skin is yum and rich in nutrients, whereas the flesh is mostly carbs. By throwing away the skin, you're not only wasting nutrients, you're getting rid of the texture and fiber it adds.

Given that the skin has up to 12 times the nutrients of the entire potato it covers I personally stopped peeling my potatoes in most situations. It also adds a great crispy texture when you're roasting or frying. With that said, you do you when peeling. If it's cathartic to peel it all in one piece go for it. Or you can cut the potato in half and simply use a knife to trim the skin off like a sweet potato.

Hey OP, I haven't read through the entire thread yet but I have a couple of suggestions. Fancy cocktails are a hobby of mine and a high quality peeler is essential for pulling thin, delicate strands of citrus zest for garnishes. The OXO Good Grips Y Peeler is a fairly popular one. With the added benefit of being able to replace the blades when they go dull. They also make a swivel peeler (the one in your picture) if you prefer that. My personal favorite is the Viski y peeler.

There's also channel knives, they're made to specifically cut continuous long, thin strips of citrus zest so you may find those pretty fun to use on your potatoes. With a little practice, you could probably peel an entire potato without stopping once. Like peelers you have a couple of options. The Triangle knives are good. You would use them in a similar way to Y-peelers. I'm not sure what the form factor for these are called but they're used in a similar way to the peeler in your picture.

Lastly, if you'd like a very quick (efficient) way of peeling them, you could always use an apple peeler. I can guarantee those will peel anything quicker than you could do by hand. And they're kinda fun to play with too

And a tip: pull the potato, not the peeler. Use your had with the peeler as leverage, but keep it still and use your hand with the potato to move it through the blade.

Bucket of water with potatoes and a drill with a toilet brush for a drill bit.

https://youtu.be/WaUoIS10dvA?si=I8U2LRj3Np0AvBPs

"most efficient" depends on what you're maximizing for

Speed?

Effort?

Potato wastage?

I would agree that the tool you use has the most impact. I really like this one. For me it works way better than the one in your picture.

Steel wool and a water bucket or running water

I don't think hands are good at peeling potatoes. Maybe if you sharpen your nails?

It depends on what exactly you're looking for in "efficiency'.

When most people peel potatoes they're looking for a time efficiency.

In the one strip method there's a lot of turning the potato going on. And a lot of careful precision. If you've been doing the one strip for enough time you might be close to the million strokes peeling being time effective but for most people...

To be honest I don't really peel potatoes anymore The only dish I would peel them for would be scalloped.

I use a lathe to peel potatoes

This is the most efficient way to peel potatoes

I want to know more about the peeler in the photo. I've never seen anything like that.

Same for peeling apples. One long continuous peel is so satisfying.

From experience in Restaurants: boil them first and usually you can peel them then by hand. Like ripping the skin of in two parts with each hand.