So the thing with toe up socks is getting the toe right. You can cast onto your DP needles and distribute them the normal way, leaving a hole at the toe that you sew up later.
But the first three videos I looked at try to prevent that with a really weird cast-on and here is the best demonstration I've seen yet.
https://www.youtube.com/watch?v=s4hhxKrylOs
You can do this with normal circular needles. Forget about that magic loop stuff, that's really just circular needles as opposed to DPs. I have tried doing this with DPs and found myself pulling off half the cast-ons. The tether of circular needles prevents that.
At first it's hard to see how she grasps the yarn. If you use the Youtube settings and put it on half speed, you can see that the tail from the slip knot does have to be rather long, because you will put your thumb in that to cast on to your upper needle while your "working yarn" casts on to the lower needle.
The second point is USE A LIGHT TENSION when you cast on. Some of you use a tension which will break most fingering yarns and some heavier yarns. Stop that. If your tension is too high, you won't be able to knit those cast-on stitches.
The third thing is that I worked the toe inside out the first time I tried. After you do the cast-on, look at both sides. One will have a tiny ditch and the other will have a tiny ridge. Make sure that when you knit that first stabilizing round, you have the DITCH facing you. If you don't, the tiny ridge will be facing out when you finish. It's not fatal, it's just not how it's supposed to look. Here's a photo of the toe. I put it on top of a sock I knitted years ago that fits me. With a 12-stitch cast-on, they look like exactly the same size.
The video does what I said, KF/B for increases at the toe. Then it uses a gusset, and then it does German short rows for the heel.
The written pattern is here.
https://verypink.com/2019/05/15/toe-up-gusset-socks/
There is a price tag on the pattern, but if you have knit socks before you can wing it once you watch the video because she tells you all the steps, she simply doesn't tell you what the stitch counts are.
What I found out by experimenting is, that the stitch counts that work in Carol Anderson's Iowa Cruise Socks pamphlet work here. In worsted weight, I would use the #5 counts; in DK/sport, the #6 counts, and in fingering weight the #7 counts.
So first I used some leftover yarn in fingering weight on size 3 DP needles. You can just about make two socks from one skein of Cotton Fine yarn.
Cast on: 8 stitches to each needle.
Increase to foot width, a total of 56 stitches. Do a knit round between every increase round.
Length to gusset: 40 rounds. On the last round, split the instep stitches between two needles and put all the sole stitches on one needle.
Gusset: KF/B in the first stitch; put a marker between the two halves. Knit across the instep, KF/B into the last stitch and put a marker between the two halves.
Put all the sole stitches onto one needle and split the instep stitches onto two needles.
From here on out you will knit the gusset stitches up to the marker, KF/B in the stitch before the marker, knit across, KF/B in the stitch after the marker, and knit back around, then do a plain round.
When there are 12 stitches outside of each marker, you're ready to turn the heel.
German short rows to turn the heel: 4 "funny double stitches" (minute 16 of the video) on each heel needle. This is the same thing as Carol's turning a heel in 8 rows but uses a different technique.
Work one round after finishing the German short rows to pick up all the "funny double stitches".
Then keep knitting and move all the instep stitches onto one needle while moving all the sole/heel stitches onto two needles. There should be 14 stitches on each heel needle.
On the side where your working yarn is, put the 12 gusset stitches onto a separate needle.
On the other side, move the 12 gusset stitches ONTO the heel needle using a 5th DP.
Now you are going to work the heel flap.
Knit across both heel needles and K2TOG the 14th stitch on the second heel needle with the first gusset stitch that is on that same needle. Put this stitch onto the heel needle.
Turn, purl back, and when you get to the other gusset stitches, P2TOG the 14th heel stitch with the first gusset stitch from your 4th DP needle. The result of the P2TOG goes on the heel needle..
Make sure you always have 14 stitches on each of the heel needles, and work back and forth while the number of gusset stitches decreases because of the TOG.
When you have worked up all the gusset stitches, you will be on the heel needle where you were purling. Slip the last instep stitch to this needle, bring the yarn to the front, slip the stitch back, turn, and knit across.
When you get to the other side of the instep, bring the yarn to the front, slip the instep stitch purlwise, put the yarn to the back, and slip the stitch back to the instep needle. These last two steps will keep you from having big holes where the heel flap joins the instep.
You should have 56 stitches again.
Work 20 rounds of the ankle.
Work K2/P2 rib for the leg.
Or work it smooth with lace insets.
Or divide in the middle of the back and work Fair Isle or Argyle or a couple of other patterns I will be posting about later. When you get to the top, work K2/P2 rib for the cuff, and sew up the back seam.
I emailed to Carol about her stitch counts and she said, "now you've taken the mystery out of things".
Except for two things.
The video's instructions work fine in worsted weight, but it uses M1 for the gusset stitches. That leaves holes if you are working with fingering weight like Cotton Fine. That's why I have you wrap stitches when you finish the heel flap. Carol's pattern doesn't need that.
The other mystery, of course, is kneesocks.
Most of us will need increases when we knit the calves of our kneesocks; I will need more than some of you. Do this.
Measure your calf at its widest point, multiply by stitches per inch, subtract out your 56 ankle stitches, and you know how many stitches you have to add. If it doesn't come out a multiple of 4, plan to do more stitches in the calf.
Measure your shin and multiply by your stitches per inch. That's how many rounds you will knit to the knee.
Use your spreadsheet if you have to, but make sure the increases are smooth up to the widest part of the calf. You may need to work another 25 rounds without increasing to get the sock up to your knee.
You will need most of a skein of Cotton Fine to work just one kneesock. Work the sock up to the ankle.
Following your chart, work 2 KF/B increases on each side of the sock. Once you've fitted the sock to the widest part of your calf, stop increasing.
When you finish the shin, decrease 8 stitches evenly around.
Do a k2/p2 rib cuff and bind off in rib.
If this seems too complicated, I agree. These kneesocks will fall down just like the ones some of us wore in high school. Those are two good reasons not to knit your own kneesocks. But you might want to try it anyway just for the experience.