If black goes for the outside (as I would sort of expect) then I can't 100 percent remember the sequence. Hoping that I can recall the major features and read to fill in the gaps. Judging the outcome may prove more difficult

Jump.

This joseki, even though it was never really played before Ke Jie vs. AlphaGo, is just required knowledge as a dan player these days. I've seen some of my online opponents connect super passively and solidly at 6-18. I win those games

It's also not a simple joseki to tenuki from and come back later. I think my winning chances go up when he goes into this, because I can play more confusing proper moves

Only move (..I'm fairly confident it is at least)

Cut.
Probe.

The idea is to get the strongest possible attack on the two stones he just played. He will respond to this now, while the fighting is light on the top side. If he plays atari down (unusual) then I get 2-2 extension in sente or an atari on the outside at 5-15 - more aji than there is now, so it's a good exchange for me. If he plays atari out then at some point I can play 4-15 to force him to let me get one stone taller on the top. Once I'm taller I can play another jump on the top, which completely seals him in, though it doesn't capture.

Some people hold off on making this probe until later in the joseki. I don't really understand that, to be honest. My view is that I'm not very likely going to play any other move first in the corner, but I could see myself playing a push instead of a jump on the top side if he responds strangely (atari down). Therefore, I play this move first, and decide on the shape on the top later. I'm curious if anyone knows a good reason not to play this probe right away.

From his passive 3-3 response earlier I half-suspect he's planning to immediately take the territory underneath my four stones in the corner, but that's too small. The influence I get from forcing the capture is going to be worth well more than a dozen points gote.

He should atari at 2-16, and then I will jump at 10-17.

I thought I remembered this exchange coming later in the sequence usually but I guess it doesn't matter.

One space jump.

Joseki. Wait for him to commit to the two stones before making further forcing moves in the corner.

Big uncertainty here if I'm honest. I feel like I could be missing something in my reading. I think I cut on my next move but I'm still thinking it through. Not sure if that squeeze on the outside is too good for black. Also feel like black could develop a framework with the outside shape that would be tough to counter.

Atari.
Probe.

Now that he's committed, it's time for me to make the exchanges for strength on this side. If he captures I can play atari outside and then connect. it becomes a good attack for black. If he extends I can extend on this side and he's surrounded. I get influence and it's endgame-ish to capture the stones.

When I said I may cut next I wasn't considering this forcing exchange. I'm grateful that the timing of these exchanges is blacks responsibility in this sequence. I expect to cut once black has finished fixing

Extension.

He played the extension, so I get a free atari. Therefore now when he pushes up at 7-16 I can atari at 6-15 before turning on top at 7-15. This is the point of those probes, to protect the cut in advance. He could cut at 6-18, but I would get the tiger's mouth at 9-18 and good influence. Capturing the corner is too small for this stage of the game.

So now is a good time for him to tenuki. I expect an approach to my 4-4 in the upper right. We'll see what happens then.

Seems like I have to cut now. I remember when I first saw this pattern and the corner looked so good to me. Right now the outside looks pretty nice. I wonder if I was supposed to do something different so the shape is slightly worse on the outside? Tough to tell how much black can build and how easy it might be to reduce and/or invade. If my bottom side group can become 2 eyed in sente that might help my invasion prospects..

Tiger's mouth.

Aha! He's made the mistake I predicted like 6 moves ago

I mean, okay, he's still winning. But every positive exchange for me makes it a little harder for him later. After he turns at 2-2, I'm going to turn on top at 7-16, he's gonna capture, and then I'm going to enclose the upper right. It's going to be all his territory versus my huge upper right. Let me try to count. Disclaimer that you probably shouldn't use this count as a good example, blind counting is hard.

White:
The bottom right: 12ish points, and maybe he deserves a little more for the slight weakness of my bottom right group.
The bottom: He captured for 4 points and will grab another eye, call it 6 points total.
The bottom left: He's going to make a move either on the side or in the corner, so I can give him 12ish points again here.
The upper left: After the capture, he's going to have 8 points under my stones, and then another 8ish on the outside.
The left: Due to the ladder break aji in the center, I expect he'll get something good on the left. Call it another 6 points coming from nowhere in particular.
So that's a total of 12+6+12+8+8+6+komi = 60ish.

Black:
The bottom left: maybe 5 points since I'm assuming I'm answering a ladder breaker.
The bottom right: captured two stones and will make a second eye, I'll call it 7 points.
The upper right: Everything else.

So I need to make 50ish points at the upper right. Obviously, that's not very likely, but that's why he's ahead right now. It's not so out of the ballpark - I can see myself making around 40 in the upper right on a good day, doing better than expected on the left, and winning in endgame. People take positions like this that are obviously better for one side and get too wrapped up over territory counts. He's an amateur like me, he's definitely going to give me at least 20 points all over the board, I just need to spot the openings.

If I did get this pattern wrong then I have no choice now..

Making this one exchange is good while he's committing to the stones. It's very good for the outside - allowing me to get more strength out of the atari at 5-14, for example.

Many people confuse themselves about preserving ko threats - if you're getting something tangible, and you're not losing another option that could be better later, then make the forcing move. Ko threats are usually a minor concern - timing is already easily the hardest part of Go, and it's really silly to not always do your very best at it, unless you know that there's a ko on the board. I think a lot of people learned a misconception because it's much easier as a strong commentator/analyzer to mention ko threats rather than the intricacies of aji that are usually at play.

Still going to play the plan I mentioned last post.

Talked myself into this. I only just realised that the squeeze moves are pretty large but essentially endgame (in that both groups should be fine and healthy either way.) I was just about to answer anyway but caught myself thinking 'something like 17-17 is probably the better move really'. Hopefully I will learn more playing this way!

If you play 17-16, R16, then I play 17-14, R14.

Ah, he wants to play away now? It's much worse than tenuki earlier in the variation, since he has already give me the strength and I still have the option to take territory. I think it's actually bigger for him to capture once he's given me this strength, because now it has all the positive value of territory but none of the negative value of losing influence. But okay, the 3-3 is more important first, so time to make some exchanges. I ended up writing a stream of consciousness for this move.

I obviously want my influence facing the top. I think it's so important that my only option is to force it. So I should play Q17 first. He'll extend and I have several options.

If I play double hane and give him a ponnuki, his ponnuki is actually not in an awful spot, where he can follow up with a move on the side to take it all as territory. So not that.

If I hane and push a bunch he should get sente. But it's not that easy to use the sente, whether it's more important to play in the center or with the territory. It also makes the right side tiny, which is good. Playable, but maybe not perfect - it would be a hard game if continued with a jump from his center group.

If I extend and he slides, I could take sente to go take the stones. They're worth about 20 points. Looks playable, but it's so obvious that his next move would be strengthening his new group that I think I would play on top of it instead. Then I expect hane, I would tiger's mouth, and he extends. Normally you use the aji of cuts on the side to get something, but what I get would be on the right side, which is nearly worthless. Looks a little bit worse than what I deserve.

If I play knight's move, he would extend. If he plays into the flying knife when I have huge influence nearby there's no way he's gonna get a good result. So he extends, I cover, and he takes the hane. I have options then, particularly to tenuki. But I'm a little afraid that he would atari and then descend under the skirt of the top, which looks absolutely ideal for him. So I would want to continue, and I can't really switch directions with the hane on the three stones. So I guess I might double hane. If he plays atari and capture, then I can take the corner with the hane. I like the look of that, actually. I don't really see a great response - if he connects then I connect and it's a dream variation. So I'll go for it.

I also considered trying to force the flying knife in the other direction. Block the other way, let him push, knights move, and then if he pushes stand up. I don't think it's really necessary, though. I might play that way if I was down 50 points instead of 25.

He seems to be going for maximum early territory. I guess it's a viable strategy, but he's going to have to be very careful with my influence later. I'm planning on eventually capping his center group, and if he has to cede 10th line territory to that, then taking 10 points in the corner might look a little silly.

I was slightly apprehensive about black blocking the other way and double hane to give me a ponnuki in blacks sphere of influence. I don't think that would have been good for black, but it seemed tough to accurately judge the health of the ponnuki so it seemed like there was room for error.
Comfortable-ish this way. Heading towards invasion/reduction difficult decisions.

I play 18-13, S13.

Continuing my plan.

I'm out of practice with go but especially out of practice with the knights move that black played (17-14). I'm quite unsure but I'm seeing this double hane as a special case joseki and I'm surprised that my opponent thinks this is the case for it. The result looks reasonable to me though. It seems to me that black is focusing on building the top side and that seems very reasonable.