Long time no see everyone, back from the summer vacation. And I agree with @mark5000 to probe at G13.
Here is one of the variations if white extend back at F14 with move 4 (it’s a terrible idea IMO). Black would be able to push through at E14 (assume white chooses to atari at G14). The difference is that the black B6 now works. It would be a ko if white answer with either of the points A, B, and C (the ko with point B is a bit different). The key is that black can now use the area around L16 for numerous ko threats, and white only has local ko threats that would run out, and has to take the ko. And black would get extra move on the top to either escape or living locally (depends on how white answer the ko before). But the area on the lower center left is presumed to be white to begin with. And black just gets an extra move to reduce the top white moyo.
If white choose to block at E14 for black E13, then black can use nose tesuji to push the center boundary right on the white’s boarder, and gain nearly 20 points, and keep sente (and use like P7 to attack the lower right white group). Black doesn’t even need to care about L16, the points along in yose would just win the game (I estimate like 90+ for black and 80+ for white).
The safer way for white to answer black F12 is probably just connect at E13. Although that by itself creates other issues further down the line (the black nose tesuji would still work, but the upper left black group is not yet alive as I pointed out months ago, so the result is still hard to say, probably a few points less than black push through E13 (which black would be connected to the center and no need to worry about life and death, and a big reason why black can afford to lose the ko in situation where white extend back at F14, and black start the ko. Even if white gets A18 to take away the second eye, black can just connect to the center and live. However, if the white disconnect the center with upper left black group with E13, then when black loses the ko, black would need to play around C18 to make it alive and gote)
And there are several ways to answer G13, clamp at H13 (I believe @mark5000 mentioned that when I brought up the G13 probe months ago), cut at G12, or jump back at H14.
H13 seems to be a safe option, but leave for black the chance to extend at G14, which later could mean a big different in the live and death or semeai in the upper right corner if black want’s to live there (or ko). I already discuss a bit about G12 cut, and even if white connect E13, it still leaves more room for black G13 as an aji to do all kinds of things later. I am not sure about jump back at H14, but it limits black’s aji the best, however it might give black a few small sente yose later. This reminded me of a Chinese Go saying 後中先, a seemingly gote move, end up cancelling the sente move for the opponent further down the line (like a special kind of sente). And finally, there is always the option of tenuki, but I don’t see a better place to play though (maybe just play around L16 to reduce its aji? Or secure the lower right corner? I don’t know if it is still in time to invade or reduce the black moyo, consider the black moyo is so high, the invasion would need to be pretty deep)
), if no more come in.
