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I'm taking a chance as images don't seem to work as expected here, but....

In the above position, Takagawa resigned against Go Seigen (no komi, Black has captured three stones and White four). This was a game in a major match and so time was not an issue. Furthermore, it attracted a bevy of strong amateurs (including sponsors) and a very strong commentator.

All were surprised that Takagawa resigned so early. They thought the games was close. The commentator added that among amateurs in general he would expect many would say White was ahead and many would say Black.

Takagawa later revealed his reason for resigning.

My first question is: what is it about this position that makes it so hard for strong amateurs to count? My second question is: what made Takagawa resign. Takagawa's own answer to the latter question is illuminating in more ways than one.

It would make most sense, as an exercise in discussing human thinking, if people refrained from quoting AI at this stage.

I will give the full actual answers later, to avoid spoilers.

OK, I'll hide my answer so people can look at it after having a try themselves.

Thanks John for the interesting Christmas present!

I can try to explain my thinking.

The context of the game is that it was part of a ten-game match to gauge how strong was. At this stage he was still officially 8-dan but as he did not play in the Oteai then he had no normal way to become 9-dan. He was pitted against the top 7 and 6-dans, giving the appropriate handicap in each case. In Takagawa's case, the game was in the W portion of B-W-B, and so everyone was already saying Takagawa had a "challenging" game ahead. But Takagawa arrived 3 or 4 days ahead of the game and it was assumed he was devising a secret strategy. Whether he did or did not, he got a good game and was considered to be perhaps marginally ahead until he made a critical mistake on move 70, and despite a promising attempt to recover momentum, he ended up making a futile move 80. The rest of the game was just a slow descent to the resignation position, so Takagawa may have became dispirited in the process.

In any event, what he said when the Yomiuri reporter caught up with him after the game, in an effort to explain to himself and the amateurs why he resigned when the game looked close either way, and even if it wasn't really that close why he didn't dig in and play on, was: "The game is close, but from here on, Black's territory will only increase, while mine will only decrease. And given my opponent is Go Seigen, it would be a considerable difference."

I drew two inferences from that. One is that at least some of the amateurs were simply counting the board as it was, and were not taking account of the possible actual moves. The other is that Go was exerting a powerful psychological effect on all other players. Another piece of evidence for that is that it was around this time that Hashimoto Utaro was complaining about hearing drums beating loudly whenever he sat opposite Go at the board. He was clearly just hearing his own heart pounding in his ears, but stress makes people think irrational things. Or perhaps rational given that Go went to win the match 8.5 to 1.5.

KaTrain appears to believe that Black is a good 10 points ahead at the resignation point. In another source, Takagawa, while making the same point that only Black could add more territory from the resignation point, said that at that resignation point White was about 5 points behind, so that presumably gives us his definition of "close" (the usual informal scale seems to be (1) jigo-ichi, (2) close, (3, above 5 points) X is ahead, or equivalent). We can infer that he had the same sort of sense of the final outcome as KaTrain.

An amusing anecdote from after the game is that a landslide triggered by a heavy storm blocked the railway lines, and so the party had to stay in Hakone. A member of the public overheard the Yomirui reporter telephoning the news back to the office and spread the word. He message was "Just seeing their faces will make you better at go." So they mobbed the inn. But instead of asking for autographs or selfies or tearing off bits of the stars' clothing, a bunch of old guys lined up in the inn vestibule and prostrated themselves on the concrete floor. Ah, the good old days...

For those who want to see the whole game, it is 1949-10-18a in the GoGoD database.