Questions about entropy

[hope366]

Thank you for adding this interesting feature called entropy. There are a few things I would like you to tell me. Thank you in advance if you don't mind. See the screenshot below.

• Entropy is usually displayed as a "small red dot", but in the middle and at the end it becomes a "slightly larger red dot". What is the difference?
• Where are the upper and lower limits of entropy display? I think the lower limit is at the bottom of the graph, but where is the upper limit?
• What kind of parameters and calculations were used to derive the entropy display?
• The game ended with a large group of whites in the lower right corner being captured. Regarding the last part, even beginners can see that the white group is captured, but the entropy seems to be quite high. Is entropy unrelated to "uncertainty" regarding the life and death of stones?

[kaorahi]

Larger red dots indicate values higher than a threshold, allowing us to identify heated situations. I find it interesting that stone entropy tends to be smaller in professional games from the Showa period and larger in recent international games.

Its lower bound corresponds to the bottom of the winrate chart. I'm not certain about the upper bound, but it's very very rare for it to exceed the 50% line on the chart.

KataGo estimates the ownership at each point on the board, assigning values that range from -1 (representing 100% white) to +1 (representing 100% black). This is indicated by small black/white squares on the board, depending on the settings in the menu (View > KataGo settings > Estimate info). The entropy of the ownership is zero for 100% black or 100% white, and attains the largest value at ownership = 0 (50% black, 50% white). The "stone entropy" is defined as the sum of such entropy over all existing stones on the board.

In the following diagram, green "8" indicates "ownership = +0.8" and pink "3" indicates "ownership = -0.3". The entropy is zero for "10" and higher for smaller digits.

The stone entropy of this board remains high due to the presence of many green "8"s at the bottom right, "1"s to "3"s at the top left, and "5"s to "8"s on the top and the left. It seems that the existence of ko on the left influences the uncertainty of the life/death status in the rest of the board.

[hope366]

Thank you very much for your detailed explanation.

In this game, the last part has the highest entropy, but I thought the reason was the result of the big battle in the bottom right. After reading your explanation, my way of thinking turned out to be wrong. The big ko in the top left happened in the last part of the game. This is the reason why the last part has high entropy. The big battle in the bottom right takes place in the middle of the game, and the big red dot in the middle of the graph seems to be caused by it.

The low entropy of old games (syowa) probably suggests that there were many games in the old days where players proceeded while confirming mutual ownership.

Finally, I will attach a record of this game. sibano-sakai.zip

P.S.: When I saved the file with entropy displayed and restarted it, the entropy was not displayed. There was no indication of ownership, so I guess it's linked to that? It was a little disappointing.