Using the table above (which is very helpful), I think the table and manual are in error for minimum supply provided by HQ. I also think the game is universally counting all supply sources as a 5, even if they are a 3 (port of Amoy).
Amoy itself has a supply value of 3, the adjacent port has a supply value of 5. Ports provide supply inland just like any other resource, as long as no enemy unit is adjacent to it. If you parked an enemy destroyer or moved a Chinese corps next to that port, the supply for the Amoy hex itself would drop to 3. This is why even small towns (such as in Norway) with a native supply of 3 are much more valuable to invade because of the port. Without a link to a Secondary Supply, it's the only way to get 5 native supply during an amphibious invasion. Other examples are most of the islands in the Pacific. The island towns are only 3 supply (again, because no links to a capital/secondary supply) but the ports themselves provide 5 as long as they are clear.
If you follow me below, I also think the game engine is using 8 as the minimum supply value from an HQ. As a test, at the start of game I used the Japanese HQ in Haikuo and I moved the I Corps to the SE corner of Nanning.
I click S once and I get 8,6,0,0 (I believe this is nonHQ supply and I believe this should be 5,3,0,0 because Haikuo has 5 supply). I click S again, and I get 8,6,5,2.
(1) I click S once:
Starting at Haikuo and going three hexes North, the nonHQ Supply is 8 (Haikuo), the next is 6, the third (Pakhoi) is 0, and the fourth hex (I Corps SE of Nanning) is also 0. So 8,6,0,0. Haikuo is a supply of 5 and without the HQ I believe this should have stayed a five, and should have been 5(Haikuo),3,0,0(I Corps).
(2) I click S twice:
I click the HQ Supply (second click, see above) and it goes 8 (HQ hex, Haikuo),6,5,2. Per the table above, this is correct because Haikuo’s 5 becomes an 8. So the “second click on S” seems to work.
(3) I move the HQ one hex north and it becomes 7,8 (HQ hex),7,4(I Corps). Considering the correct nonHQ Supply should have been 5,3,0,0, this would have placed the HQ on a hex with 3 Supply which is also is an 8.., So again all is good.
(4) Now things appear to go wrong. I move the HQ one more hex north (adjacent to I Corp) and this is supply of 0, which becomes a 5 with the HQ. But the HQ supply says 5,6,8(HQ hex),5(I Corp, SE of Nanning). I believe it should be 5,4,5,2.
You're misunderstanding lots of things here. The initial 8,6,0,0 is because that's the *current* supply from the start of this turn. At the start of this turn the last two hexes (0,0) are not yours, and provide zero supply. When you moved the corps up to Nanning they are now yours, and *next* turn will start producing supply. This is why on the second press of "S" you see the predicted supply for the next turn, and it is correct -- 8,6,5,2.
I'll break down this 8,6,5,2 for you: The 8 is from the HQ itself as per the chart (it is standing in Haikou which is providing 5 supply. If you click on the HQ you can see it says "Supply: 5(8)" to demonstrate this. The 6 is because the next hex is bad terrain (a "river" in game terms). This causes a double-dip in supply between adjacent hexes. This is why it goes from 8 to 6. The next hex, a 5, is normal drop per hex of 1 point in clear terrain (this terrain is along a road, so even if it was not clear terrain, it would still be a 1 point drop). This 5 is coming from the HQ and not Pakhoi next turn. Pakhoi will be red-numbered supply (probably 3) because you just captured it, and the HQ will provide more so his is used in the prediction. If you disbanded that HQ, then followed the exact same steps, you'd see 3 supply for the Pakhoi hex next turn.
All of the problems you have in steps 2-4 go back to misunderstanding how it works in step 1.
If we assume the game engine is correctly performing its supply calculations, then the table (and manual) is incorrect in that the GAME ENGINE IS COUNTING THE MINIMUM SUPPLY IMPACT OF AN HQ TO BE AN 8 AND INCORRECTLY COUNTING ALL SUPPLY SOURCES AS A 5 EVEN IF THEY ARE LOWER. Go thru my numbers above and that would be the solution to the multiple observations above.
PS – if I am wrong, I am going to feel like a complete idiot an I will not post for months due to extreme embarrassment.
The tables in the manual have a typo in one sentence. I mentioned this in a post above. Otherwise they are correct. The matrix I created above is correct. You are misunderstanding quite a few things, mainly the way the "S" predictions are determined, the way terrain is affecting these drops, and that ports provide their own supply inland as well.