My assumption for SIP is that it keeps the PH but loses the western grass hill to a second (or third) city over there. Is this a dangerous assumption to make?
Just because a square gets shared does not mean that it is lost to a particular City. If we are building a Wonder, are using Bureaucracy for additional Hammers, or just decide that the capital needs the Grassland Hills Mine more than a secondary City does, than nothing stops the capital from using said production square.
Another thought is that we have been settling the island to the west because it has Fish, is close, uses that Clam, etc. But there's also an island to the south (in our test game and in the real game) that could equally use that Clam but would not borrow the GH Mine at all.
Here's Mitchum's screenshot of the real game again, for reference:
So, while I see no "danger" in assuming that another City might have the opportunity to share one of the capital's squares, I also don't see why we would discount this production square from the capital.
If it turns out that we think that another City needs that production more than the capital does, then that was our decision. Say, for example, this western City turns out to be a great Heroic Epic site, then base Hammers * 100%, as opposed to Bureaucracy's base Hammers * 50%. But then, we made the choice to give up the capital's production in favour of a better reason... lacking said better reason, I think that it is fair to assume that the capital will have access to this production if it wants it.
Also, I'm secretly a fan of corn (I love high base hammers) but have yet to make a save that shows its awesomeness. Corn also almost certainly gives up a spot on the western island unless there's more seafood since Paris needs to keep all three clams in that situation.
By settling on the Corn, we almost certainly want to settle a City to the west or south-west in order to pick up the 3rd Clam.
So, I don't think that you have to "give up a spot" just because you settled on the Corn. What we give up by settling on the Corn in the long-term is the ability to run one additional Specialist (3 additional Food from working a Corn Resource minus the additional +1 Food from settle-on-Corn's City Centre of 3 Food = a difference of 2 Food = 1 Specialist by not settling on the Corn). If the short-term results can show a good payoff, then this loss of one additional Specialist (or whatever else you want to do with the Food) can be considered to be worth it...
LowtherCastle said:
PH has +1f.
SIP: 2f1h+1f3h+4h = 3f8h
PH: 2f2h+1f3h+1f3h = 4f8h
Okay, that's a pretty neat way of looking at the math!
When I'm building a Wonder, though, I'm focusing almost purely on the raw base Hammers, not whipping-based production, because whipping Wonders makes for inefficient whipping.
That said, I suppose that it could be argued that whipping other build items so that they overflow many Hammers into a Wonder could give you a bit more production, and having a bit more Food could allow you to do so slightly more often, as long as we still have additional Happiness available to whip.