I'm less familiar with VI than III - V, but as you mention "all its iterations", for at least III - V, the AI is purely single-threaded. And thus the AI turn times will be shortest with the fastest single-threaded CPU. Which currently is the Core i7-7700K.
However, I'd be hesitant to buy that now. If you solely play Civ on gigantic maps, and know that AI turn times in Civ are your main problem with your current laptop, it may make sense. But it only would if you are buying for that specific niche. But if we're talking 5 seconds per AI turn, it's not going to make a noticeable difference over a Core i5 7600K, or an AMD Ryzen 1600X. If we're talking 2 minutes per turn (I used to have that, or worse, on a Pentium IV with Civ III), the difference may be worth it.
Assuming it's closer to 5 seconds than 2 minutes, I'd recommend a Ryzen chip instead, either the 6-core 1600/1600X, or the 8-core 1700 (which is priced about the same as the quad-core 7700K). Over time, more games are starting to support multiple cores (including in graphics rendering, with DX12 and Vulkan, as well as AI), and thus for the long game Ryzen is the better choice. Buying a 7600K or 7700K today would be like buying a dual-core desktop CPU in 2008 or 2009. There were applications where it would be better than a quad core, but unless you were optimizing for specific, crucial applications that really needed that single-threaded performance, it was short-sighted versus buying a quad-core CPU. It's not all that uncommon to read about people still using a desktop with a Core 2 Quad processor from 2007 - 2009, but it's much more uncommon that someone is still using a Core 2 Duo desktop of the same vintage. The Ryzen, like the old Core 2 Quad, will have greater staying power.
Both Ryzen and a current-gen i5/i7 will also almost certainly be a notable increase over your current laptop, including in single-threaded applications like old versions of Civ's AI. You didn't mention what you have currently, but even Intel's most expensive mobile CPUs aren't going to be able to match either AMD or Intel's current desktop chips, due to thermal constraints and lower clock speeds to meet those constraints.
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My current build is from 2011, somewhat upgraded. Core i5 2500K (very mildly overclocked) quad-core, 8 GB RAM, Radeon RX 480 (haven't found a strategy game that makes it sweat yet; added last fall), Samsung 850 Evo SSD as the primary storage. Definitely agree with Jaybe, an SSD is the single biggest improvement you can make to general responsiveness; don't buy or build a new system without one. Use a hard drive for bulk storage if you need the space (I have two 2 TB HDDs, one of which is backup), but get an SSD for your operating system and frequently-used programs. I may well rebuild it into a Ryzen system this summer, but I don't really need to and I've been upgrading other aspects of my apartment instead the past couple months.