Freemium

Similar (or indistinguishable) from free-to-play model which is for MMOs or other online games.

Common gains from paying:
* Extreme increase in productivity, often eliminating waiting for hours real-time into something instantaneous (e.g. structure building, waiting for someone to return from hospital, etc.).
* Availability of more efficient buildings or units only to paying players, possibly bordering on pay-to-win if it's multiplayer.
* Purchasing in-game resources for real money, skipping harvesting them altogether.

Editor note: it might be good idea to merge free-to-play to this tag as freemium is a bit broader in where it can be used (not limited to MMOs or other online-only games for one).