The Very Long Train Game
I love the Empire Builder series of train games. With these "crayon" games, you draw railroad track on the board with a crayon or dry erase marker, then move one train between cities on the track, while cards provide cargo-to-city jobs to earn money. You win by connecting major cities and amassing a certain amount of money.
These games tickle my "optimization" pleasure center with just the right mix of build strategy, randomness, and competition for good routes and cargos. The trick is to find the balance between spending to build an efficient track network and operating to make money.
It is slow to play, particularly in the early turns, as everyone ponders possible track builds and deliveries. Called "The Very Long Train Game" in my house, my wife once self-induced labor on the first turn to get out of playing.
However, it's an ideal "play your turn when you can" game. We kept a long-term game in an empty cubicle at work and in the living room of a house I shared with some friends. A marker indicated who had the turn, and they would advance it to the next person after they played. Games could span weeks, and everyone had as much time as they wanted.
Empire Builder uses a US map, but variants cover Europe, Japan, Britain, Australia, India, the USSR, the Moon, and Mars. My favorite is a fantasy land version called Iron Dragon. Sadly, Mayfair Games shut down in 2018 and sold their assets (primarily the Catan series) to Asmodee. The crayon games are no longer in production as of 2022.
There have been several crayon rail computer adaptations. EB Pronto tries to match the Empire Builder boards closely. In 2005, Bret Mulvey created Rails, shown below, which can use predefined maps or generate them on the fly. I quite enjoy playing against five computers on a randomly generated map. I recently contacted him and he graciously released the source on Github. I hope to add some updates soon!