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Other strategy board games also have things like this. If you like Chess, you might also enjoy Go. Here is a link to an online website where you can play correspondence Go: https://online-go.com/ In general, what you are looking for are correspondence games, so here is a website with a bunch of these games: http://gamesbyemail.com/
People play Diplomacy in that manner. It give you lots of times to contact other people to make deals with them between submitting your moves.
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