This app was mentioned in 24 comments, with an average of 25.17 upvotes
My girlfriend and I just both purchased the Patchwork app (her on iOS and me on Android). We have been playing that almost non-stop. It's a great fun, little 2 player game with a cute, abstract theme. I do not own, nor have I played, the physical version of the game, but we are really enjoying being able to play that together on our phones or pass and play on our iPad. And (assuming you have smart phones) you would already be bringing it with you every where you go.
Patchwork is my favourite approachable strategy game on both real life and for phones. It's on all phone types, even Windows, and it's themed as competitive quilt building. You slot Tetris-style shapes together, and compete to get the most useful pieces so that your quilt is the least full of holes. It uses pretty clever yet simple mechanics, such as trading "time" - how close you are to having no more turns left - for quilt pieces, scaled by how good they are.
https://play.google.com/store/apps/details?id=com.digidiced.pxwrelease
Look at some of the board game apps. My wife and I are currently doing the long distance thing as well, and she really likes Patchwork. Rules are pretty simple, but the strategy is deep enough to provide a lot of replayability.
Two good puzzle boardgames that have excellent online or offline multiplayer are Patchwork and Cottage Garden .
Also on android: link
Patchwork (currently on sale for 33% off) is great, Star Realms works really well on a phone, Red7 is pretty good for a quick game
I love both. I think the app for Patchwork has replaced the base game for me however.
Azul is one of my favorite games of all-time and might be top two for me. However, it does have a more direct interaction as you can clearly take pieces your opponent is aiming for. I'm fine with that but not everyone is.
Patchwork The Game | 4.4 rating | $3.49 with IAP | 10,000+ downloads | Search manually
> In this award-winning board game for two, quilting has never been more competitive! In the long-awaited digital adaptation of Uwe Rosenberg's Patchwork, players patch their way to victory using fabric pieces of assorted sizes, colors, ...
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Looks like a few more are on sale.
Patchwork : https://play.google.com/store/apps/details?id=com.digidiced.pxwrelease
Potuon Explosion : https://play.google.com/store/apps/details?id=com.asmodeedigital.potionexplosion
Small world 2 : https://play.google.com/store/apps/details?id=com.daysofwonder.smallworld2
Patchwork. Great single-player or two-player board game. Includes online multi-player, and is still pretty active.