Our first recommendation
War.app (Warzone)
War.app, the game long known as Warzone and before that Warlight, takes the familiar Risk-style board and stretches it in every direction: hand-made community levels for solo evenings, quickmatch for a short fight, and ladders for the stubborn.
Formerly Warzone and WarlightBrowser, iOS and AndroidSolo levels plus ladders
What earns it the top of our table is range. On a slow Sunday you can work through single-player levels built by other players, each one a little logic puzzle about where to deploy and which region to finish first. On a weekday you can open a multiplayer game and take a turn on your phone while the kettle boils. The rules stay the same everywhere: deploy, attack bordering territories, and complete bonus regions for extra income. The map designer and the clan scene give it a life well beyond the default board.