There's nothing in "roll to move" that inherently forbids decisions. There are millions of ways to implement it that allow for tactical/strategic choices:

There are tons of boardgame-adaptations on iOS (and, to a lesser extent, on Android), and many of them support asynchronous online multiplayer mode. I bought an iPad just because of it. Having said that, although it scratches the itch somewhat, it's still far from the experience of getting together with your friends…

You don't seem to fully grasp the meanings of "rip-off" and "creativity". If they made a movie with the exact same story, that would be a rip-off and an indication of lack of creativity. Designing a boardgame that faithfully represents the central idea and the feel of the movie is far from trivial, it needs a ton of…

Pathfinder Adventure Card Game, Eldritch Horror, Robinson Crusoe, Firefly: The Game, Police Precinct

Guards Guards was designed by a couple of amateurs. Ankh-Morpork, on the other hand, was designed by Martin Wallace, one of the best boardgame-designers ever. The Witches is also his design. But be warned: it's a much lighter game than Ankh-Morpork, kind of a family game, with lots of dice-rolling. If you want…

Star Wars - X-Wing Miniatures Game by Fantasy Flight Games

Google: ios board games
Check the boardgamegeek, pocket gamer, and ipadboardgames links. You will find more great board game apps than you will ever have the time to play.

I love Android, but please note that the description here is a bit misleading. It's not a Clue-like deduction game. The identity of the murderer is not decided at the beginning, it's up to the players, who gets convicted. The players are not really investigators, more like mystery writers who collectively write a noir…

Some say that Mage Knight is best played solo. Just give it a try.