I am actually part of the team behind "Just Tactics" which is largely based around hidden information (fog of war, customizable cards and unit deployments) while minimizing the use of random based mechanics like dice rolls. It's also 1v1 online.
There are plenty of mind games that occur in higher level play. For instance, luring the opponent into an ambush, attempting to trick the opponent into wasting his or her cards on certain units, etc. Victory is obtained by outscoring the opponent, and points are obtained by killing units or holding "Control Towers" per turn for points.
If you are interested in it, be sure to friend me, I'm "Justin" and am available almost anytime I'm online. The website is justtactics.com.