I was wondering if anyone know good examples of competitive 1v1 games that makes fantastic use of hidden information without it becoming too "luck based" like Poker?

As far as I know, the only good example is Netrunner CCG (or its recenty reboot, Android: Netrunner). In Netrunner, one player is "the Corporation" that tries to advance hidden agendas (faced down cards) guarded by hidden defenses. The other player tries to hack into these agendas and is sometimes able to flip them up to reveal what they actually are.

I got interested in this topic when thinking about redesigning the classic Battleship guessing game. http://en.wikipedia.org/wiki/Battleship_(game) What if each player controls just 1 battleship and 2 smaller vessels, which are allowed to move around? Once discovered, a ship stays discovered until it does something to hide again. Firing your cannons reveal your position. So there is some interesting trade-offs between taking out a discovered ship and hiding all of yours etc.

that would be any decent war game that implements fog of war

Oh yes. I suppose that is correct. Perhaps I should have said that I am looking for competitive 1v1 games with a heavy focus on or is built around hidden information, but yet not too reliant on bluffing like poker.

Well, the first thing that springs to mind, even though its not a 1v1 game, is a Gary's mod game called Trouble in Terrorist Town. It is, in fact, an FPS, however its more of a mind game than anything.

http://en.wikipedia.org/wiki/Trouble_in_Terrorist_Town

I actually LOVE these sorts of games and wish there were more of them. I love hidden agendas and secret keeping in a multi-player setting. Regarding the Battleship idea, I think that sounds pretty fun, think about giving players 1 move plus 1 offensive action per turn or something like that. Maybe give players the ability to fire some kind of deception round, which wouldn't hit anything but would give a false position to the opponent.

Yeah, I love "mind games" involving deduction, that doesn't heavily rely on luck (maximizing expected returns in the long run).

I think there is a lot of design space when it comes to games that revolve around hidden information. Not sure why designers haven't tapped into it yet. Maybe its because the standard idea of such games is poker which heavily influence design to incorporate gambling, bluffing and luck.

I mean for example: you have a hidden ship in firing range of an opponent's ship that has just revealed itself. You have an opponent to fire at the ship and reveal your position, or you can play mind games and stay hidden. Also, your opponent could have chosen to reveal that ship to bait you to reveal yours. And etc.

that would be any decent war game that implements fog of war

Inaccurate.

Shroud would be more accurate.

Fog of War does not regrow, whereas shroud goes (it was the initial difference between the gameplay of Warcraft 1 & Dune 2 vs Warcraft 2 and new generation RTS games.

Shroud would be more accurate.
Fog of War does not regrow, whereas shroud goes.

shroud VS FOW is game specific terminology - many games using what you call 'shroud', use the term 'FOW' for it. In general terms, FOW just means youve got imperfect, inaccurate or conflicting information about or communication across the arena.

Yeah, I always thought FOW is the one that regrows while Shroud is the one that goes away once you explored the map.

Wiki has mixes the two terms: http://en.wikipedia.org/wiki/Fog_of_war#Simulations_and_games

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.