Diplomacy has no cards (or dice) either, and is all about bluff. In any game with 3 or more players you can pretend to ally with one person but be really planning to stab them in the back.
Many games radically change between two players and 3 players. e.g. monopoly, settlers of catan. With two players, their trading mechanics don't kick in, and they're just dice-rolling contests.
Then again, I think random chance is necessary for there to be a certain balance. If everything was static, there would be just 'One Perfect Way', and it would suck all of the fun out of games.
Like how most RPG's have damage be an X - Y figure, and include crits; just because the luck element spices up the game.
Well, chess doesn't have luck, and there's definitely no agreement on a perfect sequence of moves. Chess has been superbly balanced over 1000 years though. I'm kinda interested now in possible links between chaos theory and games like chess now. Chess is so well-balanced it's on a knife edge and deterministic yet entirely unpredictable. If you change any of the rules, it just deteriorates into a much more predictable, lesser game. These qualities sounds a lot like chaotic systems theory, where on the cusp between two stable states, you get this chaotic behavior system.