Efficient Strategy Games

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I like efficiency, and part of efficiency is eliminating redundancies and all that is inessential.
There was a game first coded in 2001 by Taro Ito called Dice Wars that embodies this idea well.

It is a game like the classic board game, RISK! or the newer Conqueror! - a territory-expansion game based on invasions and dice rolls.
But instead of having territories equal values and instead of having the number of dice rolled based on the number of territories in control, Dice Wars uses the dice themselves as the "armies".
It is an elegant interpretation.

In 2006, KDice a multi-player version was released by a different developer, Ryan Dewsbury.

And more recently, a version with an American presidential campaign theme was released - Battleground States

No credit was given to the original, unfortunately, but it is still worth playing. The rules are changed slightly. In the original, the number of armies earned at the end of each turn is based on the number of territories in the largest contiguous area.
In Battleground States, all territories are counted.

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A different, yet similar kind of game is Nano War
It is also a territory-expansion game, although more of a Real-Time Strategy (RTS) game than Dice Wars, simply because resources are generated on-the-fly, rather than at the end of each turn.
Nano Wars is also wonderfully efficient in that it does away with all aspects of the game that don't directly relate to the strategy - so no pictures of monsters or storylines about the heir to a throne, and no fussing with gold resources versus wood resources.

Like most RTSs, Nano War is winnable by a simple strategy of quick initial attack.

Nano War also has very compelling musical effects.