The Game of Go is still pretty much the ultimate strategy game. No other game distills strategy to its essence, in such simplicity, and thus lets the complexity emerge.
The board is simplicity itself: a 19 X 19 Grid:
Standard Go board
One aspect of Go is that you start from the corners, build a semi-secure formation, and then grow out from there.
For example, here is a recent game of mine in the early stages:
Both my opponent and I have staked out positions in the corners.
What if the board was a little different?
“Go (Chinese: 圍棋 wéiqí, Japanese: 囲碁 igo, [nb 2] Korean: 바둑 baduk, Vietnamese: cờ vây, common meaning: “encircling game”) is a board game for two players that originated in China more than 2,500 years ago.” — From the Wikipedia Article
I love this game. It keeps me humble. No other game teaches so much so simply. Go is about influence. But sometimes, it is about tactics. I recently lost a game. I made not 1, but 3 mistakes, that cost me the game. If I had not made any one of these three I would have won, and quite soundly. Instead, I lost by 1.5 points, a very close game.