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?

Chinese Checkers has 6 Points where people start:

The 6 corners allow 6 players a secure base to start from.

What if we adapt this idea into a Go board?

More Corners

Sometimes, less is more.

Fewer corners. Each player picks one to start.

One interesting aspect of the Stratego board is that it has terrain features in the middle:

Courtesy of Mark Alldrige. Stratego is copyright Milton Bradley, 1980

What if we cut out a some spaces in the middle of a go board, like this:

Terrain features in the middle of the battlefield

Or combine some of these ideas:

Corners and Center are now out of play.

How would each of these variations modify the game? Many of the tactical patterns would stay the same, but would have a different role in the overall strategy.