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I love the concept of spherical chess. I think one thing needs to be changed, however. Chess is already drawish enough on a square board, and more so on a round board. On a spherical board, where pieces move in all directions, draws may become the overwhelming norm. That is not my preference.
So, on a board like this, I would love to see something done about that. Possible ways to do it would be to put some restrictions on the movement of the King (as in XiangQi and Janggi), or to immobilize the King when in check, or to take away the King's ability to capture pieces, including attacking pieces.
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The only game completed so far ended in checkmate. The pole amplified the power of the Queen, allowing a checkmate in a position that would not be checkmate in Chess.
If you check the rules page for Spherical Chess, you will find multiple variants. The one called Sphere Chess has limited the King's powers of movement to those in Chess on a 2D board.