Tac-Tic-Turn

Tac-Tic-Turn is a 1987 game by Ned Strongin, published at IRWIN Games.

This is a variant of Tic-Tac-Toe played with nine 2x2 pieces that can be picked and rotated back.

Rules:

• On his turn the player either:
• drops a friendly piece on an empty square
• rotates a 2x2 grid by 90º degrees
  
• Wins the player that make a 4, or longer, in-a-row

The game had a review on GAMES #99,

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Yasuhiro Jisai mentions that a variant of this game is marketed in Japan as Pitagoras, and includes a custodian capture for pair of pieces (like in Pente).

I went searching (ピタゴラスゲーム) and found this page where it is said: 相手の駒２個を自分の駒で挟むと取ることができます（１個を挟んでも取れません）[You can capture your opponent's pieces by sandwiching two of them between your own pieces. (You cannot capture by sandwiching just one piece.)]

This game comes with more pieces (which makes sense, given that captures are allowed),

Otherwise, having just six pieces, the captured pieces should be returned to the respective player's reserve.

Some comments from the mentioned page:

You know, I think this is quite a brilliant game. If you focus too much on lining up pieces, you'll get captured. But if you only think about capturing or blocking your opponent, you might overlook the rotation mechanic. And predicting how the board will change after a rotation is really tricky!"

Yuki-Onna highly praised the game, saying that constantly considering the effects of "sandwiching," "lining up," and "rotating" makes it excellent for training flexible thinking and multi-angle strategy planning.