Perhaps the game is less deterministic if you can choose any board as soon as the board is won - not when it is filled. Then, you can only force 3 moves before

Perhaps the game is less deterministic if you can choose any board as soon as the board is won - not when it is filled. Then, you can only force 3 moves before you have to give up control. Then approaches like the Orwin gambit would not work (it is too costly to lose a board if it only lets you choose three spots.)