Anyone want a game?
Escaper chess
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Why is it called Escaper chess?
I saw some examples of games played this way, and they usually end really fast. White may also have a significant first-move advantage in this variant.
Would you consider playing "Chess on an Infinite Plane" where only pawns can be moved twice? (In one move, each player can move one piece, or any two different pawns).
An example of a normal infinite chess game is (here) so you can see with the extra pawns the idea might work.
You have 2 moves for each turn. Capture the enemy king.