I think Strategy-stealing arguments from combinatorial game theory fit into vein. Here is a classic example.

Prove that in two-move chess, Black does not have a winning strategy.

Proof. Suppose not. White can move one of her knights on her first move, and then return the knight to its original square on her second move. By symmetry, she is now playing as Black and can use Black's winning strategy against Black. $\square$

Here the 'extra camel' is to do nothing and end up as the second player.

I think Strategy-stealing arguments from combinatorial game theory are in the same vein. Here is a classic example.

Prove that in two-move chess, Black does not have a winning strategy.

Proof. Suppose not. White can move one of her knights on her first move, and then return the knight to its original square on her second move. By symmetry, she is now playing as Black and can use Black's winning strategy against Black. $\square$

Here the 'extra camel' is to do nothing and end up as the second player.