In Undefended Pawns in Chess960 Start Positions, I introduced the term 'twin',
Two start positions (SPs) which are the mirror image of each other; the pieces in one twin (running from the a- to the h-file) are in the same sequence as the other twin (running from the h- to the a-file).
and explained why I thought twins were worthy of special scrutiny:
They present exactly the same opportunities for the initial development of the pieces. Only when castling becomes possible do they start to take on individual characteristics.
In Chess960 Opening Theory, I used a familiar example of twins when I compared SP518 (RNBQKBNR, the start position for traditional chess) with SP534 (RNBKQBNR, the same as SP518 with the King and Queen switched). The concept of twins means that the same positional factors applying to one SP also apply to its twin. It reduces the number of truly distinct start positions from 960 to 480.
The following diagram is an example of 'twin thinking' suggested by a recent game of mine. I had White in a game starting with the position in the top diagram (SP448). At first glance, I was tempted to castle O-O. The Queen has only to move off the back rank, perhaps along the a7-g1 diagonal, and castling O-O is possible. Castling O-O-O takes the same amount of preparation, since both Knights only have to leave the back rank, but it is not yet clear which development of the Knights will be best.
A second glance convinced me that castling O-O was dangerous. The enemy Bishops are already aimed at that side of the board and can be quickly supported by both Knights, the g- & h-Pawns, and the heavy pieces behind those Pawns. I decided to castle O-O-O and achieved this on the fifth move. My opponent failed to take any special action for castling, realized after my O-O-O that his O-O was too dangerous, got caught with the King in the center, and had a lost game after 20 moves.
Top: Start Position 448
Bottom: Start Position 703
The position in the bottom diagram (SP703) is the twin of SP448. Now castling O-O-O is dangerous for the same reasons as O-O in the top diagram: the enemy Bishops would be aimed at the castled King, and the a- & b-Pawns, supported by the Knights and by the heavy pieces, would present a potent attacking force. The players should consider castling O-O, even though three pieces must first be developed: the two Knights and the Bishop on the g-file.
For each of the 960 different SPs, I documented its twin on my page about Chess960 [Fischer Random Chess] Start Positions.