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I've been toying with a similar idea for the last couple of days and decided to google it. I'm happy to see other people have also thought of this. All in all, I like your initial board setup but I don't like the knight movement change and the pawn promotion rules are hard to learn. Diagonal chess should be casual, fun and easy, when you are bored of the normal one! In my current design, pawn promotion only happens at the very last square (H8). This might seem near impossible to achieve, but my pawn movement is also different. You can move them in either diagonal and only eat straight forward. Exactly the opposite of the image above. This makes the game completely different and quite fun, as you can group pawns from different lanes together in creative formations. I have also toyed with dropping one of the bishops instead of the 8th pawn. The initial board setup is thus different, with a knight by each rook, the 8th pawn in the center, and the queen and bishop adjacent to the king.
A friend and I 'invented' a variation like this independently, except we had the knights moving 'normally' -- just the pawns were different. And we didn't do pawn promotion at all. It made things a lot more interesting without having to remember a whole new set of rules. Normal chess stategy almost applies, but also keeps tripping you up as you forget which way things are going! Like the description says, one nice thing about this is that you can use a regular chess set -- important as we only had the one!
At first glance I thought the promotion limits rather odd, but now I can see that the Queening squares are indeed harder to get to than other promotion squares from binomial theory. It still seems slightly odd that the Knights have been turned into Camels in all but name, although it is a good illustration of the connection between the two leapers' moves. One thing to do with the 8th Pawn would be stick it on top of the left Rook to represent a real (unbound) Knight. That way the radial linepieces would be one bound to each square colour on the left and a single unbound one on the right, and the oblique leapers would be the other way round.
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