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Ralph Betza's 'About the Value of Chess Pieces' would be an excellent place to start: http://www.chessvariants.org/d.betza/pieceval/index.html
I always use Fairy-Max to evaluate the new pieces. E.g. give white Dragon Kings in stead of Rooks, and black Dragon Horses in stead of Bishops, and let it play 1000 bullet games against itself. Then you will have a pretty good idea whether the Rook or the Bishop benefits more from the enhancement. And if you repeat the experiment by giving the winning side Pawn odds, you also know by how much.
Well a few games against myself with just the changes to the pieces do suggest that the Golddragons have an advantage. However, that's before adding in a further complication of severe restrictions on crossing between the two middle ranks. Perhaps I should explain more about thet theme. The setting is either side of the Bristol Channel, the expanse of water into which the Severn estuary opens. On one side of this is the well-known territory of Wales, whose flag features a red dragon that could reasonably be represented by Ryu Shogi's Copperdragon. On the other is the part of England that in the Dark Ages was Wessex - comprising the counties of Berkshire, Devon, Dorset, Hampshire, Somerset, Wight, and Wiltshire. Wessex was one of the many Saxon and Anglian kingdoms that merged to form the original England. Descriptions of its flag vary but some accounts credit it with a gold dragon. The suggested substitution of pieces reflects the predominance of Anglicanism (with bishops) in England and especially in southern parts such as Wessex, and of nonconformist churches (Methodist, Baptist, et cetera - without bishops) in Wales. As the Bristol Channel forms a more substantial barrier than a river, I was planning to have most pieces require a Ferry (as per Ferry Xiang Qi) to cross it. However, any kind of dragon would be presumed able to fly and therefore not require a ferry. Perhaps a good way to improve the balance would be to rule that the Rook can also fly, as its English name also means a kind of bird and its Japanese name - the language of Ryu Shogi's own name - of Hisha means Flying Chariot. Now all I need is to think of a name for the variant.
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