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As I say, the term is not my own, it just fitted with my idea for enhancing the Xiang Qi Elephant (as now finally featured in my Cannonless XQ variants at http://www.chessvariants.org/xiangqivariants.dir/xq_vars.html). It has since occurred to me that you can even have MD Pawns. 'But Pawns move only one step!' I hear you cry. Ah, but what if you extend the initial double move to captures, allowing a Pawn on its starting rank to make two successive captures in the same (diagonal) direction in one move? This thought occurred to me when devising a variant in which the Pawn's double move may be two noncapturing orthogonal moves, two capturing diagonal moves, or one of each in either order. I plan to submit the variant under the name Eurofighter Chess, as it extends a double move first introduced in Europe.
'Multiple displacers' is an awkward term. How about 'sweepers'?
Sorry, I left myself an instruction while offline and forgot to obey it! Here is the link to Anglis Qi. http://www.chessvariants.com/xiangqivariants.dir/anglis_qi.html
This page was solicited, so I just wrote down what I knew. It came about it because I referred to it in Anglis Qi [insert hyperlink]. I am happy for the page editor (Tony Quintanilla) to append a details of past uses of MD pieces, either at the end of the relevant paragraphs or in a new final paragraph. My own first encounter with the phrase was at http://www.chessvariants.com/piececlopedia.dir/taxonomy.html among many other definitions, and I make no claim of originality except for the MD versions of the Elephant and Dabbaba - and will happily be corrected on those if any previous use of them in known.
MD versions of the Single-step and rider <a href='../piececlopedia.dir/rhino.html'>Rhinos</a> would be an interesting alternative to MD Nightriders.
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