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As you know, in Chess960, the first and eighth rows are symmetric and consist of the normal pieces which have be permuted. The only constraints are that the King is between the two Rooks and the Bishops should have different colors.

In King of the Hill, the start from the standard position and we can win by either checkmating the opponent's King or by bringing our own King in the Hill (which consists of d4, e4, d5 and e5) by a legal move in normal chess.

Question: what if we combine these two variations?

The rule would be that we start from a position in Chess960 and we keep the winning possibility of King of the Hill. To ask more precise sub-question:

  1. Are there some starting positions where the Whites or Black have a huge advantage? Or even worse, a forced win?
  2. If yes, could it be more pertinent to shift the "hill"? For example, by letting it to be b4, c4, b5 and c5).
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Since I wrote a script to analyze atomic chess960 starting positions with multi-variant Stockfish some time ago, I slightly adapted it to be able to also run it for king of the hill (and other variants). A run on all 960 starting positions to depth 18 (taking ~1 hour on a single thread) resulted in a maximum score of +155 centipawns for white for position 657 brnbkrnq/pppppppp/8/8/8/8/PPPPPPPP/BRNBKRNQ w KQkq - 0 1. This indicates that white in some positions has a relatively clear edge, but there at least seems to be no easy forced win, although strictly disproving the existence of a forced win is of course infeasible. The analysis could be repeated with deeper/longer searches to get more indications.

Based on my experience and Stockfish's evaluations, I think that king of the hill (and the 960 version of it) is one of the more balanced variants, so I do not necessarily see the need for additional measures to balance it. However, if someone is interested in investigating that, one could modify Stockfish to support the shifted versions and re-run the analysis to get some data.

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    Thank you for your answer and the script. I also thing about doing other mixing of variation, for example "King of the Crazyhouse" or "960 Crazyhouse" and this will certainly help. – Davide Giraudo Jul 4 '18 at 16:21
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    In that case I have some more links for you. The original motivation for the script was a discussion about atomi960 on lichess, see lichess.org/forum/team-atomic960-analysis. I think there are similar threads about crazyhouse960 or the like. Regarding combinations like King of the Hill plus Crazyhouse, you could have a look at a Stockfish fork I started developing recently at github.com/ianfab/Fairy-Stockfish. It is not yet possible to configure variants via an INI file, but it is relatively easy to add them in the code. – Fabian Fichter Jul 4 '18 at 19:14

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