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Consider the following version of chess. The first player has a king and all bishops, while the second player has a king and all knights. The new pieces replace the normal pieces at the same location. Who has the advantage in this case? Which player will win if both play optimally?

Note: there is no castling and no pawn moves.

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  • $\begingroup$ The bishops? Because they can control more squares $\endgroup$ – new QOpenGLWidget Dec 14 '20 at 2:34
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    $\begingroup$ 1) How would one prove an answer? 2) Stockfish gives a fairly clear answer. I don’t see how this is a puzzle instead of a search. $\endgroup$ – Cardinal Dec 14 '20 at 3:04
  • $\begingroup$ @Cardinal yeah it's pretty hard to prove. I would be quite happy with analysis by Stockfish or some other program. Perhaps you can find an optimal line of play for one player that cannot be defeated? $\endgroup$ – Dmitry Kamenetsky Dec 14 '20 at 3:42
  • $\begingroup$ Would a castle-type move be allowed with the piece in the rook position? $\endgroup$ – Nilster Dec 14 '20 at 5:48
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    $\begingroup$ Do the minor pieces replace the pawns too (i.e. each player has 1 king and 15 minor pieces of his/her type), or they are only on the 1st (8th) rank? If the latter, do the players have pawns on 2nd/7th rank? $\endgroup$ – trolley813 Dec 14 '20 at 19:19
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Partial answer: Assuming the pieces are arranged as follows

board

it's probably easy to show that

White (the side with the bishops) cannot lose.

Because:

First, both knights in the corners (a8 and h8) are undefended, so White wins a piece on the very first move even with Black to move. After that, White (being a piece up) can simply exchange one for one (possible way is to build a barrier by placing bishops on adjacent diagonals so the enemy knights cannot cross them without being exchanged). It is known (using endgame tablebases) that 2 bishops vs 1 knight is a win for the bishops (although it may require more than 50 moves). So, White should at least draw.

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  • $\begingroup$ This is also probably valid if pawns are also replaced by B and N (so K+15xB vs K+15*N), as then the Ns on A7 and H7 are defended once but attacked twice. So W should still be able to get a piece up . $\endgroup$ – Penguino Dec 15 '20 at 23:16
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    $\begingroup$ @Penguino Even better, the knight on g7 is not defended at all (since the e8-square is occupied by the king), so White can play 1.Bb2xg7 and capture another knight (on h7, h8, a7 or b7) next move, being two pieces up. $\endgroup$ – trolley813 Dec 16 '20 at 7:09

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