Crafting Challenge: Piece Value Optimisation

Here is an unorthodox series of challenges. You can place any amount of pieces you desire and on any square of the 8x8 regular chess board (at most one per square). The pieces can be of any type and of any color (Black or White only), but there must be exactly one king of each color on the board. The pieces have the following numerical values:

• Pawn : +1 point if for White, -1 point if for Black
• Knight: +3 points if for White, -3 points if for Black 
• Bishop: +3 points if for White, -3 points if for Black 
• Rook: +5 points if for White, -5 points if for Black 
• Queen: +9 points if for White, -9 points if for Black 
• Kings are worth 0 points here because the challenge would be pointless otherwise

The objective is to maximise the numerical value of the pieces on the board. The higher it is, the better the solution is. The position presented must not be a checkmate or a stalemate, as at least one move must be playable by at least one of the players from the presented position to be successful at completing the objective of a challenge. And from the position presented, the move must be legal.

Here is an example:

• Challenge #0: White to play and checkmate in one

Personal answer: the maximum value I found for this objective is +538.

Here are challenges. Please indicate the optimal value you have found and present a position to back up your claim.

1. Challenge #1: White to play and checkmate in 1 move without doing a double-check +496 (KieferSmith)
2. Challenge #2: White to play and checkmate in 1 move by a discovered check +538
3. Challenge #3: White to play and checkmate in 2 moves
4. Challenge #4: White to play and checkmate in 2 moves by en passant
5. Challenge #5: White to play and checkmate in 1 move by a double-check +538
6. Challenge #6: White to play and checkmate in 1 move by castling +510 (Arisktotle)
7. Challenge #6.1: White to play and checkmate in 1 move by kingside castling, which must be its only mating move +499 (Arisktotle)
8. Challenge #7: White to play and checkmate in 1 move by a knight underpromotion without a discovered check
9. Challenge #8: White to play and checkmate in 1 move by a bishop underpromotion without a discovered check
10. Challenge #9: White to play and checkmate in 1 move by a pawn moving two squares without a discovered check
11. Challenge #10: White to play and checkmate in 1 move with Black's king on the e4 square
12. Challenge #11: Black to play and checkmate in 1 move without doing a double-check
13. Challenge #12: Black to play and checkmate in 1 move by a discovered check +522
14. Challenge #13: Black to play and checkmate in 2 moves
15. Challenge #14: Black to play and checkmate in 2 moves by en passant
16. Challenge #15: Black to play and checkmate in 1 move by a double-check +522
17. Challenge #16: Black to play and checkmate in 1 move by castling
18. Challenge #17: Black to play and checkmate in 1 move by a knight underpromotion without a discovered check
19. Challenge #18: Black to play and checkmate in 1 move by a bishop underpromotion without a discovered check
20. Challenge #19: Black to play and checkmate in 1 move +522
21. Challenge #20: Black to play and checkmate in 1 move with Black's king on the e4 square +500
22. Challenge #0: White to play and checkmate in one +544 (Arisktotle)

Good crafting !

Easy ones out if the way: Challenge #1's answer is very easy: the maximum value for this objective is +538.

Challenge #1: max is +544: (Note that it's checkmate in 1 move since white plays just 1 move. Black only starts because otherwise the king would be in illegal check. And both the standard puzzles and the rules of these challenges allow black to start).

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do we have to find a maximum or can we post the "best we can find"

It would make more sense with the boundary condition that the position is legal.

You can post the «best you can find».

Challenge list updated. Challenges 9, 14, 19 modified (9 and 19 were unclear/could cause confusion before).

@Arisktotle. You are right, I overlooked that! Thanks for your contribution!

Here are some of my best tries for some of these challenges:

• Challenge #20: Black to play and checkmate in 1 move with Black's king on e4 (proposed answer: +500)

• Challenge #19: Black to play and checkmate in 1 move & Challenge #12: Black to play and checkmate in 1 move by a discovered check & Challenge #15: Black to play and checkmate in 1 move by a double-check (proposed answer: +522)

@Kiefersmith For which challenge is it?

The first one, in post #1.

Black's legal move is Kxb8.

challenge 6

may i suggest a challenge 6.1 in which whites only move that mates is 0-0?

That would be this one (I suppose):

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Added in the list above.