What is the maximum number of moves in a position of Crazyhouse?

Question

We know that the maximum number of moves for a given colour in a legal position of standard chess (or at least record so far) is 218.

What is the record we can come up with for Crazyhouse?

Note that moves can be:

1. moves in standard chess
2. piece drops of a piece onto any empty square, or a pawn onto any empty square except on the 1st or 8th rank

A reasonable starting idea might be to have an empty board with just the two kings and White having all other pieces in its inventory. Then (let's say the kings are on e2 and d7) you have 8x2 king moves, plus piece drop of bishop, knight, rook, queen on any of 62 squares (62x4 moves), plus piece drop of a pawn on any of 44 squares for a total of 8x2 + 62x4 + 44 = 308 possible moves.

Note that, due to the stacking nature of pieces and pawns, we cannot count them individually. We may only count with what is on top of the stack.

Answer 1

446 moves

Disclaimer: this answer is based on the premise that we account for white moves only, and it treats having a full set of enemy pieces as having 5 options to place something.

[FEN "K1QQQQ1Q/Q7/Q7/6Q1/1Q6/7Q/Q6B/1QQQQQnk w - - 0 1"]

White has promoted to a queen a maximum of 15 times, with a complete set (Q, R, B, N, p) still at their crazy disposal. The last move was Ng1. White now has

• 2 king moves
• 28 vertical queen moves from eighth rank
• 3 lateral queen moves on eighth rank
• 31 diagonal queen moves from eight rank
• 14 moves for the queen on a7
• 15 moves for the queen on a6
• 21 moves for the queen on g5
• 20 moves for the queen on b4
• 16 moves for the queen on h3
• 16 moves for the queen on a2
• 7 bishop moves from h2
• 26 vertical queen moves from first rank
• 2 lateral queen move on first rank
• 28 diagonal queen moves from first rank
• 217 placements (41 à 5 + 3 à 4).

or a total of 446 moves.

Answer 2

I began the auction with a bid of 350 moves. Optimization are abound to be found.

[FEN "NQQQQQQB/Q6Q/Q6K/Q6R/Q6R/Q6R/Q5RB/nQQQQQBk w - - 0 1"]

Here is the receipt:

• Qa2-a6: 11*6
• Na8: 2
• Qb8-f8: 11*5
• Qg8: 10
• Bh8: 7
• Qh7: 11
• Kh6: 3
• Rh5-h3: 6*3
• Bh2: 5
• Rg2: 10
• Bg1: 5
• Qf1: 10
• Qe1-c1: 11*3
• Qb1: 10
• & 3 different pieces, pawn, knight, and bishop, in White's inventory*35 drop squares.

Answer 3

If I count correctly, this improvement on Peter's answer is is 432 moves. Basically, I tried to get a queen on every rank, file, and diagonal - although the long diagonal with the kings is empty, which may be a way to improve it.

[fen "KQQQ2QQ/Q7/7Q/7Q/Q7/Q6Q/Q6b/1Q2QQnk w - - 0 1"]