# What is the minimum-value piece combination necessary to checkmate in this game of Crazyhouse?

Imagine you're playing a game of crazyhouse, which operates like standard chess, except that you have a pocket of captured pieces that you can drop on the board in any legal location as your move.

This is the current state of the board with Black to move.

Here are the pieces in White's hand:

Your task: Find the minimum total-value piece combination Black must have in their pocket to force a checkmate.

Assume pawns are worth 1 point, knights and bishops are worth 3, rooks are worth 5, and queens are worth 9. The pieces in your pocket do not need to be legal (e.g. they don't depend on you actually having taken pieces off the board).

The checkmark will go to the player who finds the lowest total. Because this puzzle is trivially easy with a chess engine, I ask that participants refrain from using an engine. My total (which I'll reveal in a week), was found by manually playing out a game in an analysis board WITHOUT engine assistance.

• Is the d1 queen promoted? (Since white has 2 queens in the pocket, both of them must be original, because a promoted piece is usually returned as pawn when captured.) – trolley813 Apr 3 '20 at 20:07
• Great question! It's a real queen, not promoted. – Parseltongue Apr 3 '20 at 20:09
• So, how did White obtain these queens? – trolley813 Apr 3 '20 at 20:10
• It doesn't matter. Pockets do not have to be legal, as specified in the question – Parseltongue Apr 3 '20 at 20:19

I found an answer im satisfied with :

17 points (2 rooks, 2 knights and 1 pawn)

Reasoning and variations :

The key to solving this kind of puzzle is to add P-B-N-R-Q to your hand, then try to solve it. Here I figured out it could not be done.
So I started adding and removing some pieces and I realized we could checkmate in 6 with 3 rooks and 2 knights.
But we can do better : after trading a rook for 2 pawns (I later realized its possible with just one), I found this variation (@ means we drop the piece):
1..@h2+
if 2.Nxh2 then 2..R@h1+ 3. Kxh1 N@g3+ 4. Bxg3 Nxg3+ 5. fxg3
N@f2+ 6. Kg1 R@h1#. This is the checkmate in 6 I talked about earlier.
if 2. Kh1 then  2..R@g1+ 3. Nxg1 N@g3+ 4. Bxg3 Nxg3+ 5. Kxh2
R@h1+ 6. Kxg3 B@h4+ (using the bishop we grabbed on move 4) 7. Kg4 Rf4+ 8. Kh5 N@f6#
Then, the tricky variations : 2. Kxf1 R@h1+ 3. Ke2 N@f4+ 4. Kd2 Rxd1+ 5. Rxd1
R@e2+ 6. Kc1 N@b3+ 7. axb3 Nxb3+ 8. cxb3 Q@c2#
and 2. Kxf1 R@h1+ 3. N@g1 Rxg1+ 4. Nxg1 N@e3+ 5. Ke2
hxg1=N+ 6. Qxg1 N@d4+ 7. Kxe3 R@c3+! 8. bxc3 Nc4+ 9. Kd3
N@b2#
I won't go in detail on these two last variations (the Kxf1 ones), but they both lead to elegant checkmates.
(especially 7..R@c3+ blocking the c3 square, finding it was really satisfying!


This puzzle was fun to solve, I really enjoyed it. I still don't know if this is the best solution. With less pieces, checkmating gets really hard.

PS : My solution is computer-free, and im not good enough at programming to be able to verify my solution. If I missed something or if there is a quicker checkmate please let me know.

• This was also the best variation I could find! Impressive. – Parseltongue Apr 3 '20 at 20:00
• Thanks ! Crazyhouse chess is one of the most interesting variations : here if black runs out of checks, they lose instantly. I wonder if its possible to improve this solution. I've been told knights are the best attacking pieces and bishops are great at defending. Maybe with less rooks and more knights its possible. – classicalMpk Apr 3 '20 at 20:07