I had an idea for a type of stalemate: One side is stalemated with 8 pins in a legal position.

I wondered how many units. for both sides, could be “nessecary” in such a position. I define this as either pinning a piece, blocking a piece, or trapping the the opponent’s king.

The best I came up with was 22 units.

[FEN "b2q1bq1/1N1N1N1k/8/rP1K1P1r/8/1P1B1P2/q2q4/2q1q1qq w - - 0 1"]

Is 22 units the limit for such a pinned pieces stalemate?

As a bonus optional question, what is the maximum number of units in a legal postion with 4 “natural” pins, which means no promoted pinning pieces?

  • I suppose you want to maximise the number of useful pieces, i.e. pieces that can't be removed without breaking the stalemate ? Hence it is not good enough to add a wPh4 or a BNa1 in your diagram ? – Evargalo Apr 5 '19 at 15:11
  • A white pawn on h4 is useful-it adds one more piece that cannot move for the stalemates side. But bNa1 is a no nol because it is not trapping the white king nor pinning a white piece. So yes, use pieces is what I’m looking for. If you can improve upon my position, put it an answer then! – Rewan Demontay Apr 5 '19 at 16:30
  • Since you seemed to have had an in this question, @Evargalo, perhaps you could answer it? – Rewan Demontay Apr 10 '19 at 18:49
  • 1
    TBH, this task hurts a bit my sense of esthetics. It is usual to try to achieve a pattern with the least possible units, but to maximize the number of pieces is much less appealing to me. In this case, I wouldn't be surprised if you could include all 32 pieces (or 31, without the wQ), but with a lot of black pieces that could be replaced by one or two more effective ones, and useless blocked wPs. – Evargalo Apr 10 '19 at 20:06
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    I found this page when I searched solutions for a similar question: What is the maximum number of pieces to set White stalemate, if any piece is necessary in that sense, that the stalemate is broken if you remove just 1 piece? (Position must be legal.) My number and position I will publish here later. Good luck! – ChessLover Jan 14 at 13:33
[FEN "qn1r2b1/1N1BpRn1/1p3bP1/rN1K2Br/P3P2p/nR1N1b1P/b2r4/k7 w - - 0 1"]

Here is an (ugly) suggestion wth 28 units.

White is stalemated with 8 pins; removing any Black unit would break the stalemate.

White has promoted one of her three missing pawns (to knight) and black has promoted all of her five missing pawns (two into rooks, two into light-squared bishops, and one into a knight).

The four captures (white queen, 2 white pawns and 1 black pawn) ensure that this position is reachable. I am pretty sure we could add at least one of the missing pawns but that would require some retrograde analysis to prove the legality of the position that is beyond both my motivation and my available time. For instance, adding a white pawn on b2 doesn't work because it won't be possible anymore to promote all black pawns.

  • @RewanDemontay I am afraid not... proof games are not my forte and it would take me way too much time. – Evargalo May 16 '19 at 13:02
  • Looking at it very fast, I cannot see either how I was intending to promote bPg7. To achieve 28 units, we just have to remove e.g. wPf2. – Evargalo May 16 '19 at 13:12

For 4 “natural” pins, here is my optimization attempt of 30 in a legal, although 31 is the theoretical maximum, since the White queen would take to many piece to stalemate.

[FEN "4r3/1b1pB3/1nRP1pkb/pPp4p/PrB1K1pP/1P2PpP1/2R2P2/Nqn4N w - - 0 1"]

Additionally, I have finally found a legal 29-unit position for 8 pins, aka the limit,

[FEN "b3r3/1R1p1p1q/1p1P1P1b/1Pk1BR2/1rN1K1Nq/p7/P1P1B1P1/1qn1q1nq w - - 0 1"]

The three missing White pieces ensure that the position is legal and that Black could have promoted all four of their missing pawns.

The Black g-pawn captured the White h-pawn to produce doubled pawns on the h-file. The h-file is now clear for two out of four pawns to promote.

The Black c-pawn captured the White queen to bypass the White pawn structure and promote. That's three out of four pawns.

The White e-pawn was captured and then Black e-pawn marched down and promoted . That's four out of four Black pawns promoted. Thus the position is legal.

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