# Is KQB vs KP generally sufficient to force a selfmate?

User Hauke Reddmann noted in a previous answer that there should be a straightforward way to secure selfmate against a substantially weaker opponent (i.e., force them to checkmate you):

win all the material of your opponent, except a safely blocked pawn. Then force your own mate by zugzwang. The minimum material needed is KQB/KP.

I queried a Problem Database for White to selfmate against Black with KQB vs KP, and found 17 such positions. All of these, however, seem to require Black's pawn to be a Knight pawn (on the b or g file). There may also be some other patterns that universally hold (does the White Bishop have to be the same color as the Black pawn's promotion square?).

My question is as follows: is it generally possible to force a selfmate with KQB vs KP (for example, we may take a randomly selected position like the below), or is it a requirement Black's pawn should be a Knight pawn? If it is generally possible to force the selfmate, what procedure should one follow to do so?

[Title "KQB vs KP, White to play & selfmate if possible"]
[FEN "1Q1B4/8/6K1/3k4/3p4/8/8/8 w - - 0 1"]

Note: 'generally' means 'exceptional circumstances notwithstanding', such as for example if Black's pawn is so far advanced that it threatens promotion, or being so placed as to force White to capture it shortly, etc.

## 1 Answer

That one is a no-brainer: with a knight pawn the white king can stand in the corner, and be blocked in with just the bishop. This is impossible with another pawn - you must block both e.g. b1 and d1 and need a third White piece. (After all, Black must be forced to play d2#, so Qb1/Bd1 won't suffice!)

EDIT: Considering other material, if I recall correctly, KQR vs KQ is sufficient for forcing selfmate. (Again, check PDB.) A request at MatPlus Forum came up with this gem (Black can promote into all four pieces, always leading to a selfmate in 7 more moves): Look for 1st prize I.e. you, not surprisingly, can force a self mate with Black only having an e-pawn and White a bit more of material.

• Thank you. What about KQBN vs KP (i.e. add a White Knight to the OP in some random location)? Here again there are no examples with the d- or e-file pawn in PDB: pdb.dieschwalbe.de/… Commented May 4, 2021 at 19:45
• It's worth noting that a very important part of what I'm trying to figure out is whether - given conditions of, essentially, arbitrarily large material advantage - these are sufficient conditions for selfmate to be forceable. In other words, not just in specific problems that have been demonstrated, but whether the conditions for selfmate can be forcibly recreated from any (or mostly any) positions with that level of material imbalance. The immediate question toward that is: what is this sufficient material imbalance? (Not KQB vs KP; how about KQBN vs KP? Is KQR vs KP/KQ generally sufficient?) Commented May 4, 2021 at 19:49
• @MobeusZoom: A very good question! The obvious (partial) solutions of course are tablebases, but except private work by selfmate experts they don't exist, to my best knowledge. Adding a knight (assuming e-pawn) won't help: you can't use it as a block, as it checks, and it is too powerless to complete zugzwang. Two knights suffice for the latter, or knight and pawn, or rook. (Simply check the possible positions before the mate!) Commented May 5, 2021 at 8:17
• While tablebases make sense, it also seems like there could be an intuition - just as any beginner learns to checkmate KQ vs K without needing a tablebase! - behind how one could go about forcing a selfmate from any arbitrary position, given as much material advantage as they can ask for (maybe define as: whatever pieces of each colour they want on the board, but unable to control starting positions). I'll plan to ask a dedicated question on that but before so doing, thought I'd ask what you feel would be enough material advantage for this. (So that I can come up with examples to play from) Commented May 6, 2021 at 20:49