Position: Black king g7, bishop f7 attacked by king? Bishop on f7 is adjacent to king g7 — the bishop is attacked by the king! Wait, Bf7 and Kg7: g7 to f7 is adjacent, so king attacks bishop. Bishop is protected by... Nb7? Nb7 doesn't defend f7. Rh1? No. So bishop is attacked. I said "take away g8" last move — bishop on f7 also would attack g8 but it's attacked by king.
Wait, is the bishop defended? Nb7 attacks d8, d6, c5, a5. Not f7. So Black threatens Kxf7. Need to move bishop or defend it. Bishop moves: Be8, Bg8, Bh5, Be6, Bd5, Bc4, Bb3.
Best: mate threat? King g7, knight b7. If Be8 then threatening... King g7 escape squares: f6, g8, h7, h6, f8, f7, g6, h8. Bishop on e8 covers f7. Knight b7 covers d8, d6. Hmm, Bg8+ would be check? Bg8 attacks f7... g8 to g7? No, bishop doesn't attack along rank. Bg8 attacks f7, h7 diagonals... bishop attacks diagonally: g8-f7-e6 and g8-h7. King on g7 is adjacent to g8 but bishop doesn't give check.
Can I mate? Black king g7. Consider Be8 then Kf6... Let me think of a mating plan. Material huge; knight + bishop + rook vs bare king. Mate soon.
Check moves available: none of the legal moves give check directly? Bd5 check? d5 to g8 diagonal: e6, f7, g8 — no. Bh5? h5 attacks e8 diag, not g7. Be8: no. Knight moves: Nd8 no check. So no checks.
Actually, could I trap: play Be6 threatening Bh6#? Bh6 with bishop from... Be6 aims at h3... Be6 covers g8 and h7? e6 diagonals: d7,c8 and f7,g8 and f5,g4,h3 and d5,c4,b3,a2. So Be6 covers g8 and f7.
King g7 squares: f7 (bishop covers after Be6? Yes f7 on e6 diagonal), g8 covered, h7 covered by Rh1? Rh1 covers h-file: h7 yes! Rh1 on h1 covers whole h-file including h6, h7, h8. So king squares: f6, g6, h6, f8, h7(covered by rook), g8, f7, h8(covered by rook).
King currently can go: f6, g6, h6, f7?? Kf7 attacks bishop... wait after bishop moves away.
Plan: Be6 restricts to f6, g6, h6, f8. Then march king up? Or Rg1+ later.
Actually simpler: black only moves king; avoid stalemate. Black king on g7 with pieces to move.
Consider Be8: covers f7; then king can go g8? Be8 doesn't cover g8. Hmm.
Best concrete mate: Rg1+ first? Rg1 is legal — rook from h1 to g1, no check (king g7, g-file: g2 pawn blocks). No.
Think: mate pattern with rook on h-file, bishop controlling f7/g8, knight covering f6 area.
Let me consider Be6. Then Black king moves: f7 illegal (bishop), g8 illegal, h7 illegal (rook), f6, g6, h6, f8 possible. So Be6 then Kf6/Kg6/Kh6/Kf8.
Then Bh6#? If Kh6... Let me find a forced mate sequence.
Alternative: Bb3 aiming... Bb3 covers f7, g8 (b3-c4-d5-e6-f7-g8). Then king squares: f6, g6, h6, f8, g8 covered, f7 covered, h7 rook. Then follow with knight to... Nd8 covering f7 too? Or Rg1 then mate.
Actually with Bb3, black king confined to f6, g6, h6, f8. Then Kd2? Slow. Use knight: Nc5 heading to e4... mate on g6? Pattern: knight on e5? Hmm.
Let me think of mate: Kg6, Rg1+ with pawn? g2 pawn there...
Mate pattern: white Kc1 far. Mate likely: rook to g-file cutting, bishop + knight. E.g., black king h6, then Rg1... rook delivers along g?
Common mate: king on g6/g7, Nd5... hmm.
Let's try: 30. Be6 Kf8 (or others). 31. Nd6? covers e8, f7...
Maybe quickest: 30. Be8, planning Nd6 covering f7? Be8 covers d7... Be8 covers f7! e8-f7 diagonal. Yes Be8 attacks f7. And knight to d6 attacks f7, e8...
Let me just evaluate: after Be8, king can go g8, f6, g6, h6. Then Nd6 threatening... knight d6 attacks f7, e8, c8, b7, b5, c4, e4, f5. Covers f5, f7. Then Rh1 already covers h-file. King on g6: squares f5 (Nd6 covers), f6, f7 (covered), g7, h5?? king can't capture...
Alternative mate plan: get king to g8 corner: with bishop on h7... Bh5 then Bg6+ forcing...
Let me try a line: 30. Be6 Kf6 (say). 31. Nd8 (threat?) ... hmm.
Actually a clean known technique: rook h1, bishop controls f7/g8 line, knight controls... Mate: Kg6, Bh5+! Kf6, Rf1#? Bishop h5 covers g6, rook f1 covers f-file, mate if king can't escape to e5,e6,e7 etc. King f6 needs e5, e6, e7, f5, f7, g5, g6, g7 covered.
Simpler: push king to edge and mate with rook check on adjacent file. King g7 now.
Try: 30. Be6 Kf8 (or Kg6/Kh6/Kf6). If Kh6 31. Rg1! Kg7... wait rook g1, g-file open (g2 pawn!). g2 pawn blocks rook. So rook needs g-file: pawn g2. So Rg1 useless. Rf1? f-file: f2 pawn blocks too! All pawns on rank 2 block rook. Hmm, rook on h1 only has h-file. So mate must come via h-file or king walk.
Rook mates on h-file: king g7 with bishop covering f7 and f8? Mate pattern: Rh8+?? king escapes. Mate: king f8 with Rh8#? Rh8 check to f8? No, rook h8 attacks h-file and rank 8: f8 yes! Rh8+ on rank 8 gives check to king on f8. King f8 escapes: e7, f7, g7? Need covered. So mate pattern: king f8-ish, rook to h8 mate, with knight/bishop covering e7, f7, g7, e8? Let's construct: bishop e6 covers f7, g8. Knight d6 covers f7, e8, f5, b7... need e7, g7. Hmm.
Alternatively mate with king help: march king up. With such material advantage, no rush.
Let's find forced mate quickly-ish. Position: black king g7, black to move after our move. Let's try 30. Be8:
- Covers f7. Black: Kg8, Kh6, Kg6, Kf6.
- 31. Nd6 covers f5, f7, e8.
If Kg8: then Bh5! covers g6? h5-g6 yes and e8... then king g8 squares: f7 (B e8), f8, h8 (rook), h7 (rook). 33... hmm.
Actually mate on g8: king g8, rook h1 covers h7, h8. Bishop h5 covers g6. Knight f7?? Knight could go Nf7+? From d6, Nf7+ forks... Kxf7 no.
Knight mate: Nf7+ from... knight on d6 to f7 is check to g... f7 knight attacks h8, h6, g5, e5, d8, d6... not g8. Knight e7 attacks g8! Knight on e7 attacks g8, c8, g6, c6, d5, f5. So plan: king g8, knight to e7 covers g8?? No wait we want mate.
Mate pattern: king g8; Rh1... rook needs to give check on h-file only if king on h. King on g8: mate with bishop controlling f7/f8, knight e7... hmm knight e7 attacks g8 — that's check not mate setup.
King h8: rook h1 gives check? h-file, king h8, rook h1 check — but king escapes g8, g7 unless covered. Mate pattern: Kh8, Nf7#? Knight on f7 attacks h8, h6, d8, d6, e5, g5 — check from f7 to h8 yes. King h8 escape g8, g7. Bishop e6 covers g8, f7. So Nf7+ Kh... if Kg7 blocked? Bishop covers f7 so king can't capture knight. King h8 with Be6 (covers g8, f7) and Nf7#: king h8, knight f7 checks, escape squares g8 (bishop), g7 (knight attacks... f7 knight attacks g5, h6, h8, d8, d6, e5 — not g7!). g7 not covered by anything? Rook h1 covers h-file not g7. So Kg7 escapes. Need g7 covered: rook... hmm rook on g-file blocked.
Alternative: mate with Bf7#? no.
Let me reconsider: maybe simplest is march the king up: Kd2, Ke2... slow but with such advantage fine. But opponent could move king around; zugzwang stalemate risks.
Actually maybe faster: use rook lift via h-file: Rh8+? Rook h1 to h8: path h2 own pawn blocks. Pawns h2, g2, f2 on rank 2. Could advance pawns: h4, g4 etc. Not fast.
Knight b7 is far. Let's compute mate systematically. Black king zone confined by: rook h1 (h-file), and bishop controlling diagonals.
Try 30. Bh5. Bishop h5 covers g6, f7, e8... wait h5 diagonals: g6-f7-e8 and g4-f3 and e4? h5 up-left: g6, f7, e8. So covers g6, f7, e8. King g7 squares: f6, g6 covered, h6, f8, f7 covered, g8, h8 rook, h7 rook. Black: Kf6, Kh6, Kf8, Kg8.
If 30...Kg8 31. Nc5 (heading e6 or d7?) Hmm bishop h5 covers g6? then king g8: f7 covered, f8, h8/h7 rook. 31...Kf8.
Try 30. Be8 line deeper: 30. Be8 Kg8 31. Nd6 (covers f7, e8, f5) 31...Kf8 32. Bh5! covers g6, e8? king f8: squares e7, f7 (covered), g7, g8 (bishop e8? bishop moved to h5 — h5 covers e8-g6... doesn't cover g8). Hmm king f8 can go g7, g8, e7, e8? e8 attacked by bishop h5? h5-g6-f7-e8 yes! e8 covered. So king f8: e7, g7, g8 free.
This is getting messy. Use a different approach: known winning technique for R+B+N vs K: bring rook to a file/rank, use king. But with huge material and pawns, we can advance king: Kd2-c3... actually king can walk to f3 etc. Pawns on 2nd rank protect each other.
But actually there might be a quick mate: 30. Be6 Kf8 31. Nd6 (threat Rg1? no) ... 31...Ke8?? no wait Kf8 can take? f8 adjacent to e6? No.
Let me try: 30. Be6 Kf8 31. Nd6 Ke7?? No king can't move into... f8 to e7: attacked by bishop e6? No. By knight d6? d6 attacks e8, f7, f5, c8, b7, b5, c4, e4. e7 not attacked. So Ke7 possible? Then king approaches pieces. 32. Bf5+? e6->f5 check? f5 attacks e6... king e7: f5 diagonal to e6, g6, h7... doesn't check e7. 32. Bc8+? e6-c8: d7, c8. Check to e7? No, bishop c8 attacks b7... rook line: not check.
Hmm, maybe just bring king: 30. Be6 Kf6 31. Kd2 Kg7 32. Ke3? ... Then mate with king support: e.g., Kf3-e4 etc. But black king can approach White's pieces and attack bishop.
Honestly, engine-wise, best move probably Be6 or Be8, keeping restriction. Let's verify Be6 doesn't allow stalemate anywhere: after Be6 black has Kf6, Kg6, Kh6, Kf8 — fine.
Then plan: with king on, say, h6: 31. Nc5? covers e6... Let's find mate vs Kh6: Rook h1 covers h-file (h7, h8). King h6: g5, g6, g7, h5, h7(rook), h8(rook). Bishop e6 covers g8, f7, f5, g4. So g5, g6, g7 free. Move bishop... Bh3+? e6-h3: f5 g4 h3. Bh3 covers g4... check to h6? No. Be8 covers d7..., Be8 to check h5? No.
Vs Kh6, mate idea: Bf5+! e6-f5 check? f5 attacks g6, e6... check from f5 to h6? f5-g6-h7 diagonal — no, that's toward g6/h7, not h6. Not check. Bd7? covers g...
Knight maneuver to g4 or f5: Nf5+ from...
OK here's a known mate: king h6, Nf5+ (double? no). Nf7+ from d6: attacks h8, h6 — yes knight f7 checks h6! Then king h6 escapes g5, g6, g7, h5. Need those covered. Bishop e6 covers g4?? not these. Rook covers h-file only.
Standard mate: K on g6: Rf1... blocked.
Given complexity, maybe engine prefers king march: With K+R+B+N vs K, mate by force regardless; king walk is safe. But opponent king might harass: Kg7 can attack f7 bishop etc. After Be6, if Kf6 attacks bishop e6? King f6 adjacent e6 — yes attacks! Bishop defended by? Nothing. Hmm so Be6 Kf6 attacks bishop, we move bishop again. That's fine but let's see: 30. Be6 Kf6 31. Bc8 (keeping d7... covers b7? bishop c8 attacks b7 knight own... ) bishop retreat: Bh3, Bf5+, Bd5, Bc4, Bb3, Ba8? from e6: d5, c4, b3, a2 occupied... a2 pawn. Diagonals from e6: d7-c8, f7-g8, f5-g4-h3, d5-c4-b3-a2. So Bd7, Bc8, Bf5+, Bg4, Bh3, Bd5, Bc4, Bb3.
After Kf6, Bf5+? Check to king f6: bishop f5 adjacent — yes check. Kxf5? Is f5 defended? Knight b7 no. So Bf5+ Kxf5 loses bishop! So bishop must retreat keeping distance: Bh3, Bd5(covered? no), Bc4, Bb3.
30. Be6 Kf6 31. Bc4 (covers f7-g8 line, safe). 31...Ke7? King f6 to e7: attacked? No. Hmm king gets active.
Maybe 30. Be8 is better: covers f7, and is farther from king. 30...Kg8 31. Nd6 then? King g8: h8 rook, h7 rook, f7 bishop, f8 free, g7 back. 31...Kf8 32. Bh5 covers g6, e8, and... king f8: e7, g7, g8 free. Hmm.
Alternatively 30. Be8 Kf6 31. Nd6+? No, d6 knight doesn't check f6... knight d6 attacks f5, f7, e8, e4, c4, b5, b7, c8. Not f6.
New idea: use knight to cover g5/g6 area. From b7: Nc5 then... Nc5 attacks e6, d7, b7, a6, a4, b3, d3, e4. Then Ne4 covers g5? e4 attacks g5, f6, d6, c5, c3, d2, f2, g3. Ne4 covers g5 and f6!
Plan: 30. Be8 (cover f7) Kf6 (say) 31. Nc5 then 32. Ne4+ hitting king... e4 knight attacks f6: check! Then king moves, e4 covers g5.
Vs king g6: knight e4 covers g5, f6. Bishop covers f7? e8 covers f7? e8-f7 yes. Rook h-file covers h5,h7,h8. King g6: f5, f6(N), g5(N), g7, h5(R), h6. f5 and g7, h6 free. Hmm.
Vs king g7 with Ne4: squares f6(N), g6, h6, f8, h7(R), h8(R), g8?, f7(B). So g6, h6, f8. Then Bg6+! From e8: e8-f7-g6, check! King g7... wait if bishop goes to g6+ king g7 can capture? g6 adjacent, defended by knight e4? e4 doesn't defend g6. Rook? No. Hmm, Bg6+ Kxg6. Bad unless supported.
Maybe bring rook: Re1? f2 pawn blocks... rook can't easily get to center files. Rook is stuck on h1 behind pawns; only h-file. Unless pawns move.
Given the stalemate dangers, perhaps simply improve king: 30. Kd2!? But bishop f7 hangs: Kxf7. No.
So we must address the bishop being attacked by Kg7! Legal moves include bishop moves and also... wait, is bishop actually attacked? King g7 adjacent f7, yes. So we must move bishop or defend it. Can we defend f7? Rh1 to... no. Knight b7 can't. So bishop must move (or... no other option). Among bishop moves: Be8, Bg8, Bh5, Be6, Bd5, Bc4, Bb3.
Bg8: then Kxg8?? King g7 can take g8? g7-g8 adjacent, bishop g8 defended? Knight b7 no, rook h1: h-file — g8 not on h-file. So Bg8 Kxg8 loses bishop! Wait bishop g8 attacked by king g7? Yes adjacent. Wait but earlier I quipped about g8... Anyway Bg8 hangs. Also Be8: attacked? King g7 not adjacent e8. Safe, and e8 covers f7.
Be8 seems natural: covers f7, safe. Also Bh5 covers f7 and g6 and e8. Be6 covers f7, g8.
Which squares does Black king have:
After Be8: g8, f6, g6, h6, f8. (f7 covered, h7/h8 rook). Wait f8: attacked by knight b7? No. So Kf8 possible — then king attacks e8 bishop! Hmm: 30. Be8 Kf8 attacks bishop; bishop defended by? Nothing (knight b7 doesn't cover e8... d6 covers e8). Then we must move bishop again. Meanwhile Be6 covers f7 and g8, king f6 can attack e6.
After Bh5: king g7: f6, f8, g6 covered, g8, h6, f7 covered? h5 covers f7 yes. So Kf6, Kf8, Kg8, Kh6. Kf6 doesn't attack h5? f6-h5 not adjacent. Good. Kg8 attacks h5? No. King never attacks Bh5 except from g6/g4/f4/f6? h5 adjacent: g6, g4, f4... f6 no. Only g6 attacks h5, but Bh5 covers g6 so king can't go there (moving into check? King can't move to a square attacked by bishop — g6 attacked, so illegal). So Bh5 is safe from king permanently while it stays! Nice.
So 30. Bh5: covers f7, g6, e8, g4, f3. Black: Kf6, Kf8, Kg8, Kh6.
Now plan: knight to e4 or d6, and rook... Mate construction with Bh5: covers g6, f7, e8, g4.
Black king on g8: squares f8, g8, h8(R), h7(R), f7(B). King g8 must go f8 (or f7 illegal).
Black king on f8: e7, e8(B), f7(B), g8, g7, h8(R). e7, g7 free.
King f6: e5, e6, e7, f5, f7(B), g5, g6(B), g7, h5(B), h6, h7(R). Many free.
Knight maneuvers: Nc5-e4 or Nd6. Knight d6 covers f7, e8, f5. With Bd... hmm.
Mate idea with Bh5 + Ne4? Ne4 covers f6, g5, d6, c5, c3, d2, f2, g3. King g7 then: f6(N), g6(B), h6, f7(B), f8, g8, h7(R), h8(R). Free: h6, f8, g8. Then Bf7+?? bishop h5 to f7: check to g8? f7 attacks g8 yes. If king g7: Bf7+?? king takes. Hmm.
With Ne4, if black Kh6: Rg1 no. If Kg8: 32...?
Let me consider knight route to f5 or h... Mate pattern for king h6: Bf...
Classic R+B+N mate: e.g., king h6, Bg4? covers h5... Nf5+ then...
Try concrete: 30. Bh5 Kf8 (trying e7) 31. Kd2? Slow. Or 31. Nc5 (threat Ne6? c5-e6 attacks... e6 from c5: d7, e6 — attacks e6, d7; king f8... ) Hmm.
Alternative approach: 30. Bh5 Kg8 31. Nc5 Kf8 32. Ne6! attacks d8, f8? knight e6 attacks f8! Check? King f8, knight e6 attacks f8 — but bishop h5 pins? No. So Ne6+ Kf... wait king f8 in check from knight e6: escapes e7? attacked by knight? e6 knight attacks d8, f8, g7, g5, f4, d4, c5, c7. e7 not attacked; bishop h5 attacks g6, f7, e8, g4. So Ke7. Then 33. Nc7+? attacks e8, e6... king e7: Nc7+ forks? knight c7 attacks e8, e6, a8, a6, b5, d5. Check to e7? No. Nc5+? from e6-c5... knight e6 to c5 attacks e4, d7... not e7. Bg6+? h5-g6 check to e7? No, g6 attacks f7, h7, f5, h5. No.
33. Nc7+ Kd6?? king can chase knight.
Hmm, this king is slippery. Standard technique: confine to corner and mate: Kh8 mate: Nf7# requires g8, g7 covered. With Bh5: covers g6... rook h1 covers h7. So Kh8: Nf7+ (from d6 or e5): escape g8? g8 attacked by? Bishop h5? No (h5 attacks e8,f7,g6 diag and g4). Rook? No. So g8 free. Need bishop on diagonal covering g8: bishop on f7...
Mate on h8: pieces: Rook h1 checks? Rook can't reach h8 (pawn h2). Move h-pawn? h4, h5, h6! March h-pawn: h4-h5-h6 with king g7? Then rook... but pawn h6 could be captured? Black king g7 attacks h6. Hmm.
Alternatively mate on g8: Bf7+ Kxg...
Honestly, maybe I should consider 30. Nd6!? — bishop f7 is attacked, so no.
OK, practical decision: choose a strong, safe restricting move. Between Bh5 and Be8 and Be6 and Bd5.
Bd5 covers g8, f7? d5 diagonals: e6-f7-g8 and c6 pawn blocked, e4, c4, b3, a2. So Bd5 covers f7, g8 (if e6 empty — yes). Also safe from king. Black king: f6, f8, g6, h6 (g8 covered, f7 covered, h-file rook). Similar to Bh5 but also covers g8. Then knight to e4/f5 next.
Actually Bd5 vs Bh5: Bd5 covers g8 and f7; Bh5 covers g6 and f7 and e8. King can go g6 vs Bd5? g6 attacked by? Nothing? Bd5 attacks f7... no wait d5-e6-f7-g8: doesn't touch g6. So Kg6 possible, then Kg5-h4 escape route toward center! That's bad — king could run via g5/f5 toward center and attack our pawns. With Bh5, g6 is covered, king confined more: Kf6, Kf8, Kg8, Kh6 — still Kf6 then e5, e6, e7... king can escape via f6 to e5/e6. Hmm, but then knight covers: Nd6 covers f5, e8, f7. King f6: e5, e6, e7, g5, g7...
To prevent central escape, need knight covering e5/e6/e7 region or king support. Knight from b7: Nc5 covers e6, d7; then Ne4 covers f6, g5, d6, e... covers f6 and g5. King f6 can't stand? If knight e4 and king f6: Ne4 gives check? e4 attacks f6 yes. So king at f6 gets checked.
Line: 30. Bh5 Kf6 31. Nc5! (threat Ne4+ driving king to edge) 31...Ke7? King f6 to e7: 32. Ne4 covers f6... then 33. Nd6? threats...
Or 31...Ke5? attacked by knight c5? c5 covers d7, e6, b7, a6, a4, b3, d3, e4. e5 not attacked. But then Bh5-g6? hmm, 32. Nd7+? no.
Honestly, we have all the time in the world; even simplest: keep bishop safe, bring king up: Kd2-e2-f3... Actually with king walk, mate is easy: e.g., king to g3/f3 area, then mate with K+B+N+R. But careful about stalemate — with correct play no stalemate since we have pawns and multiple pieces; black king always has squares.
But the game presumably wants best move now. Let me try to find forced mate within reasonable depth. Material: R, B, N, K, 6 pawns vs lone K. Any reasonable line wins. Best practical: 30. Bh5 Kf6 (best?) 31. Nc5 (heading e4/d7) ...
Alternatively, check the possibility of immediate trap: black king g7 currently; after 30. Bh5, black moves:
- Kf6: then 31. Be2!? covering b5... hmm. Or 31. Nc5 Kf5?? 32. Nd7? ... 31. Nc5 threatening Ne4+ next: if 31...Kf5 32. Nd7? no. 32. Ne4 no wait knight on c5 can go e4? c5-e4 yes! 32. Ne4+ Kf4?? attacked... king f5 in check from e4: king must not capture (e4 defended by? nothing... Kxe4?? then Bh5 covers e8... after Kxe4 black king free, bad). Hmm Ne4+ from c5: is e4 defended by bishop h5? No. But king f5 adjacent e4: Kxe4 wins knight unless defended! So don't do that.
OK let me stop trying to calculate mate fully and just pick a clean strengthening move. I think 30. Bh5 is good: keeps bishop safe, covers f7/g6, confines king.
But wait — maybe there's something better: 30. Bd5!? keeps g8 covered, and plan Nd6 next covering f5, f7, e8 — then king has only... after Bd5, black Kf6/Kg6/Kh6/Kf8. If Kg6 31. Nd6?? doesn't cover g5. King g6 threatens g5-h4 run. 31. Nc5 covering e6, then Ne4 covers f6, g5. King g6: f5, f6? e4 covers f6, g5. So f5, g7, h5?? h5... rook covers h5? Rook h1: h-file: h5 yes! Rook covers entire h-file (no blockers). So h5, h6, h7 covered by rook. King g6: f5, f6(N), g5(N), g7, h5(R), h6(R), h7(R), f7(B d5). Free: f5, g7. Then Bh1?? Hmm, then Bf7?? no wait bishop on d5: could play Be4+! d5-e4: check to g6! King g6 in check from e4 (e4-f5-g6 diagonal). Escape: f5? e4 adjacent... f5 attacked by bishop e4? e4 covers f5 yes. g5 (knight), g7, h5(R), h6(R), h7(R), f7(B), f6(N). So Kg7 forced. Then...
Interesting. Let me evaluate line: 30. Bd5 Kg6 (black's most active) 31. Nc5 (threat Ne4) 31...Kg7 32. Ne4 threatening Bf7+?? or... king g7: f6(N now? knight e4 attacks f6 yes), g6, h6, f7(B), f8, g8(B), h7(R), h8(R). Free: g6, h6, f8. Hmm 33. Bf7? no. 33. Nd6+? e4-d6: check? knight d6 attacks f7, f5, e8, c8, b7, b5, c4, e4 — not g7. No.
This isn't converging quickly. In R+B+N vs K mates, knight+rook coordination: e.g., king g7, Rg1? blocked.
Let me think about the h-pawn idea: advancing h4-h5 forces... King g7 stops h6 (Kxh6? h6 defended by... after h6, king g7 can take h6 if undefended — defended by rook h1? No, pawn h6 blocked... rook behind on h-file: pawn h6, rook h1 — rook defends h6 along file? Path h2-h5 must be clear: h2 empty after pawn moves. So rook defends h6. Then Kxh6?? illegal (defended by rook). So h4, h5, h6 creates luft and rook defends. Then black king must avoid h-file... then rook still behind pawn. Hmm.
Alternatively, plan: mate in the h8 corner with the classic Bf7... no wait, with pawn h6 and rook, etc.
Let me just search mentally for mate in 4-5 vs typical defenses. Take 30. Bh5 as move 1 of plan. Black replies: Kf6, Kf8, Kg8, Kh6.
Case A: 30...Kg8 31. Nc5 Kf8 (only? g8: f8, h8(R), h7(R), f7(B). Yes only Kf8!) 32. Ne6+ Kf... wait knight e6 attacks f8: check. King f8 escapes: e7, g7? g7 attacked by Ne6? e6 knight attacks g7 yes! f7 (B), e8 (B). So only Ke7. 33. Nc7+? no. 33. Nc5? Hmm. After 32...Ke7 33. Bf3!? covers b7... or 33. Nd8+? e6-d8: knight d8 attacks f7, b7... check to e7? No. 33. Nc7+? attacks e8, e6: no check to e7... c7 attacks e6, e8, a8, a6, b5, d5. Not e7. 33. Nc5+? from e6: knight to c5 attacks d7, e6, e4, b7, a6, a4, b3, d3. No check. Hmm.
After 32...Ke7, white pieces: Bh5, Ne6. King e7 fairly central. 33. Kd2 heading to support. E.g., Kd2-d3-e4/e5 then net closes.
Alternatively at move 31: 31. Nd6!? from b7 directly: covers f5, f7, e8. Then king g8: f8? f8 attacked by Nd6? No (d6 covers e8, c8, f7, f5, b7, b5, c4, e4). King g8: f8, h8(R), h7(R), f7(B h5? h5 covers f7 yes... wait Nd6 also covers f7). So Kf8 forced again, then... bishop h5 gives g6 coverage; king f8: e7, e8(Nd6), f7(N), g7, g8. So Ke7 or Kg7. Then 32. Nc4? hmm.
Case B: 30...Kh6 31. Nc5 (threat: Ne4 covering g5) — king h6: g5, g6(B), h5(R), h7(R), h8(R), g7. Free: g5, g7. Threat Ne4 covers g5... then 31...Kg7 32. Ne4 g7→ f6(N), g6(B), h6, f7(B), f8, g8, h7(R), h8(R). Free: h6, f8, g8. 33. Nf6?? e4-f6: knight f6 attacks g8, h7, h5, e8, d7, d5, e4, g4 — attacks g8! and h7. King g7... Nf6 is not check. But covers g8, h7... hmm king g7 attacked by knight f6? No. Then black king: f7(B), g6(B), h6, h8(R), f8, h7(N), g8(N). Free: h6, f8. Getting tight! 33...Kf8 (or Kh6). If Kh6: 34. Bf7?? no. 34. Ng8!? f6-g8: attacks h6! Check! Knight g8 attacks h6, f6, e7. King h6: g5, g6(B), h5(R), h7(R), h8(R), g7. Free: g5, g7. Hmm not mate. 35. Nd...
If instead 33...Kf8 34. Nd7+!? f6-d7: check to f8? d7 attacks f8 yes! King f8: e7, e8(B h5), f7(B), g7, g8, h... e7 free? d7 knight attacks f8, b8, b6, c5, e5, f6. e7 not attacked, g7 not attacked. 34...Ke7 or Kg7.
I keep going in circles; mate probably around move 35-40 with king walk needed. Fine — but for this single move, choose between Bh5/Be8/Be6/Bd5.
One more consideration: 30. Be6!? covers f7 and g8; if 30...Kf6 31. Bc4 (retreat) 31...Ke7?? king wanders... but actually black king coming out is fine for us? It can't do anything; we can always push it back. But engine would prefer keeping it boxed.
Bh5 keeps king most restricted and bishop untouchable. Also covers e8 and g4, f3. I'll go with 30. Bh5.
Wait — double-check legality: Bf7 to h5: path f7-g6-h5, g6 empty yes. Bishop lands h5. Legal (in list). Good.
Also quip: opponent said bishop's square first on eviction notice. Respond playfully.