No. 124 supplement - (Vol.VIII)

ISSN-0012-7671 Copyright ARVESReprinting of (parts of) this magazine is only permittedfor non commercial purposes and with acknowledgement.

April 1997

Editorial BoardeditorsJohn Roycroft, 17 New Way Road, London, England NW9 6PLEd van de Gevel, Binnen de Veste 36, 3811 PH Amersfoort, The NetherlandsSpotlight-column: J. Fleck, Neuer Weg 110, D-47803 Krefeld, GermanyOpinions-column: A. Pallier, La Mouziniere, 85190 La Genetouze, FranceTreasurer: J. de Boer, Zevenenderdrift 40, 1251 RC Laren, The Netherlands

Contents:

Reciprocal zugzwangs in GBR class 0400.10Reciprocal zugzwangs in GBR class 1300.01GBR class 4000.10 in practiceStiller and the 6 pieces endgamesGBR-codeEG Subscription

106-109109-113113-114114-115115-116

116

105

COMPUTER SECTIONeditor: John Roy croft17 New Way RoadNW9 6PL London

*C* GBR class 0400.10

The 209 reciprocal zugzwangs in the5-man ending rook and pawn againstrook are listed below, in two sequences:first, by wK position; second, by solutiondepth. In every case, White to move can-not win. Cross-reference between the listsis either by depth value or serial number.Attention to all but No.32 below is drawnin IGM John Nunn's computer-assistedbook Secrets of Rook Endings (Batsford1992). We again have to thank Lars Ras-mussen in Denmark for thecomputer-intensive labour involved. Withthis force it is still (in August 1996) notknown if there are any reciprocalzugzwangs of the types 'whoever movesloses' or to the advantage of the pawnlessside.The last column digits are 'black tomove, White wins' solution depth values:

1: wKa8, Rb8, Pa7; bKc7, Rc8 42:3:4:5:6:7:8:9:

10:11:12:13:14:15:16:17:18:19:20:21:22:23:

wKa8,wKc7,wKc7,wKc7,wKf7,wKa5,wKa4,wKe4,wKa3,wKa2,wKal,wKb8,wKc6,wKf6,wKa4,wKa4 ,wKe4,wKa3,wKa3,wKa3,wKa2,wKc8,

Ra6,Ra8,Rb7,Rb7,Re7,Ra8,Ra8,Ra8,Ra8,Ra8,Ra8,Ra8,Rb6,Re6,Ra7,Ra5,Ra8,Ra8,Ra7,Ra5,Ra4,Ra8,

Pa7;Pa7;Pa7;Pa7;Pa7;Pa7;Pa7;Pa7;Pa7;Pa7;Pa7;Pa6;Pa6;Pa6;Pa6;Pa6;Pa6;Pa6;Pa6;Pa6;Pa6;Pa 5;

bKb4,bKa5,bKa5,bKc5,bKf 5,bKc5,bKc4,bKd6,bKc3,bKc2,bKcl,bKf 6,bKc4,bKf 4,bKc4,bKc4,bKe6,bKc3,bKc3,bKc3,bKc3,bKe7,

Rb5Ra6Ra8Ra8Rh8Rc7RC7Rd7Rc7Rc7Rc7Re7Ra7Rh7Rc6Ra7Rd7Rc4Rc6Ra7Ra7Rd7

14479

1347789102517211014121415151315

24: wKb6, Ra6, Pa5; bKg6, Rf5 24

25:26:27:28:29:30:31:32:33:34:35:36:37:38:39:40:41:42:43:44 :45:46:47:48:49:50:51:52:53:54:55:56:57:58:59:60:61:62:63:64:65:66:67:68:69:70:71:72:73:74:75:76:77:78:79:80:81:82:83:84:85:86:87:88:89:90:91:

wKb6,wKc5,wKe3,wKf3,wKa2,wKb5,wKe4,wKe4,wKf6,wKf3,wKd4,wKal,wKe8,wKf8,wKg8,wKh8,wKd7,wKd7,wKf7 f

wKd5,wKd4,wKf4,wKgl,wKb8,wKf8,wKg8,wKh8,wKc7,WKC7,wKc7,wKd7,wKg7,wKd6,wKf6,wKf4,wKg7,wKb6,wKa5,wKd5,wKe5,wKf5,wKg5,wKg5,wKd4 #wKe2,wKel,wKb7,wKb6,wKa 5,wKe3,wKf3,wKdl,wKel,wKb5,wKb4,wKe4,wKf4,wKd2,wKe2,wKe2,wKdl,wKa6,wKb6,wKb5,wKb4,wKf4,wKf4,

Ra6,Rb5,Ra6,Ra6,Ra3,Ra5,Rb4,Rd4,Rg3,Ral,p-g2,Rh2,Rb8,Rb8,Rb8,Rb8 #

Rb8,Rc7,Re7,Ra7,Ra7,Rb8,Rb8,Rb7,Rb8,Rb8,Rb8,Rc6,Rb8,Rb7,Rb7,Rb7,Rc6,Re6,Rb8,Rb7,Rb7,Ra8,Rc5,Rc5,Rc5,Rc5,Rf5,Rd5,Ra5,Ra5,Rb5 f

Rb5,Ra4,Ra4,Ra4,Ra4,Ra4,Rb4,Rb6,Ra3,Ra3,Re3,Re3,Ra3,Ra3,Rb6,Rb4,Rb3,Rb6,Rg2,Rbl,

Pa5;Pa5;Pa5;Pa5;Pa5;Pa4;Pa4;Pa4;Pa3;Pa3;Pa2;Pa2;Pb7;Pb7;Pb7;Pb7;Pb7;Pb7;Pb7;Pb7;Pb7;Pb7;Pb7;Pb6;Pb6;Pb6;Pb6;Pb6;Pb6;Pb6;Pb6;Pb6;Pb6;Pb6;Pb6 ;Pb5;Pb5;Pb5;Pb5;Pb5;Pb5;Pb5 ;Pb5;Pb5;Pb5;Pb5;Pb4;Pb4;Pb4;Pb4;Pb4;Pb4;Pb4;Pb3;Pb3;Pb3;Pb3;Pb3;Pb3 ;Pb3 ;Pb3;Pb2;Pb2;Pb2;Pb2;Pb2;Pb2;

bKh6,bKe5,bKg5,bKh5 7

bKG2,bKh5,bKg4,bKg4,bKh7,bKh2,bKh5,bKfl,bKe6,bKf 6,bKg6,bKh6,bKb5,bKd5,bKf 5,bKb5,bKb3,bKe6,bKf 3,bKd8,bKf 6,bKg6,bKh6,bKa6,bKb5,bKc5,bKd5,bKg5,bKd4,bKf 4,bKf 6,bKh.5,bKa4,bKc7,bKd3,bKe3,bKf 3,bKg3,bKg3,bKe7,bKg3,bKg2,bKd6,bKb2,bKc4,bKg4,bKh4,bKf 2,bKg2,bKbl,bKd5,bKg5,bKh5,bKf 4,bKf 5,bKg3,bKf 2,bKa2,bKd5,bKd4,bKd5,bKh5,bKh3,

Rg5Ra6Rf5Rg5Ra6Rg4Ra5Re 5Ra8Ra4RclRa8Ra7Ra7Ra7Ra7Rb6Rb8Rh8Rb6Rb5Re 7Rf7Ra6Ra6Ra6Ra6Rb5Ra6Ra6Ra6Rh6Rb7Rh7Re 7Rh6Ra8Rb7Rb6Rb6Rb6Rb6Rd6RclRf3Rf2Ra4Rb3RblRf4Rg4Re2Rf2Rb2Ra8Rf5Rg5Ra3Ra3Rf3Re2RalRblRblRd8Rb8Rb3

261526271627252637223635776747

10877

128

1513147

101112169

141017149

131415161820212419181923282023 12126282925382924172825273123 I

106

92:93 :94 :95:96:97:98:"99:100:101 :102:103:104:105:106:107:108:109:110:111:112:113:114 :115:116:117:118:119:120:121:122:123 :124:125:126:127:128 :129:13 0:131:132:133:134:135:136:137:13 8:139:140:141:142 :143:144 :145:146:147:148:149:150:151:152:153:154 :155:156:157:158:

wKb3,wKf3,wKf2,wKbl,wKbl,wKcl,wKel,wKfi,wKa7,wKa7,wKe7,wKe7,wKf7,wKh7,wKbt6,wKb'6,wKc6,wKd6,wKa 5,wKb5,wKe5,wKb"4,wKe4,wKg4,wKb3,

wKlfo,wKb2,wKh2,wKli2fwKbl,wKhl,wKhl,wKb8,wKc8,wKg7,wka6,wkb6,wKe6,wKf6,wkg4,wKh3,wkhl,wkc7,w4c7,wKa5,wKb5,wke5,wkf5,wkf5,wkf 5,wkg5,wkg5,wke4,wkc7,wKb6,wkb5,wke4,wKbS,wke5,wKc4,wKc4,wKf4,wKf4,wKb3,wKf2,wKe6,

Rb5,Rg2,Rg2,Rf6,Rf2,Rf2,Ra2,Rg2,Rb7,Rc8,Rc8,Rd7,Re7,Rg7,Ra7,Rb7,Rb6,Rb6,Rd7,Rb7,Rb7,Rb7,Rb7,Rc8,Rb7,Rc8,Rb7,Rc8,Rc8,Rb7,Rc8,Rc8,Ra6fRc7,Rc7,Rb6,Rb7,Rd6,Re6,Rc8,Rc8,Rc8,Rc6,Re5,RbS,Rb8,Rd5,RhS,Rd5,Re 5,Rd5,Rf5,Re5,Rc5,Rc8,Rb4,Re5,Rc8,Rd5,Rc6,Rc8,Ra3,Ra4,Rb4,Rg3,Rh3,Rc3,

Pb2;Pb2;Pb2;Pb2;Pb2;Pb2;Pb2;Pb2;PC7;Pc7 ;P C 7 ;

P C 7 ;

P C 7 ;

PC7;P C 7 ;

P C 7 ;

P C 7 ;

P C 7 /

Pc7;PC7 ;PC7;PC7;PC7;PC7;Pc7;P C 7 ;

P C 7 ;

P C 7 ;

P C 7 ;

P C 7 ;

P C 7 ;

P C 7 ;

P C 6 ;

P C 6 ;

P C 6 ;

Pc6;PC6;PC6;PC6;PC6;PC6;PC6;PC5;PC5;Pc5;Pc5;PC5;Pc5;Pc5;Pc5;Pc5;Pc5;Pc5;P C 4 ;

P C 4 ;

P C 4 ;

P C 4 ;

Pc3;Pc3;Pc3;Pc3;PC3;PC3;Pc3;PC3;PC2;Pc2;

bKd4,bKh5,bKh6#

bKg4,bKg4,bKg4,bKg2,bKh7,bKa5,bKc5,bKc5,bKe5,bKf5,bKe8,bKd7,bKd6,bKc8,bKc8,bKc5,bKd5,bKc5,bKd4,bKc3;bKf6,bKd3,bKg5,bKd2,bKg6,bKg4,bKdl,bKg5,bKg3,bKd8,bKe8,bKg5,bKa4,bKa8,bKe4,bKf4,bKg6,bKg5,bKg5,bKa5,bKa5,bKa3,bKd7,bKe3,bKg7,bKf3,bKf3,bKg3,bKg3,bKf 6,bKe6,bKb4 /

bKd4,bKf 1,bKb3,bKg5,bKe5,bKa3,bKh5,bKf 2,bKg6,bkh4,bKe4,bKe4,

Ra8Re8Re8Rb8Rh8Rb8Rf2Re 8Rc8Rc6Rc6RC8Rh8Rc6RC8Re 8Ra6Ra8RC6Rc8Rc6Rc8Rc5Rf7Rc8Rg7Rc8Rg7Rg7Rc8Rg7Rg7Rc7Rb6Rh6Re 7Rb8Rc7Rh7Rf7•Rg'6Rg6Rb5Rb5Rc6Rc7RC6Rg6Rc6Rh6Rc6Re6Rd8Rb4Ra5RclRd8Ra4R e 6

Rb8Rb3Rg5R e 8

Rf8RhlRd4Rcl

293233373635353454479

144521868777899

101110121299

14849

111310131412139

141815161617182013181918222320 :

361924241623

1591601611621631641651661671681691701711721731741751761771781791801811821831841851861871881891901911921931941951961971981992 002012022032042052062072082 09

*c*

: wKd5: WKC4: WKC1: wKb7: wKb7: wKf 7: wKf7: WKC6: wKb5: wKf5: wKh4: wKg2: wKgl: wKc8: wKd8: wKc7: WKC7: wKe7: wKe7: wKe7: wKe7: wKb6: WKC6: wKf6: wKd8: wKe8: wKd7: wKd6: wKa5: wKb5: wKf5: wKd3: wKd6: wKd5: wKf5: WKfl: wKe7: wKe6: wKe6: wKd5: wKg4: wKc2: wKd2: wKcl: wKe6: wKc5: wKc5: wKd3: wKb2: WKf 2: wKdl

, Rh2, RC6, Rb2, Rc7, Rd8, Rd8, Re7, Ra7, Re7, Rc7, Rd8, Rg7. Rg7, Ra6, Rd7, Rb7, Rb7, Rh7, Rh7,. Rd8, Rd7, Rc6, Rc7/ Re6, Rd7, Rh5, Rd6, Ra6, Rc5, Rc5, Re5, Rc5, Ra6, Ra6, Re5, Rc4, Rc4, Rh3

, Re3, Rd4, Rel, Rb8, Re 3, Rd6, Ra6, Rd4, Rb3, Ra4, Re2. Rg7

The same,depth value:0102040404040404040404040405

109:108:001:003:007:041:•101:102:106:128 :163:164:166:100:

wKd6,wKc6,wKa8,wKc7,wKa5,wKd7,wKa7,wKe7,wKb6,wKb6,wKb7f

wKf7,wKc6,wKa7,

, Pc2 ;, PC2 ;. PC2 ;, Pd7;, Pd7 ;. Pd7;, Pd7;/ Pd7;. Pd7;, Pd7;, Pd7;, Pd7;, Pd7 ;, Pd6;, Pd6;, Pd6;, Pd6;, Pd6;, Pd6;, Pd6;, Pd6;, Pd6;, Pd6;, Pd6;, Pd5;, Pd5;, Pd5;, Pd5;, Pd5;, Pd5;, Pd5;, Pd5;, Pd4;, Pd4;, Pd4 ;, Pd4;, Pd3;.• P d 3 ;

, Pd3 ;, Pd3;, Pd3;, Pd3;, Pd3;, Pd3/, Pd2;, Pd2 ;, Pd2;, Pd2;, Pd2;, Pd2;, Pd2;sorted

Rb6,Rb6,Rb8,Ra8,Ra8,Rb8,Rc8,Rc8,Ra7,Rb7,Rd8,Rd8,Ra7,Rb7,

bKe3bKe5bKalbKb5bKd5bKd5bKf5bKe7bKd5bKd5bKg6bKh4bKh3bKe8bKf 8bKe8bKe6bKc8bKc6bKd5bKe5bKb4bKb8bKf4bKf8bKf6bKb5bKd8bKb3bKb3bKf 3bKf 5bKd8bKf 5bKf 3bKh2bKg5bKf8bKg6bKf 7bKg2bKa3bKa3bKelbKg6bKe5bKa3bKdlbKf 2bKh2bKh3

, RC3, Re8, Ra4, Rd8, Rd6, Rd6, Rd8, Rd8, Rd6, Rd6, Rg7, Rf8, Rf8, Rd7, Rc6, Ra8, Ra8, Rg8, Rga, Ra6, Ra6, Rd7, Rc8, Rd7, Rc5, Rd6, Rc5, Rb8, Rd8, Rd6, Rd6, Re 5, Rc8, Rc8, Rh6, Rg2, Rf4, Rd4, Ra3, Rc3, Rf3, Rb3, Rd7, Re3. Rf3, Rh4, Rdl, Ral. Rf3, Rd3, Ra8

212424544748879

101015131316161011899

171319141514142415261920234228313523254332242419412539

by solution

Pc7;Pc7;Pa7;Pa7;Pa7;Pb7;Pc7;PC7;PC7;P C 6 ;

Pd7 ;Pd7 ;Pd7 ;PC7;

bKc8,bKc8,bKc7,bKa5,bKc5,bKb5,bKc5,bKc5,bKd7,bKa8,bKd5,bKdS,bKe7,bKa5,

Ra8Ra6RC8Ra6Rc7Rb6RC6Rc6Rc8Rb8Rd6Rd6Rd8Rc8

107

05 107: wKb6, Rb7, Pc7; bKdS, Rc805 162: wKb7, Rc7, Pd7; bKbS, Rd806 039: wKgB, RbS, Pb7; bKg6, Ra706 111: wKbS, Rb7, Pc7; bKdS, Rc807 004: wKc7, Rb7, Pa7; bKaS, Ra807 008: wKa4, Ra8 , Pa7; bKc4, Rc707 009: wKe4, RaS, Pa7; bKd6, Rd707 037: WKeS, RbS, Pb7; bKe6, Ra707 038: wKfS, RbS, Pb7; bKf6, Ra707 040: wKhS, RbS, Pb7; bKh6, Ra707 042: wKd7, Rc7, Pb7; bKdS, Rb807 045: wKd4, Ra7, Pb7; bKb3, RbS07 046: wKf4, RbS, Pb7; bKe6, Re707 052: WKC7, Rc6, Pb6; bKa6, RbS07 103: wKe7, Rd7, Pc7; bKeS, Rc807 113: wKb4, Rb7, Pc7; bKd4, Rc807 114: wKe4, Rb7, Pc7; bKc3, RcS07 115: wKg4, RcS, Pc7; bKf6, Rf707 165: wKf7, Re7, Pd7; bKfS, RdS07 169: wKh4, Rd8, Pd7; bKgS, Rg708 010: wKa3, RaS, Pa7; bKc3, Rc708 044: wKdS, Ra7, Pb7; bKbS, RbS08 048: WKbS, Rb7, Pb6; bKdS, Ra608 110: wKaS, Rd7, Pc7; bKcS, Rc608 112: WKeS, Rb7, Pc7; bKcS, Rc608 116: wKb3, Rb7, Pc7; bKd3, RcS08 127: wKa6, Rb6, Pc6; bKa4, Rc708 167: WKbS, Re7, Pd7; bKdS, Rd608 168: WKfS, Rc7, Pd7; bKdS, Rd608 180: wKb6, Rc6, PdS; bKb4, Rd709 005: WKC7, Rb7, Pa7 ; bKcS, RaS09 011: wKa2, Ra8, Pa7 ; bKc2, Rc709 057: wKd6, RC6, Pb6; bKd4, Rb709 062: wKaS, Ra8, PbS; bKc7, Rb709 104: wKf7, Re7, Pc7; bKfS, Rh809 117: wKh3, RcS, PC7; bKgS, Rg709 118: wKb2, Rb7, Pc7; bKd2, Rc809 124: wKbS, RaS, Pc6; bKdS, Rc709 125: wKc8, Rc7, Pc6; bKeS, Rb609 129: WKeS, RdS, PcS; bKe4, Rc709 137: WKbS, RbS, PcS; bKd7, Rc709 170: wKg2, Rg7, Pd7; bKh4, Rf809 181: wKcS, Rc7, PdS; bKbS, Rc809 182: WKfS, ReS, PdS; bKf4, Rd710 012: wKal, RaS, Pa7; bKcl, Rc710 016: wKa4, Ra7, PaS; bKc4, Rc610 043: wKf7, Re7, Pb7; bKfS, Rh810 053: wKc7, RbS, PbS; bKbS, Ra610 059: wKf4, RbS, PbS; bKf6, Re710 119: wKh2, RCS, Pc7; bKgS, Rg710 121: wKbl, Rb7, Pc7; bKdl, RcS10 132: wKh3, Rc8, PcS; bKgS, RgS10 171: wKgl, Rg7, Pd7; bKh3, RfS10 172: wKcS, RaS, Pd6; bKeS, Rd710 178: wKe7, Rd8, Pd6; bKdS, Ra611 054: wKc7, Rb7, Pb6; bKcS, RaS11 120: wKh2, RcS, Pc7; bKg4, Rg711 130: WKfS, ReS, PcS; bKf4, Rh711 179: wKe7, Rd7, PdS; bKeS, RaS12 018: wKe4, RaS, PaS; bKeS, Rd712 047: wKgl, RbS, Pb7; bKf3, Rf712 055: wKd7, Rb7, PbS; bKdS, RaS12 122: wKhl, RcS, Pc7; bKgS, Rg712 123: wKhl, RC8, PC7; bKg3, Rg712 135: WKC7, ReS, PCS; bKaS, RbS13 006: wKf7, Re7, Pa7; bKfS, Rh813 022: wKa2, Ra4, Pa6; bKc3, Ra7

13 OSO wKg8, RbS, PbS; bKg6 , RaS13 063 WKdS, RcS, PbS; bKd3, Rb613 131 wKg4, RcS, PcS; bKg6, Rf713 133 wKhl, RcS, PcS; bKgS, RgS13 136 WKaS, RbS, PcS; bKa3, RcS13 146 WKbS, RcS, Pc4; bKb4, RaS13 174 wKc7, Rb7, PdS; bKeS, RaS13 175 wKc7, Rb7, PdS; bKe6, RaB13 184 wKe8, RhS, PdS; bKf6, RdS14 002 wKaS, RaS, Pa7; bKb4, RbS14 017 wKa4, RaS, PaS; bKc4, Ra714 019 wKa3, RaS, PaS; bKcS, Rc414 051 WKhS, RbS, PbS; bKhS, RaS14 058 WKfS, ReS, PbS; bKf 4, Rh714 061 WKbS, Rb7, PbS; bKa4, RaS14 064 WKeS, RcS, PbS; bKe3, RbS14 105 wKh7, Rg7, Pc7; bKeS, RcS14 126 wKg7, Rc7, Pc6; bKgS, RhS14 134 wKc7, Rc6, PCS; bKaS, RbS14 138 WKeS, RdS, PcS; bKe3, RcS14 186 WKdS, RaS, PdS; bKdS, Rb814 188 WKbS, RcS, PdS; bKb3, RdS14 189 wKfS, ReS, PdS; bK£3, RdS15 020 wKa3, Ra7, PaS; bKc3, RcS15 021 wKa3, RaS, Pa6,- bKc3, Ra715 023 WKC8, RaS, PaS; bKe7, Rd715 026 wKcS, RbS, PaS; bKeS, RaS15 049 WKfS, Rb8, PbS; bKf 6 , RaS15 065 WKfS, RcS, PbS; bKf3, RbS15 140 WKfS, RdS, PCS; bKf3, RcS15 173 wKdS, Rd7, PdS; bKf8, RcS15 187 WKaS, RcS, PdS; bKb3, RdS15 191 WKdS, RaS, Pd4; bKdS, Rc816 029 wKa2, Ra3, PaS; bKc2, Ra616 056 wKg7, Rb7, PbS; bKgS, RhS16 066 wKgS, RcS, PbS; bKg3, RbS16 141 WKfS, ReS, PcS; bKf3, Rh616 142 wKgS, RdS, PCS; bKg3, RcS16 157 WKeS, Rh3, PC2; bKe4, Rd416 176 wKe7, Rh7, PdS; bKcB, RgS16 177 wKe7, Rh7, Pd6; bKcS, RgS17 014 WKcS, RbS, Pa6; bKc4, Ra717 OSO wKg7, Rb7, PbS; bKhS, Rh617 086 WKaS, RbS, Pb2; bKa2, Ral17 143 WKgS, RfS, PcS; bKg3, ReS17 183 wKdS, Rd7, PdS; bKf8, RcS18 067 wKgS, RfS, PbS; bKg3, Rd618 072 WKbS, RbS, Pb4; bKb2, Rb318 139 WKfS, RhS, PcS; bKg7, Rg618 144 wKe4, ReS, PcS; bKf6, RdS18 147 WKbS, Rb4, PC4; bKd4, Rcl18 149 wKbS, RcS, Pc3; bKb3, Ra419 071 wKb7, RbS, Pb4; bKd6, Ra419 073 WKaS, Ra4, Pb4; bKc4, Rbl19 14B wKe4, ReS, Pc4; bKf7, RdS19 154 wKf4, Ra4, Pc3; bKf2, ReB19 185 wKd7, Rd6, PdS; bKbS, RcS19 193 WKfS, ReS, Pd4; bKf3, Rh619 206 wKd3, Rb3, Pd2; bKdl, Ral20 068 wKd4, RdS, PbS; bKe7, Rcl20 076 wKdl, Ra4, Pb4; bKf2, Re220 145 WKC7, RcS, Pc4; bKe6, Rb420 152 WKC4, RcS, Pc3; bKa3, Rb320 194 wKfl, RC4, Pd4; bKh2, Rg221 015 wKf6, ReS, PaS; bKf4, Rh721 069 wKe2, RaS, PbS; bKg3, Rf321 078 WKbS, Rb4, Pb3; bKbl, Rb2

108

21222223232323232323242424242424242424242525252525252626262626272727282828282929293131323233343535353536363637373839414243

159:034:150:074 :077:091:151:158:195:200 :024:070:085;155:156:160;:161:190:204i:205:013:031:082:088:201:208:025:027:032:079:192:028:030:089:075:080:087:197:081:084:092:09!0:198:093:203:094 :099:036:097:098:199:035:096 :153:033:095:083:209:207:196:202:

wKd5,wKf3,wKe5,wKe3,wKel,wKf4,wKc4,wKc5,wKe7,wKc2,wKb6,wKel,wKdl,wKb3,wKf2,wKc4,wkcl,wKd3,wKcS,wKc5,wKb8,wKe4,wKd2,wKb5,wKd2,wKf2,wKb6,wKe3,wKe4,wKb4,wKd5,wKf3,wKb5,wKb4,wKf3,wKe4,wKb6,wKe6,wKf4,wKe2,wKb3,wKf4,wKdS,wKf3,wKe6,wKf2,wKfl,wKal,wKcl,wKel,wKg4,wKd4,wKbl,wKf4,wKf6,wKbl,wKe2,wKdl,wKb2,wKe6,wKcl,

Rh2,Ral,Rd5,Ra4,Ra4,Rbl,Rc6,Rc3,Rc4,Rel,Ra6,Ra5,Ra3,Rb4,Rg3,Rc6,Rb2,Rc5,Ra6,Rd4,Ra8,Rb4,Re3,Rb3,Rb8,Re2,Ra6,Ra6,Rd4,Rb6,Ra6,Ra6,Ra5,Rb6,Ra4,Ra3,Rb4,Rd6,Ra3,Ra3,Rb5,Rg2,Re3,Rg2,Rd6,Rg2,Rg2,Rh2,Rf2,Ra2,Rd4,Rg2,Rf2,Ra3,Rg3,Rf6,Re3,Rg7,Ra4,Rh3,Rc3,

PC2;Pa3;PC3;Pb4;Pb4;Pb2;PC3;Pc2;Pd3;Pd3;Pa5;Pb5;Pb3;Pc3;PC3;Pc2;PC2;Pd5;Pd2;Pd2 ;Pa6;Pa4;Pb3;Pb2;Pd3;Pd2;Pa5;Pa5;Pa4;Pb3;Pd4;Pa5;Pa4;Pb2;Pb4;Pb3 ;Pb2;Pd3;Pb3;Pb3;Pb2;Pb2;Pd3;Pb2;Pd2;Pb2;Pb2;Pa2;Pb2;Pb2;Pd3;Pa2;Pb2;Pc3;Pa3;Pb2;Pb3;Pd2;Pd2;Pd3;Pd3;

bKe3,bKh2,bKg5,bKg4,bKg2,bKh3,bKe5,bKe4,bKg5,bKa3,bKg6,bKg2,bKf2,bKg6,bKh4,bKe5,bKal,bKf 5,bKe5,bKa3,bKf 6,bKg4,bKf 4,bKd4,bKa3,bKh2,bKh6,bKg5,bKg4,bKd5,bKf 5,bKh5,bKh5,bKd5,bKh4,bKg5,bKd5,bKg6,bKh5,bKg3,bKd4,bKh5,bKf 1,bKh5,bKg6,bKh6,bKh7,bKfl,bKg4,bKg2,bKg2,bKh5,bKg4,bKh5,bKh7,bKg4,bKf 5,bKh3,bKf 2,bKf 8,bKel,

Rc3Ra4Rc6Rf4Rf2Rb3Rb8RclRf4Rb3Rf5Rf2Re 2Rf8RhlRe 8Ra4Re 5Rh4RdlRe7Ra5Ra3RblRd7Rd3Rg5Rf5Rc5Ra8Re 8Rg5Rg4Rd8Rg4Rf5RblRa3Rg5Rf3Ra8Rb8Re 3Re 8

Rf3Re8Re8Ra8Rb8Rf2Rf3RclRh8Rg5Ra8Rb8Ra3Ra8Rf3Rd4Re 3

*C* AH Reciprocal Zugzwangs inthe GBR class 1300.01

Next in our gripping serial REC1ZUGSFOR ALL it is the turn of queen againstrook and pawn. There are 240 'normal*Type 1 instances, and two 'reverse' caseswhere the 'inferior side' wins, but thereare no Type 3 cases of 'whoever movesloses'. Our thanks, as usual, to Lars Ras-mussen. The sequence is by pawn rankwithin pawn file. For the subgroup ofrecizugs with the pawn on the samesquare the sequence depends on the rankof the white king, then on the file. Giventhe algebraic system and that we are'running down the board from the top'this means that higher numbers precedelower numbers.

1:2 :3:4 :5:6 :7 :8 :9:

10:11:12 :13 :14 :15:16:17:18:19:20:21:22:23:24:25:26:27:28:29:30:31:32 :33:34 :35:36:37:38:

wKelwKa6wKc5wKc4wKc4WKC4WKC4wKd3wKe3wKg2wKflwKhlwKa8wKa7wKc7wKd7wKg7wKd6wKh6wKg5wKd4wKc3WKC3wKd3wKe3wKf3wKe2wKf2wKh2wKh2wKalwKalwKalwKalwKalwKflwKflwKfl

, QC2;, Qa2;, Qh2 ;, Qb8;, Qb7 ;, Qb6 ;, Qb5;, Qal;, Qal;, Qcl;/"Qd5;, Qdl;/ Qdl;, Qdl;, Qdl;, Qal;, Qfl;, Qcl;, Qhl ;, Qfl;, Qfl;, Qdl;. Qa5;, Qal;, Qd4;. Qd4;, Qc3;, Qcl ;, Qc3;, Qa5;, Qe3;, Qf3;, Qb3;, QC3;, Qa4 ;, Qd4;, Qel;. Oa3;

bKal,bKb4,bKb3,bKa2,bKa2,bKa2,bKa2,bKb3,bKb4,bKe2,bKb4#

bKe3,bKc8,bKc7,bKe7,bKb7,bKe7,bKd3,bKa8,bKe7f

bKd2,bKcS,bKe 1,bKb3,bKg3#

bKel,bKe4,bKd3,bKf 2,bKfl,bKc4,bKh4#

bKd2,bKe2,bKdl,bKf 3,bKf 3,bKh2,

Rb3,Rb3,Rb7,Rh3,Rg3,Rf3,Re3,Rb2,Rb2,Rd3,Rh4,Rc3,Rc4 (

Rc4,Re6,Ra4,Re6,Rb3,Rb7,Re6,Rc2,Rb4,Rd2,Ra3,Rc2,Rc2,ReB,Rb3,Re2,Re3,Rc2,Rh2 ;

Rc2,Rd2 #

Rc2,Rf5,Rf5,Rc2.

Pa4Pa3Pa3Pa 3Pa 3Pa3Pa3Pa 3Pa3Pa 3Pa3Pa 3Pa2Pa2Pa 2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa 2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2Pa2

237115546

10167

2725873

125

119746

225

102

a5

2426326875

114

109

39:40:-41 :42:43:44 :45:46:47:48:49:50:51:52:53:54:55:56:57:58:59:60:61:62:63:64:65:66:67:68:69:70:71:72 :73:74:75:76:77:78 :79:80:81:82:83:84:85:86:87:88:89:90:91:92:93:94:95:96:97:98:99:

100:101:102:103 :104 :105:

wKhl,wKe8,wKf7,wKg5,wKa4,wKd4,wKd4,wKa3,wKa3,wKa3,wKb3,wKc3,wKc3,wKb2,wKbl,wKb4,wKb3,wKa2,wKal,wKd3,wKd2,wKfl,wKf6,wKe4,wKf4,wKf4,wKf3,wKal,wKdl,wKh8,wKa7,wKb7,wKc7,wKd7,wKh6,wKc4,wKf4,wKd3,wKe3,wKe3,wKb2,wKb2,wKe2,wKg2,wKbl,wKel,wKfl,wKgl,wKgl,wKhl,wKf8,wKd7,wKf7,wKf7 ;

wKg7,wKg7,wKe6,wKf6,wKf6,wKg6 ,wKa5,wKe5,wKe5,wKg5,wKg5,wKg5,wKd4,

Qc3;Qe5;Qb8;Qh8;Qd4;Qd8;Qd5 ;Qd6;Qe5;Qf5;Qa8;Qe6;Qa3;Qb8;Qb8;Qd7;Qd7;Qa6;Qa6;QaS;Qd3;Qb2;Qb3;Qa4;Qb5;Qc5;Qh6;Qdl;Qd2;Qhl;QC4;Qd4;Qf2;Qf2;Qh4;Qa4;Qcl;Qb2;Qa6;Qe2;Qd6;Qc8;Qe6;Qa6;Qd8;Qdl;Qdl;Qe4;Qdl;Qd2;Qb6;Qe4;Qb6;Qb5;Qel ;Qfl;Qh7;Qb5;Qel;Qb5;Qfl;Qg6;Qb3 ;Qbl;Qb4;Qb4;Qd3;

bKfl,bKc8,bKb6,bKc7,bKa6,bKc6,bKb4,bKa5#bKc4,bKc4,bKb5,bKc5,bKd5,bKa4;

bKa4,bKa6,bKa6,bKb8,bKb8,bKb3,bKb2,bKc5,bKd6,bKc4,bKd4,bKa3,bKb3,bKa3,bKbl,bKc7,bKa5VbKb5,bKc5fbKd5,bKa5,bKc2,bKd3,bKb5,bKc3,bKc3,bKc8,bKd6,bKc5,bKc5,bKc6,bKe3,bKe3,bKc5,bKe3,bKc4,bKd7,bKb8,bKd7,bKd6,bKd7,bKg5,bKb8,bKd6,bKf4,bKe6,bKc5,bKc7,bKa5,bKg8,bKe6 ibKe5,bKb4,

Re2,Rc6,Rh5,Re2,Rbl,Rb5,Rc6,Rb5,Rc6,Rb6,Rb6,Rb5,Rb5,Rc6,Rc5,Rc5,Rcl,Rb4,Rb3,Rc5,Rc4,Rh3,Rb5,Rc3,Rc4,Rbl,Rel,Rc3,RC3,Ra2,.%Rb5,Ra5,Rd4,Rd4,Rfl,Rb8,Rd5,Rb4,Rc4,Rb4,Rb7,Rb6,Rd5,Rf7,Rb7,Rc2,Rc3,Rf7,Rc2,Rg8,Rg2,Rh2,Rd2,Rg2,Rd4,Rd2,Rd2,Rd2,Rh2,Rd2,Rd5,Rd2,Rd2,Rb7,Rd2,Re2,Ra4,

Pa 2Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb7Pb6Pb6Pb6Pb6Pb5Pb5Pb5Pb4Pb4Pb4Pb4Pb4Pb4Pb4Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb3Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2

25104641252035

2827237

63212229301617263

3320121728261514102

14133168

2116151559

169

113

126

1323291622242530182227233221151125244

106:107:108:109:110:111 :112:113:114:115:116:117:118:119:120:121:122:123 :124:125:126:127:128:129:130:131:132:133:134:135:136:137:138:139:140:141.:142:143:144:145:146:147:148:149:150:151:152:153:154:155:156:157:158:159:160:161:162:163:164:16 5:166:167:168:169:170:171:172:

wKd4,wKg2,wKh2,wKbl,wKbl,wKbl,wKfl,wKgl,wKhl,wKhl,wKhl,wKhl,wKe6,wKa5,wKa5,wKd5,wKd5,wKa4,wKb4,wKb4,wKc4,wKb3,wKc3,wKb2,wKe2,wKf2,wKa2,wKa77

wKe6,wKf6,wKel,wKd8,wKe8,wKa7,wKa7,wKb6,wKa5,wKb5,wKh5,wKa4,wKe4,wKe4,wKf4,wKg4,wKe3,wKg3,wKh3;

wKh3,wKh3,wKc2,wKc2,wKe8,wKf8,wKf8,wKg8,wKh8,wKf7,wKh7,wKa6,wKf6,wKg6,wKd5,wKa4,wKa4 ,wKe4,wKe4,wKe4,

Qbl;Qdl;Qe4;QC6;QC4 ;QC7;Qb3;Qb3;Qd4;Qe4;Qb3;Qd3;Qd2;Qb4;Qe8;Qh6;QC4;Qb4;Qb5;Qa8;Qe6 ;Qa7;Qb8;Qa7;Qb5;Qb5;Qa3;Qb7;Qg5;Qg8;Qe2;Qd7;Qf8;Qa4;Qe4;Qdl;Qe3;QC2;Qg8;Qa3;Qd3;Q93;Qb5;Qc5;QC4;QC2;Qg4;Qc2;Qb3;Qe6;Qd8 ;Qhl;QC4;QC3;Qfl;Qgl;QC4 ;Qfl;Qe3;QC4;Qfl;Qf4;Qe3 ;Qb2;Qa3 ;Qd2 ;Qcl;

bKd2,bKe3,bKf2,bKd8,bKb6,bKd5,bKh2,bKel,bKel,bKfl,bKfl,bKfl,bKc8,bKa7,bKd6,bKc8,bKb7,bKa8,bKd7,bKb6,bKd8,bKb5,bKc5,bKb4,bKa8,bKa8,bKc2,bKa4,bKb4,bKb3,bKel,bKc5,bKc5,bKc5,bKc5,bKe3,bKc4,bKd7,bKd5,bKc4,bKa3,bKa3,bKd4,bKe4,bKa3,bKe3,bKd5,bKf3,bKf2,bKd8,bKe6,bKb8,bKd6,bKd5,bKg6,bKh6,bKd6,bKe7,bKc8,bKd6,bKg4,bKd7,bKc4,bKc4,bKc4,bKc4,bKe2,

Rc2,Rc3,Rd2,Rb8,Rb5,Rb5,Rd2,Rd2,Ra2,Rd2,Rd2,Re2,Rh7,Ra8,Rb6,Rf2,Re3,Rh2,Rc6,Rcl,Ra5,Rc6,Rc6,Rc6,Rgi,Ral,Rb4,Re2,Rdl,Rb5,Rd3,Rf3,Rd6,Rf6,Rc6,Re5,Rd4,Rc8,Re6,Rb2,Rc6,Rc5,Rel,Rd3,Rb2,Rd3,Rf8,Re3,Re4,Rc7,Rc6,Rd6,Re2,Re2,Rg5,Rh3,Rg2,Re4,Rd7,Re2,Rh2,Rd8,Rd4,Re2,Rb4,Ra2,Rd2,

Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pb2Pc7Pc7Pc7Pc7Pc7PC7Pc7Pc7Pc7PC7Pc7PC7PC7PC7PC5PC4PC4PC4PC4Pc3PC3Pc3Pc3Pc3Pc3Pc3Pc3Pc3Pc3Pc3Pc3Pc3PC3Pc3Pc3Pc3Pc3Pc3Pc3Pc2Pc2PC2Pc2Pc2Pc2Pc2Pc2Pc2Pc2Pc2Pc2Pc2Pc2Pc2Pc2

15

252

13216

232

2626253440162014383628424

214135343

25444 8257

2321171684151011223

169

1616145

1125252628202319281720178

175

101

110

173: wKd3, Qf2; bKa2, Rc7 , Pc2 4 240: wKfl, Qbl; bKd3, Rc2, Pd2 7174: wKd3, Qb3; bKdl, Ra2, Pc2 4 The same sorted by ascending depth175: wKe3, Qb2; bKg2, Rc7, Pc2 17 value:176: wKg3, Qh6; bKd7, Re2, Pc2 15 106: wKd4, Qbl; bKd2, Rc2, Pb2 l177: wKg3, Qe4; bKfl, Rd2, Pc2 3 172: wKe4, Qcl; bKe2, Rd2, Pc2 l178: wKh3, Qh6; bKd7, Rf 2, Pc2 16 225: wKb4, Qdl; bKb2, Rc2, Pd2 l179: wKh2, Qc3 ; bKf2, Re2, Pc2 18 229: wKf4, Qdl; bKf 2, Re2, Pd2 l180: wKal, Qel; bKc3, Rd2, Pc2 8 1: wKcl, Qc2; bKal, Rb3, Pa4 2181: wKcl, Qd6; bKeS, Rc8, Pc2 2 26: wKf3, Qd4; bKel, Rc2, Pa2 2182: wKcl, Qd7; bKe4, Rc3, Pc2 7 32: wKal, Qf3; bKh4, Rh2, Pa2 2183: wKcl, Qd6; bKe4, Rc4, Pc2 6 69: wKa7, Qc4; bKaS, Rb5, Pb3 2184: wKcl, Qb5; bKa3, Rc4, Pc2 2 109: wKbl, Qc6; bKd8, Rb8, Pb2 2185: wKel, Qal; bKc3, Rb2, Pc2 5 114: wKhl, Qd4; bKel, Ra2, Pb2 2186: wKgl, Qfl; bKg3, Re2, PC2 4 136: WKel, Qe2; bKel, Rd3, Pc4 2187: wKhl, Qc3; bKfl, Re2, Pc2 20 181: wKcl, Qd6; bKeS, Rc8, PC2 2188: wKdS, QaS; bKb7, Rb6, Pd7 8 184: wKcl, Qb5; bKa3, Rc4, Pc2 2189: wKf4, Qc4; bKdS, Ra5, Pd7 30 209: wKal, Qbl; bKa3, Rc2, Pd3 2190: wKg8, Qg4; bKeS, Rc2, Pd3 39 235: wKdl, Qc6; bKb8, RdS, Pd2 2191: WKC6, Qh7; bKc2, Ra5, Pd3 32 236: WKdl, Qe6,- bKfS, Rd8, Pd2 2192: wKe6, Qhl; bKd2, Rd4, Pd3 35 15: wKc7, Qdl; bKe7, Re6, Pa2 3193: wKcS, Qd2; bKe7, Rd8, Pd3 8 31: wKal, Qe3; bKc4, Rc2, Pa2 3194: wKcS, Qa6; bKe2, Rh4, Pd3 22 45: wKd4, QdS; bKb4, Rc6, Pb7 3195: WKdS, Qh7; bKc2, Rg4, Pd3 29 59: wKd2, Qd3; bKb2, Rc4, PbS 3196: wKdS, Qg6; bKc2, Rf4, Pd3 23 84: wKel, Qdl; bKe3, Rc2, Pb3 3197: WKdS, Qa6; bKe2, Rb4, Pd3 23 132: wKa2, Qa3; bKc2, Rb4, PCS 3198: wKe5, Qd2; bKc7, RdS, Pd3 7 149: wKg4, QcS; bKe4, Rd3, Pc3 3199: wKb4, Qa3; bKe3, Rc7, Pd3 23 177: wKg3, Qe4; bKfl, Rd2, PC2 3200: wKf4, Qg3; bKc3, Re7, Pd3 32 212: wKgl, Qfl; bKg3, Re2, Pd3 3201: wKb2, Qa3; bKe3, Rc7, Pd3 25 6: wKc4, Qb6; bKa2, Rf3, Pa3 4202: wKb2, Qb3; bKe3, Rc6, Pd3 19 21: wKd4, Qfl; bKd2, Rc2, Pa2 4203: wKd2, Qb6; bKcB, Rd7, Pd3 5 38: wKfl, Qa3; bKh2, Rc2, Pa2 4204: wKd2, Qf 6; bKeS, Rd7, Pd3 5 105: wKd4, Qd3; bKb4, Ra4, Pb2 4205: wKd2, Qe8; bKf6, Rd6, Pd3 9 127: wKb3, Qa7; bKb5, RcS, Pc7 4206: wKd2, Qa6; bKcS, RdS, Pd3 7 144: wKhS, Qg8; bKdS, Re6, Pc3 4.207: wKf2, Qf3; bKc3, Re6, Pd3 19 173: wKd3, Qf2; bKa2, Rc7, Pc2 4208: wKf2, Qg3; bKc3, Re7, Pd3 34 174: wKd3, Qb3; bKdl, Ra2, Pc2 4209: wKal, Qbl; bKa3, Rc2, Pd3 2 186: wKgl, Qfl; bKg3, Re2, Pc2 4210: WKdl, Qa6; bKcS, Rd7, Pd3 13 4: wKc4, Qb8; bKa2, Rh3, Pa3 5211: wKel, Qhl; bKd, RfS, Pd3 16 5: wKc4, Qb7; bKa2, Rg3, Pa3 5212: WKgl, Qfl; bKg3, Re2, Pd3 3 17: wKg7, Qfl; bKe7, ReS, Pa2 5213: wKg8, Qh5; bKf 6, Rf 2, Pd2 27 24: wKd3, Qal; bKb3, Ra3, Pa2 S214: WKhS, Qgl; bKh6, Rh3, Pd2 24 28: wKf 2, Qcl; bKd3, Rb3, Pa2 S215: wKb7, Qal; bKd7, Rg4, Pd2 16 36: wKfl, Qd4; bKf3, Rf5, Pa2 S216: wKb7, Qgl; bKd7, Rf4, Pd2 15 46: wKa3, QdS; bKaS, Rb5, Pb7 5217: wKf7, Qal; bKd7, Rb4, Pd2 11 79: wKb2, Qd6; bKcS, Rb7, Pb3 5218: wKf7, Qgl; bKd7, Ra4, Pd2 13 107: wKg2, Qdl; bKe3, Rc3, Pb2 5219: wKh7, Qd4; bKe6, Rg2, Pd2 20 137: wKd8, Qd7; bKcS, Rf3, Pc3 S220: wKa6, Qbl; bKa3, Rc3, Pd2 10 155: wKc2, Qe6; bKdS, Rc7, Pc3 5221: wKh6, Qd4; bKf 5, Rg2, Pd2 19 170: wKe4, Qa3; bKc4, Rb4, PC2 S222: wKg5, Qa4; bKeS, Rb2, Pd2 16 185: wKel, Qal; bKc3, Rb2, PC2 5223: wKb4, Qf 3; bKd4, Re4, Pd2 7 203: wKd2, Qb6; bKcS, Rd7, Pd3 5224: wKb4, Qc2; bKd4, Rf 2, Pd2 16 204: wKd2, Qf6; bKeS, Rd7, Pd3 5225: wKb4, Qdl; bKb2, Rc2, Pd2 l 227: wKf4, Qb3; bKd4, Rc4, Pd2 5226: wKe4, Qf 2; bKa2, Rd7, Pd2 16 232: wKe3, QO3; bKel, Rb2, Pd2 5227: wKf4, Qb3; bKd4, Rc4, Pd2 5 7: wKc4, QbS; bKa2, Re3, Pa3 6228: wKf4, Qe2; bKd4, Rb2, Pd2 12 22: wKc3, Qdl; bKcS, Rb4, Pa2 6229: WKf 4, Qdl; bKf 2, Re2, Pd2 l 33: wKal, Qb3 ; bKd2, RC2, Pa2 6230: wKh4, Qdl; bKh8, Rd7, Pd2 11 73: wKh6, Qh4; bKaS, Rfl, Pb3 6231: wKe3, Qc7; bKdl, Rf2, Pd2 11 86: wKgl, Qe4; bKcS, Rf7, Pb3 6232: wKe3, Qc3; bKel, Rb2, Pd2 5 112: wKfl, QbS; bKh2, Rd2, Pb2 6233: wKf3, Qdl; bKd3, Rb4, Pd2 14 183: wKcl, Qd6; bKe4, Rc4, Pc2 6234: wKbl, Qfl; bKd3, Re2, Pd2 8 239: wKdl, Qe6; bKf 4, Rd4, Pd2 6235: WKdl, Qc6; bKb8, Rd8, Pd2 2 10: wKg2, Qcl; bKe2, Rd3, Pa3 7236: wKdl, Qe6; bKfS, RdS, Pd2 2 14: wKa7, Qdl; bKc7, Rc4, Pa2 7237: WKdl, Qc6; bKb4, Rd4, Pd2 7 20: wKgS, Qfl; bKe7, ReS, Pa2 7238: wKdl, Qe7; bKf 4, Rd3, Pd2 7 35: wKal, Qa4; bKdl, Rc2, Pa2 7239: wKdl, Qe6; bKf4, Rd4, Pd2 6 50: wKc3, Qe6; bKcS, Rb5, Pb7 7

138:182 :198 :206 :223:237:238:240:13:27:34:74:

143:168:180:188:193:234:19:80:82:

151:205:

8:25:40:G3:

146:171:220:

3:18:37:83:

102:147:156:217:230:231:16:62:85:

228:71:87:

110:210:218:67:70:

122:154:233:66:77:78:

101:145:176:216:

9:56:76:81:90:

120:

: wKe8,wKcl,wKe5,wKd2,wKb4,wKdl.,wKdl,wKfl,wKa8,wKe2,wKal,wKc4,wKb5,wKa4,wKal,wKd5,wKc5,wKbl,wKh6,wKb2,wKg2,wKg3,wKd2,wKd3,wKe3,wKe8,wKh8,wKe4,wKe4,wKa6,wKc5,wKd6,wKfl,wKbl,wKg5,wKe4,wKc2,wKf7,wKh4,wKe3,wKd7,wKe4,wKfl,wKf4,wKc7,wKgl,wKbl,wKdl,wKf7,wKdl,wKb7,wKd5,wKh3,wKf3,wKal,wKe3,wKe3,wKe5,wKa4,wKg3,wKb7,wKe3,wKa2,wKd3,wKe2,wKd7,wKa5,

Qf8;Qd7;Qd2;Qa6;Qf3;Qc6;Qe7;Qbl;Qdl;Qc3;Qc3;Qa4;Qc2;Qe3 ;Qel;Qa5 ;Qd2;Qfl;Qhl;Qc8;Qa6;QC2;Qe8;Qal;Qd4;Qe5;Qhl ;Qd3 ;Qd2;Qbl;Qh2;Qcl;Qel;Qd8;Qbl;Qg3;Qd8;Qal;Qdl;QC7;Qal;Qa4;Qdl;Qe2;Qf2;Qdl;Qc4;Qa6;Qgi;Qd2;Qd4;QC4 ;Qb3;Qdl;Qdl;Qa6;Qe2;Qb3;Qa3;Qh6;Qgi;Qal;Qa6 ;Qb2;Qe6;Qe4 ;Qe8;

bKcS,bKe4,bKc7,bKcS,bKd4,bKb4,bKf4#

bKd3,bKc8,bKe4,bKe2,bKc2,bKd7,bKc4,bKc3,bKb7,bKe7,bKd3,bKa8,bKd6ybKc5,bKe3,bKf6,bKb3,bKg3,bKc8,bKc7,bKa3,bKc4,bKa3,bKb3,bKd3,bKf3,bKc6,bKg8,bKa3,bKe6,bKd7,bKhS,bKdl,bKb7,bKc4,bKe3,bKd4,bKc5,bKe3,bKb6,bKc5,bKd7,bKbl,bKb5,bKb7,bKf2,bKd3,bKa3,bKc3,bKc3,bKa5,bKc4,bKd7,bKd7,bKb4,bKb8,bKb5,bKc5,bKb8,bKd6,

Rd6,Rc3,Rd8;

Rd5,Re4,Rd4,Rd3,Rc2,RC4,Re5,Rd2,Rb8,Rc8,Rd4,Rd2,Rb6,Rd8,Re2,Rb7,Rb6,Rf7,Rd3,Rd6,Rb2,Rc2,Rc6,Ra2,Rc6,Ra2,Rc3,Rb7,Rb3,Rf5,Rb7,Rb7,Rc5,Rc6,Rb4,Rd7,Rf2,Ra4,Rc3,Rc3,Rb2,Rd4,Rc2,Rb5,Rd7,Ra4,Rc3,Ra5,Re3,Re4,Rb4,Rc3/Rc4,Rb4,Rd2,Rb2,Re2,Rf4,Rb2,Rb4,Rb4,Rd5,Rh2,Rb6,

Pc 3Pc2Pd3Pd3Pd2Pd2Pd2Pd2Pa2Pa2Pa2Pb3Pc3Pc2Pc2Pd7Pd3Pd2Pa2Pb3Pb3Pc3Pd3Pa3Pa 2Pb7Pb3Pc3Pc2Pd2Pa3Pa2Pa2Pb3Pb2Pc3Pc3Pd2Pd2Pd2Pa2Pb4Pb3Pd2Pb3Pb3Pb2Pd3Pd2Pb4Pb3Pc7Pc3Pd2Pb4Pb3Pb3Pb2Pc3Pc2Pd2Pa3Pb6Pb3Pb3Pb2Pc7

77777777888888888899999

1010101010101011111111111111111111121212121313131313141414141415151515151515161616161616

142:150:152:153:178:211:215:222:224:226:57:63:

141:165:167:169:175:95:

179:163:202:207:221:44:61:

121:161:166:187:219:52:75:

100:111:128:140:23 :53:91:96:

148:194:49:88:98:

113:13 9:162:196:197:199:29:92:

104:214:12:39:43:93:

103:108:117:133:157:158:201:30:

: wKa5,: wKe3,wKh3,wKh3,wKh3,wKel,wKb7,wKg5,wKb4,wKe4,wKal,wKf4,wKb6,wKf6,wKd5,wKa4,wKe3,wKe6,wKh2,wKh7,wKb2,wKf2,wKh6,wKd4;

wKf6,wKd5;

wKh8,wKg6,wKhl,wKh7,wKb2;

wKf4,wKe5,wKbl,wKc3,wKa7,wKc3,wKbl,wKf7,wKf6,wKf4,wKc5,wKb3,wKhl,wKg6,wKgl,wKa7,wKf7,wKd5,wKd5,wKb4,wKh2,wKf7,wKgS,wKh8,wKhl,wKhl,wKa4,wKg7,wKg5,wKh2,wKhl,wKa7,wKe8,wKf8,wKb2,wKh2,

Qe3;QC4 ;Qg4 ;Qc2;Qh6;Qhl;Qal;Qa4;Qc2;Qf2;Qa6;Qb5;Qdl;Qc4;Qf4;Qb2;Qb2;Qh7;Qc3;Qfl;Qb3;Qf3;Qd4;Qd8;Qb3;Qh6;Qgi;Qfl;QC3;Qd4;Qb8;Qcl;Qg6;Qc7;Qb8;Qe4;Qa5;Qb8;Qb6;Qb5;Qb5 ;Qa6;Qa8;Qd2;Qb5;Qb3;Qa4;QC4;Qg6;Qa6;Qa3;QC3;Qb5;Qb4;Qgi;Qdl;Qc3;Qd4;Qel ;Qb4;Qe4;Qd3;Qb7;Qhl;QC4;Qa3;Qa5;

bKc4,bKa3,bKd5,bKf3,bKd7,bKcl,bKd7,bKe5,bKd4,bKa2,bKb8,bKd4,bKe3,bKd6,bKd7,bKc4,bKg2,bKb8,bKf2,bKe7,bKe3,bKc3,bKf5,bKc6,bKd6,bKc8,bKh6,bKg4,bKfl,bKe6,bKa4,bKd3,bKc7,bKd5,bKc5,bKc5,bKel,bKa4,bKd7,bKd6,bKd4,bKe2#

bKb5,bKc4,bKe6,bKel,bKcS,bKd6,bKc2,bKe2,bKe3,bKf2,bKd6,bKe5,bKh6,bKe3,bKfl,bKa6,bKd7,bKe6,bKf2,bKfl,bKa4,bKb8,bKd6,bKe3,bKfl,

Rd4;Rb2,Rf8,Re3,Rf2,Rf6,Rg4,Rb2,Rf2,Rd7,Rb3,Rc4,Re5,Re2,RdS,Re2,Rc7,Rd2,Re2,Re4,Rc67Re6,Rg2,Rb5,Rb5,Rf2,Rh3,Rh2,Re2,Rg2,Rc6,Rd5,Rd2,Rb5,Rc6,Rc6,Rd2,Rc5,Rd2,Rd2,Rel,Rh4,Rb6,Rg8,Rd2,Rd2,Rf6,Rg2,Rf4,Rb4,RC7,Re2,Rg2,Re2,Rh3,Rc3,Re2,Rbl,Rd4,Rd2,Rd2,Re2,Re2,Rd6,Re2,Rc7,Re3,

Pc3Pc3Pc3Pc 3Pc2Pd3Pd2Pd2Pd2Pd2Pb6Pb4Pc3Pc2Pc2Pc2Pc2Pb2Pc2Pc2Pd3Pd3Pd2Pb7Pb4Pc7Pc2Pc2Pc2Pd2Pb7Pb3Pb2Pb2Pc7Pc3Pa2Pb7Pb2Pb2Pc3Pd3Pb7Pb3Pb2Pb2Pc3Pc2Pd3Pd3Pd3Pa2Pb2Pb2Pd2Pa3Pa 2Pb7Pb2Pb2Pb2Pb2Pc4Pc2Pc2Pd3Pa2

16161616161616161616171717171717171818191919192020202020202021212121212122222222222223232323232323232324242424252525252525252525252526

112

58:6 5 :!:

115::1 1 6 :i:

159:111::4 8:i'97:

213:4 7 :|.64:

12 5:;16 0:164:54 :89:

195:55:94 :

18 9:7 2 :•

99:191:200:60:

118:131:208:130:192:124 :

2:123:190:119:42 :

12 9:12 6:134:41:

13 5:51:

Type

wKd3,wKf3,wKhl,wKhl,wKf8,wKfl,wKa3,wKf6,wKg8,wKa3,wKf4,wKb4,wKg8,wKa6,wKb4,wKf8,wKd5,wKb3,wKg7,wKf4,wKd7,wKa5,wKc6,wKf4,wKfl,wKe6,wKf2,wKf2,wKe2,wKe6,wKb4,wKa6,wKa4,wKg8,wKa5,wKg5,wKb2,wKc4,wKe6,wKf7,wKf6,wKc3,

Qa5;Qh6;Qe4 ;Qb3;Qc3;Qd5;Qf5;Qel;Qh5;Qe5;QC5;Qa8;Qfl;Qe3;Qd7;Qb6;Qh7;Qd7;Qfl;QC4;Qf2;Qfl;Qh7;Qg3;Qb2;Qd2;Qb5 ;Qg3;Qb5;Qhl;Qb5;Qa2;Qb4;Qg4;Qb4;Qh8;Qa7;Qe6;Qg5;Qb8;Qg8;Qa3;

bKb3,bKb3,bKfl..bKfl,bKd5,bKb4,bKc4,bKf4,bKf6,bKc4,bKa3#

bKb6,bKg6,bKc8,bKa6,bKd7,bKc2,bKa6(bKg5,bKd8,bKd5,bKc5,bKc2,bKc3,bKcB,bKc8,bKa8,bKc3,bKa8,bKd2,bKd7,bKb4,bKaS,bKe5,bKa7,bKc7,bKb4,bKd8,bKb4,bKb6,bKb3,bKd5,

Rc5,Rel,Rd2,Rd2,Re2,Rh4,Rb6,Rh2,Rf2,Rc6,Rbl,Rcl,Rg5,Rd7,Rc5,Rg2,Rg4,Rcl,Rd2,Ra5,Rd4,Rd5,Ra5,Re7,Rh3,Rh7,Ral,Re7,Rgi,Rd4,Rc6,Rb3,Rh2,Rc2,Ra8,Re2,Rc6,Ra5,Rdl,Rh5,Rb5,Rb5,

2 reciprocal zugzwangto move loses,draw;0011002 :

5 :wKal,wKal,

Qa2;Qa2;

Black

bKe2,bKf2,

Pb5Pb4Pb2Pb2Pc2Pa3Pb7Pb2Pd2Pb7Pb4Pc7Pc2Pc2Pb6Pb2Pd3Pb6Pb2Pd7Pb3Pb2Pd3Pd3Pb5Pc7PC?Pd3PC7Pd3Pc7Pa3Pc7Pd3Pc7Pb7Pc7Pc7Pc4Pb7Pc4Pb7

262626262627272727282828282829292930303031323232333434343535363738394041414244464863

: Whiteto move

Rc6,Rc7,

Pc2Pc2

22

training match between Germany andArmenia.

Kindermann vs. A.Petrosianposition after 63.g8Q alQ

*C* QPQ - or GBR class 4000.10- in practice!

Witfi grateful acknowledgement toRochade Europa 9/96 (which itself ack-nowledges borrowing from Schachreport8/96^ EG offers its readers this fas-cinating insight into the o-t-b skill levelof top-level masters confronted by (orconfronting?) a Q+P vs. Q ending. Thegame conclusion comes from the topboard in a hard-fought pre-Olympiad

h7b6 4000.10 g8al .g2 3/2 WTM.The commentator reports with some as-tonishment that the player of Black,trainer to the Armenian team (and, in-cidentally, chosen to write the obituarypiece on Kasparyan for New in Chess),confessed to having no idea of how toplay this ending.Numbers between square brackets recordthe *C* optimal win-depth resulting fromthe immediately preceding half-move(even if the latter precedes theleft-bracket).64.Qg6+? [Qg5! 55] Ka5 65.Qf5+ Ka6?[K-4=] 66.g4 [47] Qhl+ 67.Kg7 Qb7+68.Qf7 [Kf6! 45] Qg2 [47] 69.Qf6+?[Qf5 45] Ka5 70.g5 Qb7+ 7i.Kg6 Qg2?[Qc7/Qhl=] 72.Qe6? [Qc3+ 63] Qhl73.Kg7 Qb7+? [31 Ka4/Kb4!] 74.Kf6[30] Qhl 75.g6 [29] Qh4+ 76.Kg7(?) [39Kf7! 28] Qd4+(?) [27 Ka4! 39] 77X17(7)[29 Kg8 27] Qf2+ [19 Qf4+ 28] 78.Ke7?[27 Kf5 19] Qa7+(?) [4 Qh4+ 18] 79.Kf6Qb8?? {Well! Time trouble, apparently.Yawn.} 8O.Qe7?? [Qe5+ (or Qa2+ AJR)]Qb6+? [25] 81.KH [26] Qb3+ 82.Kf8?[40 Ke6 26] QB+ 83.Kg8 [41] Qd5+[38] 84.Kg7 [39] Qd4+ [23] 85.KH(?)[30] Qd3 [15 Qf4+ 30] 86.Qe5+ [16]. Atthis point the scoresheet dried up. White,we read, had 8 seconds left. It was

113

enough because Black resigned a fewmoves later. An ('optimal') win fromhere on: Ka4 87.g7 QO+ 88.Ke7 Qb7+89.Kf6 Qf3+ 9O.Kg5 Qg2+ 91.KM Qhl +92.Kg4 Qdl+ 93.Kg5 Qd8+ 94.Qf6 Qd5+95.Qf5 Qd8+ 96.Kg6 Qa8 97.Qc2+ Kb498.Qb2+ Kc5 (Kc4;Qa2+) 99.Qc3+ Kd6100.Qf6+Kc7 10LQf7+.The Rochade commentary concludes:"Anyone scared stiff by this endgame cantake comfort. IGM Roberto Cifuentesscanned 457,000 games electronically tofind just 321 QPQ endings. This meansthat on average one game in 1424 reachesthis material. And even 24-carat masterscommit blunder after blunder, un-punished! Cifiientes found 45% won bythe stronger side - 144 were wins and177 were draws, which, he says, wasabout 'right' according to the theoretical-ly 'correct' results. cP/fP scored best (41wins in 70 - 58.6%); dP/eP 16 from 31 -51.6%; aP/hP 33 from 110 - 30%.AJR plans a database-assisted book onQPQ - unless someone else gets in first!

Stiller and the 6 pieces endgames

In the august 1996 edition of the Dutchmagazine Computerschaak contains twoarticles - in Dutch - aboutendgamedatabases. The second article is amore or less technical story how toconstruct those databases. The first is ahistorical overview, including the 243maximin in GBR-class 0107. From thisfirst article we give here a list of GBR,maximin, percentage wins and number ofzugzwangs. In the article the list is sortedby maximin, we give the list three times:once on GBR, once on percentage ofwins and once on number of zugzwangs:Remark: in these lists:0009 = KNNNKN, 0039 = KNNNKB,0390 = KBBBKR, 3900 = KRRRKQ,1090 = KQKBBB, 1009 = KQKNNN,

List by GBR:GBR maximin0009.000024.000026.000039.000107.000116.000134.000143.000161.000161.000170.000260.000312.000321.000390.000503.000510.000800.001009.001063.001090.001601.001610.003021.003111.003120.003201.003210.003900.004002.004004.004013.004031.004040.004103.004130.004301.004310.004400.005300.008000.00

86313892

24322319098

140527537496869735418356351

15385129944

1018265722936324671732732924844

wins94%99%63%86%78%96%72%87%77%65%72%94%53%95%80%81%73%67%75%85%82%86%92%62%69%75%94%96%98%94%63%68%61%66%90%87%57%62%83%92%83%

zugzwangs12,918

581,6626, 300

18,176456

8,0301,4781,634

2569526

1,2708348

1,4101,030

1617,6886, 6702, 8201,858

34218

1,010396

'1,520388

62,228

152783522

1,7801,410

36

2433232

There are two cases of 0161 in this list,the maximin of 52 is for bishops on dif-ferent colours, the other one is for thegeneral case. And now the same list bywin percentage:

GBR maximin w i n s zugzwangs0 3 1 2 . 0 0 . 49 53% 1,2704 3 0 1 . 0 0 27 57% 34 0 3 1 . 0 0 32 61% 353 0 2 1 . 0 0 12 62% 18

114

4310.004004.000026.000161 r004040:000800.004013.003111.000170.000134.000510.003120.001009.000161.000107.000390.000503,001090.008000;. 004400.001063.001601.000039.004130.000143.004103.001610.005300.000009.000260.003201.004002.000321.000116.003210.003900.000024.00

322938524618369975

190544435140243697351449263

1539273987185488637

1017268

223826531

62%63%63%65%66%67%68%69%72%72%73%75%75%77%78%80%81%82%83%83%85%86%86%87%87%90%-̂92%92%94%94%94%94%95%96%96%98%99%

6152

1,662256221678

1,01095

8,0301,030

39617,6881,63418,176

481,4102,820

32243

6,6701,8586,3001,4101,4781,780

34232

12,91826

1,5202,228

83456388

658

And finally the list by number ofzugzwangs:

GBR maximin4301.00 273900.004310.000800.003021.004040.000260.008000.005300.00

.00

wins zugzwangs

4031.0390.000024.004013.00

653218124637444832693136

57%98%62%67%62%66%94%83%92%61%80%9 9%68%

366

16182226323235485878

0321.000170.004004.004400.000161.001610.003210.003120.000116.003111.000510.000312.004130.000503.000143.003201.000161.000026.004103.001601.004002.001090.000039.001063.000134.000009.001009.000107.00

6875299252858244

223995449737398

1011403871

15372519263

1908635

243

95%72%63%83%65%92%96%75%96%69%73%53%87%81%87%94%77%63%90%86%94%82%86%85%72%94%75%78%

8395

152243256342388396456

1,0101,0301,2701,4101,4101,4781,5201,6341,6621,7801,8582,2282,8206,3006,6708,03012,91817,68818,17693,683

So there are still a lot of zugzwangs tocome, and we just might publish them allin EG.EvdG - 5iv97

GBR code

(after Guy/Blandford/Roycroft)concisely denotes chessboard force in atmost 6 digits. Examples: two whiteknights and one black pawn codes into0002.01; wQ bQ wR codes as 4100;wBB vs bN codes as 0023; the fullcomplement of 32 chessmen codes as4888.88. The key to encoding is to com-pute the sum 'l-for-W-andS-for-BV foreach piece type in QRBN sequence, withwhite pawns and black pawns uncodedfollowing the 'decimal point*. The keyfor decoding is to divide each QRBNdigit by 3, when the quotient and

115

remainder are in each of the 4 cases thenumbers of Bl and W pieces respectively.The GBR code permits unique sequen-cing, which, together with the fact that acomputer sort of several thousand codesand the reference attached to each is amatter of a second or two, enormouslyfacilitates the construction of look-updirectories.A consequence of the foregoing is thecode's greatest overall advantage: itsuser-friendliness. The GBR code has theunique characteristic of equally suitinghumans and computers. No special skillor translation process is required whetherthe code is encountered on a computerprintout or whether it is to be created (forany purpose, including input to a com-puter) from a chess diagram.A natural extension of the GBR code isto use it to represent a complete position.A good convention is to precede the GBRcode with the squares of the kings, andfollow the code with the squares of thepieces, in W-before-Bl within code digitsequence, preserving the 'decimal point'to separate the pieces from the pawns, ifany (where all W pawns precede all Bl).The 223-move optimal play solutionposition in the endgame wR wB bN bNwould be represented: a7d3 0116.00b2b3c6d6 3/3+. The '3/3' is a controlindicating 3 W and 3 Bl men, with '+'meaning W wins, while '=' would meanWhite draws. The win/draw indicators areoptional. Note that although in thisexample there are no pawns the GBRcode decimal point and immediatelyfollowing pair of zeroes are obligatory(enabling a scan of a text file searchingfor encoded chess positions) but the ab-sence of a decimal point in the list ofsquares confirms that there are no pawns.A° position with pawns but no pieceswould be coded in this manner: a2c40000.32 .d4e3f2e4f3 4/3 WTM. To in-dicate Black to move (but still with theimplied win or draw for White) it is

suggested that '-+' and '-=' be employed.Where the position result is unknown orundecided or unknowable it is suggestedthat the computer chess convention'WTM' (White to move) and 'BTM' befollowed. The redundancy checkpiece-count (including the V separator)and terminating full stop are bothobligatory.

EG Subscription

EG is produced by the Dutch Associationfor Endgame Study ('Alexander RuebVereniging voor schaakEindspelStudie')ARVES. Subscription to EG is not tied tomembership of ARVES.The annual subscription of EG is NLG35 (Dutch guilders) for 4 issues. If or-ganizational problems make the produc-tion of 4 issues in one year impossible,the subscription fees are considered aspayment for 4 issues. Payments should beonly in NLG and can be made by banknotes, Eurocheque (please fill in yourvalidation or garantee number on theback), postal money order, Eurogiro orbank cheque. To compensate for bankcharges payments via Eurogiro or bankcheque should be 41.50 and 55 respec-tively, instead of 35.All payments can be addressed to thetreasurer (see Editorial Board) exceptthose by Eurogiro which should bedirected to: Postbank, accountnumber54095, in the name of ARVES, Laren(NH), The Netherlands.It is of course possible to save charges bypaying for more years of for more per-sons in one country together, like somesubscribers already do.

116