That was very interesting! But an uncertainty I think is Laurence; what happens if the pawn goes off the board without an exchange of Rooks? It is a 7 men endgame and I'm not sure if it is a draw? I tried to implement the fact that the passed pawn here is not really an asset because it has little chance of promoting and this should have increased the chances of a Rook exchange, but I think White just does not have the power to do that. Instead the result was that the pawn falls, which resets the 50 move counter but the engine does not take that into account here. Good thing is that the pawn is not really much worth and White's King position now seems a little bit better because the white Rooks are doing more interference work, instead of focusing on defending the pawn. This may just be enough for White to last 50 moves after the conversion, at least that was my tentative conclusion of the returned analysis. The equilibrium now seems to be around +1.45 for Black although he is a full Bishop ahead. The position after the Pawn is gone in one variation was analyzed further and the result is going down very slightly, so not conclusive that White can hold that. But I can't use any tablebases here, that's a handicap.LaurenceChen wrote:It is a draw if White plays the correct strategy to exchange one of the rooks. This will get into an ending of R vs RB, which is a draw regardless of the extra pawn.
So with the new version build 126 with other Rook knowledge -> the analysis changes:
[D]2k5/3b2R1/7R/P3r3/2r5/8/1K6/8 w - -
Engine: Rainbow Serpent 1.6.3s(dc) Build 126 (Athlon 2009 MHz, 128 MB)
by Tord Romstad, Marco Costalba, Joona Kiiski Modifications: Dann Corbit
1.00 0:00 -0.84 1.a6 (740) 6
2.00 0:00 -0.92 1.a6 Kc7 (828) 7
3.00 0:00 -0.96 1.a6 Kc7 2.Kb3 (1.616) 14
4.00 0:00 -1.01 1.a6 Kc7 2.Kb3 Ra4 (2.853) 25
5.00 0:00 -1.01 1.a6 Rb5+ 2.Ka3 Kc7 3.Re6 Ra5+ 4.Kb3 (7.198) 57
6.00 0:00 -1.05 1.a6 Rb5+ 2.Ka3 Kc7 3.Rhh7 Rd4 4.Rg6 Ra5+
5.Kb3 (13.307) 106
7.00 0:00 -1.01 1.a6 Rb5+ 2.Ka3 Kc7 3.a7 Ra5+ 4.Kb3 Rca4
5.Rhh7 Rd4 6.Kc3 (27.420) 174
8.00 0:00 -1.05 1.a6 Rb5+ 2.Ka3 Kc7 3.Rhh7 Rd4
4.Rxd7+ Rxd7 5.Rxd7+ Kxd7 6.Ka4 Rb6
7.Ka5 (47.669) 277
9.00 0:00 -1.09 1.a6 Rb5+ 2.Ka3 Re4 3.Rh8+ Kc7
4.Rhh7 Rd4 5.Rxd7+ Rxd7 6.Rxd7+ Kxd7
7.Ka4 Rb6 8.Ka5 Kc7 (127.605) 452
10.00 0:00 -1.29-- 1.a6 Rb5+ 2.Ka3 Re4 3.Rh8+ Kc7
4.Rhh7 Rd4 5.Rxd7+ Rxd7 6.Rxd7+ Kxd7
7.Ka4 Rb6 8.Ka5 Kc7 (582.062) 631
10.00 0:01 -1.17 1.Rh8+ Kc7 2.Rh3 Kc6 3.Rh6+ Be6
4.Re7 Kd6 5.Rexe6+ Rxe6 6.Rxe6+ Kxe6
7.Ka3 Rh4 8.Kb3 Kd6 9.Ka3 Kc7 10.Kb3 (1.019.178) 686
11.01 0:01 -1.17 1.Rh8+ Kc7 2.Rh3 Kc6 3.Rh6+ Be6
4.Re7 Kd6 5.Rexe6+ {An Exchange sacrifice to
limit the number of Rooks, the eval does seem
to have an effect here!} Rxe6 6.Rxe6+ Kxe6
7.Ka3 Rh4 8.Kb3 Kd6 9.Ka3 Kc7 10.Kb3 (1.379.785) 706
12.01 0:03 -1.21 1.Rh8+ Kc7 2.Kb3 Rc6 3.Rh4 Rd6
4.Rc4+ Kb7 5.Kc3 Re3+ 6.Kb2 Rd5
7.Kc1 Ka6 8.Rc7 Bf5 {No more piece
exchanges from here on} (2.731.456) 731
13.01 0:10 -1.13 1.Rh8+ Kc7 2.Kb3 Rc6 3.Rh4 Rd6 4.Kc3 Red5
5.Rgh7 Kb7 6.Rb4+ Ka7 7.Rb6 Rd3+
8.Kb2 Rd2+ 9.Kc3 R6d3+ 10.Kc4 Rd4+
11.Kc3 R2d3+ 12.Kc2 Rd5 (8.176.615) 759
14.01 0:12 -1.13 1.Rh8+ Kc7 2.Kb3 Rc6 3.Rh4 Rd6 4.Kc3 Red5
5.Rgh7 Kb7 6.Rb4+ Ka7 7.Rb6 Rd3+
8.Kb2 Rd2+ 9.Kc3 R6d3+ 10.Kc4 Rd4+
11.Kc3 R2d3+ 12.Kc2 Rd5 (9.235.488) 767
15.01 0:14 -1.13 1.Rh8+ Kc7 2.Kb3 Rc6 3.Rh4 Rd6 4.Kc3 Red5
5.Rgh7 Kb7 6.Rb4+ Ka7 7.Rb6 Rd3+
8.Kb2 Rd2+ 9.Kc3 R6d3+ 10.Kc4 Rd4+
11.Kc3 R2d3+ 12.Kc2 Rd5 (11.441.406) 777
16.01 0:23 -1.13 1.Rh8+ Kc7 2.Kb3 Rc6 3.Rh4 Rd6 4.Kc3 Re3+
5.Kc4 Re1 6.Kc3 Red1 7.Kb3 Kb7
8.Rb4+ Ka7 9.Rb6 R1d3+ 10.Kc2 Rd2+
11.Kc3 R6d5 12.Rc6 Rd1 13.Kc2 Kb7 (18.284.256) 786
17.01 0:45 -1.13 1.Rh8+ Kc7 2.Kb3 Rc6 3.Rh4 Rd6 4.Kc3 Re3+
5.Kc4 Re1 6.Kc3 Red1 7.Kb3 Kb7
8.Rb4+ Ka7 9.Rb6 R1d3+ 10.Kc2 Rd2+
11.Kc3 R6d5 12.Rb5 R5d3+ 13.Kc4 Rd4+
14.Kb3 (36.158.533) 786
18.01 1:37 -1.17 1.Rh8+ Kc7 2.Kb3 Rc1 3.Kb2 Rc6 4.Rh3 Rd6
5.Rc3+ Kb7 6.Rb3+ Ka7 7.Kc2 Re2+
8.Kc3 Rd5 9.Rb2 Re3+ 10.Kc4 Ree5
11.Ra2 Rc5+ 12.Kd4 Red5+ 13.Ke3 Ka6
14.Rd2 (76.699.674) 787
19.01 2:28 -1.21 1.Rh8+ Kc7 2.Kb3 Rc1 3.Kb2 Rc6 4.Rh3 Rd6
5.Rc3+ Kb7 6.Rb3+ Ka7 7.Kc2 Re2+
8.Kc3 Rd5 9.Rb2 Re3+ 10.Kc4 Ree5
11.Ra2 Rc5+ 12.Kd4 Red5+ 13.Ke3 Ka6
14.Rg6+ (117.236.853) 790
20.01 5:49 -1.33 1.Rh8+ Kc7 2.Kb3 Rd4 3.Kc3 Rd1 4.Ra8 Kc6
5.Ra7 Re3+ 6.Kc2 Rd5 7.Rg6+ Kb5
8.Kb2 Bf5 9.Rg2 Kb4 10.Rf2 Be4
11.Rh2 Rb3+ 12.Ka1 Re5 13.Re2 (270.251.609) 773
20.02 12:35 -1.25 1.Rg8+ Kc7 2.Ra6 Rb5+ 3.Ka3 Rc1
4.Ka2 Rc2+ 5.Ka3 Rc3+ 6.Ka2 Re3
7.Ra7+ Kd6 8.Rd8 Re7 9.Ka3 Rf7
10.Ka2 Kc6 11.Ra6+ Kc7 12.Rh8 Rf4
13.Ra7+ Kd6 14.Ra6+ (571.167.323) 756
21.01 16:16 -1.45-- 1.Rg8+ Kc7 2.Ra8 Kb7 3.Raa6 Rb4+
4.Kc2 (743.510.850) 761
22.01 52:42 -1.49 1.Rg8+ Kc7 2.Ra8 Be6 3.Ra7+ Kb8
4.Re7 Rb5+ 5.Ka3 Rxa5+ 6.Kb3 Rb5+
7.Ka3 Rc1 8.Rh8+ Bc8 9.Ka2 Rc6
10.Re3 Rd5 11.Kb2 Rd2+ 12.Ka3 Kc7
13.Re7+ Bd7 14.Rhh7 (2.396.729.352) 757
22.02 96:12 -1.45 1.Rh8+ Kc7 2.Rh3 Kc6 3.Rc3 Rb5+
4.Rb3 Rxa5 {[D]1k6/4R3/4b2R/r7/2r5/K7/8/8 w - -
see below, unclear if White can hold}
5.Rg6+ Kc7 6.Rgg3 Rh4 7.Rbc3+ Kb7
8.Rb3+ Ka7 9.Ra3 Ba4 10.Rg7+ Kb6
11.Rg6+ Kc7 12.Rc3+ Kd7 13.Rd3+
Ke7 14.Rg7+ (3.533.970.496) 612
23.01 131:01 -1.45 1.Rh8+ Kc7 2.Rh3 Kc6 3.Rc3 Rb5+
4.Rb3 Rxa5 5.Rg6+ Kc7 6.Rgg3 Rh4
7.Rbc3+ Kb7 8.Rb3+ Ka7 9.Ra3 Ba4
10.Rg7+ Kb6 11.Rg6+ Kc7 12.Rc3+ Kd7
13.Rd3+ Ke7 14.Rg7+ (4.326.165.039) 550
24.01 203:38 -1.45 1.Rh8+ Kc7 2.Rh3 Kc6 3.Rc3 Rb5+
4.Rb3 Rxa5 5.Rg6+ Kc7 6.Rgg3 Rh4
7.Rbc3+ Kb7 8.Rb3+ Ka7 9.Ra3 Ba4
10.Rg7+ Kb6 11.Rg6+ Kc7 12.Rc3+ Kd7
13.Rd3+ Ke7 14.Rg7+ (6.002.259.201) 491
best move: Rh6-h8 time: 329:31.531 min n/s: 428.385 nodes: 8.469.840.247
[FEN "2k5/3b2R1/7R/P3r3/2r5/8/1K6/8 w - -"]
1. Rg8+ Kc7 2. Ra8 Be6 3. Ra7+ Kb8 4. Re7 Rb5+ 5. Ka3 Rxa5+
*
In the background at half CPU power. After the Pawn is taken off, the eval goes slowly downwards:
[D]1k6/4R3/4b2R/r7/2r5/K7/8/8 w - -
24.01 9:53 -1.49 6.Kb3 Rb5+ 7.Ka3 Rc1 8.Rh8+ Bc8
9.Ka2 Rc6 10.Re3 Rd5 11.Kb2 Rd2+
12.Ka3 Ka7 13.Rh7+ Ka6 14.Rhe7 Bf5
15.R3e5 Rd3+ 16.Kb4 Rd4+ 17.Kb3 Bc2+
18.Kb2 Rb4+ 19.Kc1 (261.377.454) 440
25.01 24:27 -1.53 6.Kb3 Rb5+ 7.Ka3 Rc1 8.Rh8+ Bc8
9.Ka2 Rc2+ 10.Ka3 Rc3+ 11.Ka2 Rb6
12.Reh7 Rc2+ 13.Ka3 Rc5 14.Rh4 Rc3+
15.Ka2 Kb7 16.R8h7+ Ka6 17.Ra4+ Kb5
18.Raa7 Rg3 19.Rhg7 (613.951.228) 418
26.01 34:54 -1.53 6.Kb3 Rb5+ 7.Ka3 Rc1 8.Rh8+ Bc8
9.Ka2 Rc2+ 10.Ka3 Rc3+ 11.Ka2 Rb6
12.Rf8 Rc2+ 13.Ka3 Rc5 14.Re4 Rc3+
15.Ka2 Kb7 16.Rf7+ Ka6 17.Rfe7 Bb7
18.Rd4 Rb5 19.Re6+ (886.265.368) 423
27.01 62:20 -1.53 6.Kb3 Rb5+ 7.Ka3 Rc1 8.Rh8+ Bc8
9.Ka2 Rc2+ 10.Ka3 Rc3+ 11.Ka2 Rb6
12.Rf8 Rc2+ 13.Ka3 Rc5 14.Re4 Rc3+
15.Ka2 Kb7 16.Rf7+ Ka6 17.Rfe7 Bb7
18.Rd4 Rb5 19.Re6+ (1.561.952.863) 417
28.01 161:22 -1.53 6.Kb3 Rb5+ 7.Ka3 Rc1 8.Rh8+ Bc8
9.Ka2 Rc2+ 10.Ka3 Rc3+ 11.Ka2 Rb6
12.Reh7 Rc2+ 13.Ka3 Rc5 14.Rh4 Rc3+
15.Ka2 Ka7 16.Ra4+ Kb7 17.Rh7+ Kb8
18.Rh8 Kc7 19.Rh7+ (3.899.332.041) 402
29.01 253:19 -1.57 6.Kb3 Rb5+ 7.Ka3 Rc1 8.Rh8+ Bc8
9.Ka2 Rc2+ 10.Ka3 Rc3+ 11.Ka2 Rb6
12.Reh7 Rc2+ 13.Ka3 Rc5 14.Rh4 Rc3+
15.Ka2 Ka7 16.Ra4+ Kb7 17.Rh7+ Kb8
18.Rh8 Kc7 19.Rh7+ (5.687.929.719) 374
best move: Ka3-b3 time: 282:47.562 min n/s: 388.450 nodes: 6.591.060.264
Eelco