hgm wrote:Don wrote:Even for chess it's almost impossible to pre-calculate EVERY possible material signature without imposing some limitations. You can have legal positions with 10 knights for one side for example. And there are people who will set up such positions so you have to be able to handle them.
I did not consider material signatures only reachable through promotion. They do not occur in practice, and if someone sets them up (which you detect in the root) you can redefine the mapping and recalculate the table with the material combinations that are still reachable. If promoting pieces survive during the search, this would basically give you some random material correction, but the possible range {-100, 100} is such that this is negligible to the promotion gain. The mapping would be such that you would never map into a signature that has special handling by taking an extra Queen.
syzygy wrote:Apart from the fact that a huge table takes up RAM that might be useful for other purposes (e.g. for a larger TT table or for caching tablebases), both methods should be about equally cheap for the reason that a search will see relatively few unique material signatures. I guess the question is, is it cheaper to (incrementally?) calculate the multidimensional index or is it cheaper to (incrementally) calculate the material signature hash key.
Well, what I meant by 'huge' was something like 3-5MB, so not really significant on the scale of today's hash tables. But larger than L2/L3 (although even that might no longer be true, nowadays).
The multidimensional index is nothing but a (perfect) hash key. There is no difference in how you calculate them incrementally (for an additive key). Each piece has the key increment for its type stored in its piece list. E.g. wB=1, wB'=2, bB=4, bB'=8, wN=16, bN=48, wR=144, ..., where you would otherwise store random keys. The code is identical.
syzygy wrote:For KBNK it seems important to me to distinguish between good corners and bad corners. There will always be a time control short enough that the search will not be able to figure out a win when the opponent king is in a bad corner.
Oh yes, of course you are right. In fact even with top engines this would probably be true at any reasonable time control, (say shorter than a few weeks per move), in KBNK, as you will need about 60 ply to drive from one corner to the other. I do actually do use a PST with a gradient towards the deadly corner (and very large values), when it detects KBNK in the root.
In fact detecting the existence of a deadly corner (and determining which one it is) was an interesting problem in itself.
I think that you understimate the search of top engines.
You do not need 60 plies to drive the king from one corner to another.
Smart use of the hash tables together with single reply extension
can clearly help here.
Here is some analysis by Qazar (not a top engine that seems not to have knowledge about the right corner of KBN vs K)
You can see based on the pv at depth 32 that the king is still in the wrong corner so Qazar does not seem to have the knowledge but it does not prevent Qazar to find later mate by search.
[D]7k/8/6KN/7B/8/8/8/8 w - - 5 1
Quazar_0.4_x64:
1 00:00 3 10 +9.57 Kg6-f5
2 00:00 25 88 +9.61 Nh6-f7+ Kh8-g8 Kg6-f5
3 00:00 68 241 +9.63 Nh6-f7+ Kh8-g8 Kg6-f5 Kg8-g7
4 00:00 143 508 +9.56 Nh6-f7+ Kh8-g8 Kg6-f5 Kg8-g7 Kf5-e4
5 00:00 397 1,412 +9.81 Kg6-f6 Kh8-h7 Nh6-f5 Kh7-g8 Bh5-f7+ Kg8-f8
6 00:00 795 2,829 +9.99 Nh6-f5 Kh8-g8 Kg6-f6 Kg8-f8 Nf5-d6 Kf8-g8 Bh5-f7+ Kg8-f8
7 00:00 1,852 6,590 +10.20 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-f7+ Kg8-h8 Ng5-e4 Kh8-h7
8 00:00 3,713 13,213 +10.63 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-f8 Ng5-e6+ Kf8-g8 Kf6-e5 Kg8-h8 Bg6-d3
9 00:00 15,195 51,334 +10.37 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-e4 Kh8-g8 Be4-g6
10 00:00 21,174 71,533 +10.40 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-f7+ Kg8-h8 Bf7-e8 Kh8-g8 Be8-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d4 Kh8-g8 Kd4-d5 Kg8-h8 Bg6-e4
11 00:00 30,760 103,918 +10.41 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-f7+ Kg8-h8 Ng5-e6 Kh8-h7 Ne6-d4 Kh7-h6 Nd4-f5+ Kh6-h7 Bf7-e6 Kh7-h8 Kf6-e5 Kh8-h7
12 00:00 68,302 208,874 +10.41 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-f7+ Kg8-h8 Ng5-e6 Kh8-h7 Ne6-d4 Kh7-h6 Nd4-f5+ Kh6-h7 Bf7-e6 Kh7-h8 Kf6-e5 Kh8-h7 Be6-f7 Kh7-h8 Bf7-d5 Kh8-h7
13 00:00 98,355 273,969 +10.41 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-f7+ Kg8-h8 Ng5-e6 Kh8-h7 Ne6-d4 Kh7-h6 Nd4-f5+ Kh6-h7 Bf7-e6 Kh7-h8 Kf6-e5 Kh8-h7 Be6-f7 Kh7-h8 Bf7-d5 Kh8-h7
14 00:00 144,752 387,037 +10.52 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d5 Kh8-g8 Kd5-d4 Kg8-h8 Bg6-e4 Kh8-g8
15 00:00 458,788 865,637 +10.43 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d5 Kh8-g8 Kd5-d4 Kg8-h8 Kd4-e5 Kh8-g8 Ke5-e4 Kg8-h8 Bg6-f7 Kh8-h7
16 00:00 695,472 1,061,789 +10.37 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d5 Kh8-g8 Kd5-d4 Kg8-h8 Kd4-e5 Kh8-g8 Ke5-e4 Kg8-h8 Ke4-f4 Kh8-g8 Kf4-e3 Kg8-h8 Bg6-e4 Kh8-g8
17 00:00 834,621 1,164,046 +10.37 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d4 Kh8-g8 Kd4-d5 Kg8-h8 Kd5-e5 Kh8-g8 Ke5-e4 Kg8-h8 Ke4-f4 Kh8-g8 Kf4-e3 Kg8-h8 Bg6-e4 Kh8-g8
18 00:00 1,399,523 1,447,283 +10.37 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d4 Kh8-g8 Kd4-d5 Kg8-h8 Kd5-e5 Kh8-g8 Ke5-e4 Kg8-h8 Ke4-f4 Kh8-g8 Kf4-e3 Kg8-h8 Bg6-e4 Kh8-g8
19 00:01 2,321,423 1,710,702 +10.37 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d4 Kh8-g8 Kd4-d5 Kg8-h8 Kd5-e5 Kh8-g8 Ke5-e4 Kg8-h8 Ke4-f4 Kh8-g8 Kf4-e3 Kg8-h8 Ke3-d3 Kh8-g8 Kd3-d4 Kg8-h8 Kd4-e5
20 00:01 3,133,199 1,877,291 +10.37 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Ke5-d4 Kh8-g8 Kd4-d5 Kg8-h8 Kd5-e5 Kh8-g8 Ke5-e4 Kg8-h8 Ke4-f4 Kh8-g8 Kf4-e3 Kg8-h8 Ke3-d3 Kh8-g8 Kd3-d4 Kg8-h8 Kd4-e5
21 00:02 4,140,345 2,010,852 +10.39 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-f5 Kh7-h8 Kf6-e5 Kh8-h7 Ke5-d5 Kh7-h8 Kd5-d4 Kh8-h7 Kd4-d5
22+ 00:02 4,152,240 2,001,079 +10.54 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-f5 Kh7-h8 Bf7-a2 Kh8-h7 Ba2-e6 Kh7-h8 Nf5-d4 Kh8-h7 Be6-f7 Kh7-h6 Nd4-b5 Kh6-h7 Nb5-d4
22- 00:03 7,056,887 2,185,471 +10.31 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-f5 Kh7-h8 Bf7-a2 Kh8-h7 Ba2-e6 Kh7-h8 Nf5-d4 Kh8-h7 Be6-f7 Kh7-h6 Nd4-b5 Kh6-h7 Nb5-a3 Kh7-h8 Na3-c2 Kh8-h7 Nc2-e3 Kh7-h8 Ne3-d5 Kh8-h7 Nd5-f4 Kh7-h6 Bf7-d5 Kh6-h7 Bd5-f7
22 00:03 8,800,685 2,265,881 +10.41 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-f5 Kh7-h8 Bf7-a2 Kh8-h7 Ba2-e6 Kh7-h8 Nf5-d4 Kh8-h7 Be6-f7 Kh7-h6 Nd4-f5+ Kh6-h7 Nf5-d4
23- 00:05 12,851,694 2,401,736 +10.33 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-f5 Kh7-h8 Nf5-d4 Kh8-h7 Nd4-f5
23 00:07 17,120,598 2,438,831 +10.31 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-f5 Kh7-h8 Nf5-d4 Kh8-h7 Bf7-d5 Kh7-h6 Nd4-f5+ Kh6-h7 Bd5-f7
24+ 00:07 17,131,110 2,434,779 +10.39 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-f5 Kh7-h8 Nf5-d4 Kh8-h7 Bf7-d5 Kh7-h6 Nd4-f5+ Kh6-h7 Bd5-a2 Kh7-h8 Ba2-f7 Kh8-h7 Kf6-e5 Kh7-h8 Bf7-e6 Kh8-h7 Be6-f7
24 00:08 19,853,250 2,461,655 +10.41 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-g6+ Kh7-g8 Ng7-e6 Kg8-h8 Bg6-c2 Kh8-g8 Bc2-e4 Kg8-h8 Be4-c2
25+ 00:08 19,869,333 2,463,649 +10.54 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-g6+ Kh7-h8 Ng7-f5 Kh8-g8 Kf6-e7 Kg8-h8 Bg6-f7 Kh8-h7 Ke7-f6 Kh7-h8 Kf6-e5 Kh8-h7 Ke5-d4 Kh7-h8 Kd4-e4 Kh8-h7 Nf5-d6 Kh7-h6
25 00:09 23,831,484 2,525,056 +10.54 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Kf6-e5 Kh6-h7
26 00:13 37,773,986 2,708,589 +10.58 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Kf6-e5 Kh6-h7
27- 00:20 56,579,070 2,770,767 +10.50 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-a2 Kh7-h8 Ba2-d5 Kh8-h7 Ng7-f5 Kh7-h8 Bd5-f7 Kh8-h7 Kf6-e5 Kh7-h8 Ke5-d4 Kh8-h7 Kd4-e4 Kh7-h8
27- 00:26 72,610,516 2,780,520 +10.42 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-a2 Kh7-h8 Ba2-d5 Kh8-h7 Ng7-f5 Kh7-h8 Bd5-f7 Kh8-h7 Kf6-e5 Kh7-h8 Ke5-d4 Kh8-h7 Kd4-e4 Kh7-h8
27 00:32 90,677,792 2,799,907 +10.30 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Bd5-e6 Kh6-h7 Be6-f7 Kh7-h6 Ng7-f5+ Kh6-h7 Kf6-e5 Kh7-h8 Ke5-d4 Kh8-h7 Kd4-e4 Kh7-h8 Ke4-e5 Kh8-h7 Ke5-f6 Kh7-h8 Nf5-g7 Kh8-h7
28+ 00:32 90,719,628 2,799,902 +10.39 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Bd5-e6 Kh6-h7 Be6-f7 Kh7-h6 Ng7-f5+ Kh6-h7 Kf6-e5 Kh7-h8 Ke5-d4 Kh8-h7 Kd4-e4 Kh7-h8 Ke4-e5 Kh8-h7 Ke5-f6 Kh7-h8 Bf7-d5 Kh8-h7 Bd5-e6 Kh7-h8 Kf6-e5 Kh8-h7 Be6-f7
28 00:35 98,135,719 2,792,150 +10.39 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Bd5-e6 Kh6-h7 Ng7-f5 Kh7-h8 Be6-d5 Kh8-h7 Bd5-f7 Kh7-h8 Bf7-a2 Kh8-h7 Ba2-e6
29+ 00:35 98,188,514 2,791,190 +10.58 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Bd5-e6 Kh6-h7 Ng7-f5 Kh7-h8 Be6-d5 Kh8-h7 Bd5-f7 Kh7-h8 Kf6-e5 Kh8-h7 Ke5-e4 Kh7-h8 Ke4-d4 Kh8-h7 Kd4-e5 Kh7-h8 Bf7-e6 Kh8-h7 Be6-f7
29+ 00:35 98,189,903 2,791,230 +10.58 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Bd5-e6 Kh6-h7 Be6-f7 Kh7-h8 Bf7-g6 Kh8-g8 Ng7-e6 Kg8-h8 Kf6-f5 Kh8-g8 Kf5-g5 Kg8-h8 Bg6-e4 Kh8-g8 Kg5-f6 Kg8-h8 Ne6-g5 Kh8-g8 Ng5-e6
29 00:38 109,229,579 2,802,986 +10.41 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-g6+ Kh7-h8 Ng7-e6
30 00:48 138,769,727 2,841,080 +10.41 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Ng7-e6
31+ 00:49 139,694,423 2,837,356 +10.58 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Ng7-f5+ Kh6-h7 Bd5-e6 Kh7-h8 Be6-f7 Kh8-h7 Kf6-e5 Kh7-h8 Ke5-d4 Kh8-h7 Kd4-d5 Kh7-h8 Kd5-e4 Kh8-h7 Ke4-d3 Kh7-h8
31+ 00:49 139,697,555 2,837,420 +10.58 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Ng7-f5+ Kh6-h7 Bd5-e6 Kh7-h8 Be6-f7 Kh8-h7 Kf6-e5 Kh7-h8 Ke5-d4 Kh8-h7 Kd4-d5 Kh7-h8 Kd5-e4 Kh8-h7 Ke4-d4 Kh7-h8 Bf7-e6 Kh8-h7 Be6-f7
31 00:53 153,941,899 2,857,814 +10.43 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Ng7-f5+ Kh6-h7 Bd5-e6 Kh7-h8 Be6-f7 Kh8-h7 Nf5-g7 Kh7-h6 Bf7-a2 Kh6-h7 Ba2-d5
32 01:15 215,148,052 2,867,264 +10.43 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Ng7-f5+ Kh6-h7 Bd5-e6 Kh7-h8 Nf5-e3 Kh8-h7
33+ 01:15 215,311,574 2,865,853 +10.58 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Ng7-f5+ Kh6-h7 Bd5-e6 Kh7-h8 Nf5-e3 Kh8-h7 Be6-f7 Kh7-h6 Ne3-f5+ Kh6-h7 Kf6-e7 Kh7-h8 Ke7-e6 Kh8-h7 Ke6-d5 Kh7-h8 Kd5-e4 Kh8-h7 Ke4-d4 Kh7-h8 Kd4-d5 Kh8-h7 Kd5-d6 Kh7-h8 Kd6-c5 Kh8-h7 Kc5-d4
33+ 01:15 215,319,295 2,865,956 +10.69 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Kf6-e5 Kg8-h8 Bg6-f7 Kh8-h7 Ke5-f6 Kh7-h6 Ne6-g7 Kh6-h7 Bf7-d5 Kh7-h6 Ng7-f5+ Kh6-h7 Bd5-e6 Kh7-h8 Nf5-e3 Kh8-h7 Be6-f7 Kh7-h6 Ne3-f5+ Kh6-h7 Kf6-e5 Kh7-h8 Ke5-e4 Kh8-h7 Ke4-d4 Kh7-h8 Kd4-d5 Kh8-h7 Kd5-d6 Kh7-h8 Kd6-c5 Kh8-h7 Kc5-d4
33+ 01:15 216,512,248 2,866,345 +150.93 Nh6-f7+ Kh8-g8 Nf7-g5 Kg8-f8 Kg6-f6 Kf8-g8 Bh5-g6 Kg8-h8 Ng5-e6 Kh8-g8 Ne6-d4 Kg8-h8 Bg6-e4 Kh8-g8 Nd4-e6 Kg8-h8 Ne6-d8 Kh8-g8 Nd8-f7 Kg8-f8 Be4-d5 Kf8-g8 Kf6-g6 Kg8-f8 Nf7-e5 Kf8-e7 Ne5-c4 Ke7-e8 Kg6-f6 Ke8-f8 Nc4-b6 Kf8-e8 Bd5-f7+ Ke8-d8 Kf6-e6 Kd8-c7 Nb6-a4 Kc7-d8 Bf7-h5 Kd8-c7 Bh5-e2 Kc7-d8 Be2-b5 Kd8-c7 Ke6-e7 Kc7-c8 Ke7-d6 Kc8-b8 Na4-b2 Kb8-c8 Kd6-e7 Kc8-c7 Nb2-c4 Kc7-c8 Bb5-e8 Kc8-c7 Be8-d7 Kc7-b8 Ke7-d6 Kb8-b7 Bd7-h3 Kb7-a6 Kd6-c6 Ka6-a7 Bh3-c8 Ka7-b8 Nc4-d6 Kb8-a7 Kc6-c7 Ka7-a8 Bc8-b7+ Ka8-a7 Nd6-c8+
34 02:24 389,748,493 2,694,238 +M23 Kg6-f6 Kh8-h7 Nh6-f7 Kh7-g8 Bh5-g6 Kg8-f8 Bg6-h7 Kf8-e8 Nf7-e5 Ke8-d8 Kf6-e6 Kd8-c7 Ne5-d7 Kc7-b7 Bh7-d3 Kb7-c6 Bd3-c4 Kc6-c7 Bc4-b5 Kc7-d8 Ke6-d6 Kd8-e8 Bb5-c4 Ke8-d8 Bc4-f7 Kd8-c8 Nd7-c5 Kc8-d8 Bf7-g6 Kd8-c8 Bg6-e4 Kc8-d8 Be4-c6 Kd8-c8 Bc6-d7+ Kc8-b8 Kd6-c6 Kb8-a7 Kc6-c7 Ka7-a8 Kc7-b6 Ka8-b8 Nc5-a6+ Kb8-a8 Bd7-c6+
35 02:38 425,887,469 2,681,235 +M23 Kg6-f6 Kh8-h7 Nh6-f7 Kh7-g8 Bh5-g6 Kg8-f8 Bg6-h7 Kf8-e8 Nf7-e5 Ke8-d8 Kf6-e6 Kd8-c7 Ne5-d7 Kc7-b7 Bh7-d3 Kb7-c6 Bd3-c4 Kc6-c7 Bc4-b5 Kc7-d8 Ke6-d6 Kd8-e8 Bb5-c4 Ke8-d8 Bc4-f7 Kd8-c8 Nd7-c5 Kc8-d8 Bf7-g6 Kd8-c8 Bg6-e4 Kc8-d8 Be4-c6 Kd8-c8 Bc6-d7+ Kc8-b8 Kd6-c6 Kb8-a7 Kc6-c7 Ka7-a8 Kc7-b6 Ka8-b8 Nc5-a6+ Kb8-a8 Bd7-c6+
36 03:06 494,574,782 2,653,881 +M23 Kg6-f6 Kh8-h7 Nh6-f7 Kh7-g8 Bh5-g6 Kg8-f8 Bg6-h7 Kf8-e8 Nf7-e5 Ke8-d8 Kf6-e6 Kd8-c7 Ne5-d7 Kc7-b7 Bh7-d3 Kb7-c6 Bd3-c4 Kc6-c7 Bc4-b5 Kc7-d8 Ke6-d6 Kd8-e8 Bb5-c4 Ke8-d8 Bc4-f7 Kd8-c8 Nd7-c5 Kc8-d8 Bf7-g6 Kd8-c8 Bg6-e4 Kc8-d8 Be4-c6 Kd8-c8 Bc6-d7+ Kc8-b8 Kd6-c6 Kb8-a7 Kc6-c7 Ka7-a8 Kc7-b6 Ka8-b8 Nc5-a6+ Kb8-a8 Bd7-c6+
37 03:34 567,164,780 2,644,877 +M23 Kg6-f6 Kh8-h7 Nh6-f7 Kh7-g8 Bh5-g6 Kg8-f8 Bg6-h7 Kf8-e8 Nf7-e5 Ke8-d8 Kf6-e6 Kd8-c7 Ne5-d7 Kc7-b7 Bh7-d3 Kb7-c6 Bd3-c4 Kc6-c7 Bc4-b5 Kc7-d8 Ke6-d6 Kd8-e8 Bb5-c4 Ke8-d8 Bc4-f7 Kd8-c8 Nd7-c5 Kc8-d8 Bf7-g6 Kd8-c8 Bg6-e4 Kc8-d8 Be4-c6 Kd8-c8 Bc6-d7+ Kc8-b8 Kd6-c6 Kb8-a7 Kc6-c7 Ka7-a8 Kc7-b6 Ka8-b8 Nc5-a6+ Kb8-a8 Bd7-c6+
38 04:09 659,770,885 2,645,941 +M22 Kg6-f6 Kh8-h7 Nh6-f7 Kh7-g8 Bh5-g6 Kg8-f8 Bg6-h7 Kf8-e8 Nf7-e5 Ke8-d8 Kf6-e6 Kd8-c7 Ne5-d7 Kc7-b7 Bh7-d3 Kb7-c6 Bd3-e2 Kc6-c7 Be2-f3 Kc7-c8 Ke6-d6 Kc8-d8 Bf3-e4 Kd8-e8 Be4-g6+ Ke8-d8 Nd7-c5 Kd8-c8 Bg6-e4 Kc8-d8 Be4-c6 Kd8-c8 Bc6-d7+ Kc8-b8 Kd6-c6 Kb8-a7 Kc6-c7 Ka7-a8 Kc7-b6 Ka8-b8 Nc5-a6+ Kb8-a8 Bd7-c6+
39 04:48 768,448,517 2,659,930 +M22 Kg6-f6 Kh8-h7 Nh6-f7 Kh7-g8 Bh5-g6 Kg8-f8 Bg6-h7 Kf8-e8 Nf7-e5 Ke8-d8 Kf6-e6 Kd8-c7 Ne5-d7 Kc7-b7 Bh7-d3 Kb7-c6 Bd3-e2 Kc6-c7 Be2-f3 Kc7-c8 Ke6-d6 Kc8-d8 Bf3-e4 Kd8-e8 Be4-g6+ Ke8-d8 Nd7-c5 Kd8-c8 Bg6-e4 Kc8-d8 Be4-c6 Kd8-c8 Bc6-d7+ Kc8-b8 Kd6-c6 Kb8-a7 Kc6-c7 Ka7-a8 Kc7-b6 Ka8-b8 Nc5-a6+ Kb8-a8 Bd7-c6+
40 05:23 865,861,324 2,678,744 +M22 Kg6-f6 Kh8-h7 Nh6-f7 Kh7-g8 Bh5-g6 Kg8-f8 Bg6-h7 Kf8-e8 Nf7-e5 Ke8-d8 Kf6-e6 Kd8-c7 Ne5-d7 Kc7-b7 Bh7-d3 Kb7-c6 Bd3-e2 Kc6-c7 Be2-f3 Kc7-c8 Ke6-d6 Kc8-d8 Bf3-e4 Kd8-e8 Be4-g6+ Ke8-d8 Nd7-c5 Kd8-c8 Bg6-e4 Kc8-d8 Be4-c6 Kd8-c8 Bc6-d7+ Kc8-b8 Kd6-c6 Kb8-a7 Kc6-c7 Ka7-a8 Kc7-b6 Ka8-b8 Nc5-a6+ Kb8-a8 Bd7-c6+