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Subject: Re: Mate that every program will solve...

Author: Heiner Marxen

Date: 10:57:35 04/17/01

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On April 17, 2001 at 13:12:22, leonid wrote:

>On April 17, 2001 at 11:13:02, Heiner Marxen wrote:
>
>>On April 17, 2001 at 07:43:30, leonid wrote:
>>
>>>Hello!
>>>
>>>If you like to solve very "regular" mate position, then you have one.
>>>
>>>[D]R7/4P1Pq/1rR5/2pb1rnk/1Q3B2/4Nn2/1PB2Np1/2K1b1Q1 w - -
>>>
>>>Please, indicate your result.
>>>
>>>Thanks,
>>>Leonid.
>>
>>According to Chest there are two key moves for mate in 7 moves:
>>
>>Qxg2 Bd2+ Qxd2   Bxc6 g8=Q   Qxg8  Rxg8   Bd5  e8=Q+  Bf7  Nxf5   Nd4  Rxg5#
>>Rh8  Bd2+ Qxd2   Be4  e8=Q+  Rf7   Qxf7+  Nxf7 Qd5+   Bf5  Rxh7+  Nh6  Rhxh6#
>>
>>(K7/600, 350MB hash, 9.3 minutes)
>>
>>Heiner
>
>Thanks, Heiner! My program demonstrate the worst possible branching factor for
>this position. Even for seeing the 6 moves by brute force it took already 38 min
>(Celeron 600. No hash). Only after your indication I went to see  7 moves by
>brute force. It took for mine hefly 1 hours 5 min. And this is after my last
>improvement that cut 6 moves brute force search already by 48%.
>
>Previously this position my solved by selective search in 10 moves.
>
>Leonid.

Hi Leonid,

From depth=6 in 38 minutes to depth=7 in 1h5min is a factor of less than 2.
Even with the 48% improvement, the factor is just 4.  That is quite
different from Chest's timing (see below), and is unexpectedly low (for me).

My program shows a branching factor significantly larger than usual, but
not "worst possible".  Here is the timing info for increasing depths:

depth  seconds speed   hash in    hash out
#  1      0.00  0.87          1-         0
#  2      0.01  1.00          1-         0
#  3      0.03  0.97         83-         0
#  4      0.26  1.06        907-         0
#  5      2.59  1.30      13215-         0
#  6     31.77  1.58     184695-         0
#  7    559.19  1.81    3425552-      2347

559.19 / 31.77 = 17.60  which is much smaller than 79 (initial legal moves).

Here is statistics over remaining depth:

                 moves              quotient
depth     attacker   defender     att     def
mvx  7:         79        192  [ 79.000  2.430]    mvskip     lvskip
mvx  6:       1167       1863  [  6.078  1.596]          5
mvx  5:      22875      25690  [ 12.279  1.123]        679
mvx  4:     299329     334138  [ 11.652  1.116]       7313          4
mvx  3:    3752287    3769416  [ 11.230  1.005]
mvx  2:   22524391    7352320  [  5.976  0.326]
mvx  1:    2394158          0  [  0.326       ]

The "refutation table" shows which defender moves were chosen top level.
Selecting the "right" defender moves is important for small search trees:

refu  1: e8=Q+   Bf7     [  6-]
solu          4: Nf7     [  5+]
solu          5: Kh4     [  1+]
refu  2: e8=B+   Bf7     [  6-]
solu          6: Nf7     [  5+]
solu          7: Kh4     [  1+]
refu  3: Rh6+    Qxh6    [  6-]
refu  4: Qh1+    gxh1=Q  [  6-]
refu  5: Qh2+    Nxh2    [  6-]
refu  6: g8=Q    Bd2+    [  6-]
refu  7: g8=N    Bd2+    [  6-]
refu  8: g8=R    Bd2+    [  6-]
refu  9: g8=B    Bd2+    [  6-]
refu 10: e8=N    Bd2+    [  6-]
refu 11: e8=R    Bd2+    [  6-]
refu 12: b3      Bd2+    [  6-]
refu 13: Nd3     Bd2+    [  6-]
refu 14: Nfd1    Bd2+    [  6-]
refu 15: Ne4     Bd2+    [  6-]
refu 16: Nfg4    Bd2+    [  6-]
refu 17: Nh3     Bd2+    [  6-]
refu 18: Nh1     Bd2+    [  6-]
refu 19: Nc4     Bd2+    [  6-]
refu 20: Nxd5    Bd2+    [  6-]
refu 21: Ned1    Bd2+    [  6-]
refu 22: Nxf5    Bxf2    [  6-]
solu          9: Bd2+    [  6+]
solu         10: Nxg1    [  3+]
solu         11: Nd2     [  2+]
solu         12: Nd4     [  2+]
solu         13: Ne5     [  2+]
solu         14: Qxf5    [  5+]
solu         15: Ra6     [  3+]
solu         16: Qxg7    [  3+]
solu         17: cxb4    [  5+]
solu         18: Rxb4    [  5+]
solu         19: Bxb4    [  5+]
solu         20: Rxc6    [  6+]
solu         21: Bxc6    [  6+]
refu 23: Nf1     Bd2+    [  6-]
refu 24: Neg4    Bd2+    [  6-]
refu 25: Nxg2    Bd2+    [  6-]
refu 26: Bxg5    Rxb4    [  6-]
solu         22: Bd2+    [  6+]
solu         23: Nxg1    [  1+]
solu         24: Ne5     [  1+]
solu         25: Nd2     [  1+]
solu         26: Nd4     [  3+]
solu         27: Qxg7    [  1+]
solu         28: Ra6     [  1+]
solu         29: cxb4    [  6+]
refu 27: Bg3     Bd2+    [  6-]
refu 28: Bh2     Bd2+    [  6-]
refu 29: Be5     Bd2+    [  6-]
refu 30: Bd6     Bd2+    [  6-]
refu 31: Bc7     Bd2+    [  6-]
refu 32: Bb8     Bd2+    [  6-]
refu 33: Bd3     Bd2+    [  6-]
refu 34: Be4     Bd2+    [  6-]
refu 35: Bxf5    Rxc6    [  6-]
solu         30: Bd2+    [  6+]
solu         31: Nxg1    [  4+]
solu         32: Nd4     [  2+]
solu         33: Nd2     [  2+]
solu         34: Ne5     [  2+]
solu         35: Rxb4    [  2+]
solu         36: Qxf5    [  5+]
solu         37: Qxg7    [  2+]
solu         38: Ra6     [  2+]
solu         39: cxb4    [  2+]
solu         40: Bxb4    [  2+]
refu 36: Bb1     Bd2+    [  6-]
refu 37: Bd1     Bd2+    [  6-]
refu 38: Bb3     Bd2+    [  6-]
refu 39: Ba4     Bd2+    [  6-]
refu 40: Rd6     Bd2+    [  6-]
refu 41: Re6     Bd2+    [  6-]
refu 42: Rf6     Bd2+    [  6-]
refu 43: Rg6     Bd2+    [  6-]
refu 44: Rxb6    Bd2+    [  6-]
refu 45: Rc7     Bd2+    [  6-]
refu 46: Rcc8    Bd2+    [  6-]
refu 47: Rxc5    Bd2+    [  6-]
refu 48: Rb8     Bd2+    [  6-]
refu 49: Rac8    Bd2+    [  6-]
refu 50: Rd8     Bd2+    [  6-]
refu 51: Re8     Bd2+    [  6-]
refu 52: Rf8     Bd2+    [  6-]
refu 53: Rg8     Bd2+    [  6-]
refu 54: Rh8     Bd2+    [  5-]
solu         41: Bd2+    [  6+]
solu         42: Nxg1    [  5+]
solu         43: Nd2     [  2+]
solu         44: Nd4     [  2+]
solu         45: Ne5     [  2+]
solu         46: Ra6     [  4+]
solu         47: cxb4    [  4+]
solu         48: Rxb4    [  2+]
solu         49: Bxb4    [  4+]
solu         50: Rxc6    [  6+]
solu         51: Bxc6    [  6+]
solu         52: Qxh8    [  2+]
solu         53: Rxf4    [  4+]
solu         54: Bxf2    [  5+]
solu         55: c4      [  4+]
solu         56: Ba2     [  4+]
solu         57: Rb7     [  2+]
solu         58: Bb3     [  4+]
solu         59: Be4     [  5+]
solu         60: Nf7     [  2+]
solu         61: Nh4     [  5+]
solu         62: Bf7     [  4+]
solu         63: Rf7     [  2+]
solu         64: Kh4     [  2+]
solu         65: Rb8     [  2+]
solu         66: Rb5     [  2+]
solu         67: Ne6     [  2+]
solu         68: Ne4     [  1+]
solu         69: Nh3     [  1+]
solu         70: Nh2     [  2+]
solu         71: Bc3     [  4+]
solu         72: Be6     [  5+]
solu         73: Bg8     [  5+]
solu         74: Bc4     [  4+]
solu         75: Re5     [  2+]
solu         76: Rf6     [  5+]
solu         77: Rf8     [  2+]
solu         78: Qh6     [  1+]
refu 55: Ra7     Bd2+    [  6-]
refu 56: Ra6     Bd2+    [  6-]
refu 57: Ra5     Bd2+    [  6-]
refu 58: Ra4     Bd2+    [  6-]
refu 59: Ra3     Bd2+    [  6-]
refu 60: Ra2     Bd2+    [  6-]
refu 61: Ra1     Bd2+    [  6-]
refu 62: Qf1     Bd2+    [  6-]
refu 63: Qgxe1   g1=Q    [  6-]
refu 64: Qxg2    Bd2+    [  5-]
solu         79: Bd2+    [  6+]
solu         80: Ng1     [  1+]
solu         81: Nd2     [  1+]
solu         82: Nd4     [  1+]
solu         83: Ne5     [  2+]
solu         84: Qxg7    [  1+]
solu         85: Ra6     [  1+]
solu         86: cxb4    [  1+]
solu         87: Rxb4    [  1+]
solu         88: Bxb4    [  1+]
solu         89: Rxc6    [  6+]
solu         90: Bxc6    [  6+]
solu         91: Rxf4    [  2+]
solu         92: Bxf2    [  1+]
solu         93: c4      [  1+]
solu         94: Rb7     [  1+]
solu         95: Bb3     [  1+]
solu         96: Ba2     [  1+]
solu         97: Be4     [  1+]
solu         98: Nf7     [  1+]
solu         99: Nh4     [  1+]
solu        100: Bf7     [  1+]
solu        101: Rf7     [  1+]
solu        102: Kh4     [  1+]
solu        103: Rb8     [  1+]
solu        104: Rb5     [  1+]
solu        105: Ne6     [  1+]
solu        106: Ne4     [  1+]
solu        107: Nh3     [  1+]
solu        108: Nh2     [  2+]
solu        109: Bc3     [  1+]
solu        110: Be6     [  5+]
solu        111: Bg8     [  1+]
solu        112: Bc4     [  1+]
solu        113: Re5     [  1+]
solu        114: Rf6     [  4+]
solu        115: Rf8     [  1+]
solu        116: Qh6     [  1+]
solu        117: Qg6     [  3+]
solu        118: Qh8     [  1+]
solu        119: Qg8     [  1+]
refu 65: Qc4     Bd2+    [  6-]
refu 66: Qd4     Bd2+    [  6-]
refu 67: Qe4     Bd2+    [  6-]
refu 68: Qa4     Bd2+    [  6-]
refu 69: Qb5     Bd2+    [  6-]
refu 70: Qxb6    Bd2+    [  6-]
refu 71: Qb3     Bd2+    [  6-]
refu 72: Qxc5    Bd2+    [  6-]
refu 73: Qa3     Bd2+    [  6-]
refu 74: Qc3     Nxg1    [  6-]
refu 75: Qd2     Bxd2+   [  6-]
refu 76: Qbxe1   Rxc6    [  6-]
solu          1: Nd4     [  2+]
solu          2: Nd2     [  2+]
solu          3: Nxe1    [  2+]
solu        120: Nxg1    [  6+]
solu        121: Ne5     [  2+]
solu        122: Qxg7    [  6+]
solu        123: Ra6     [  6+]
refu 77: Qa5     Bd2+    [  6-]
refu 78: Kd1     Bb3     [  6-]
solu          8: Ne4     [  5+]
refu 79: Kb1     Nd2+    [  6-]

Have a nice day!

Heiner



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