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Re: [Bug-gnubg] Positions on which 0-ply and 2-ply would disagree
|
From: |
Christian Anthon |
|
Subject: |
Re: [Bug-gnubg] Positions on which 0-ply and 2-ply would disagree |
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Date: |
Tue, 28 Jul 2009 22:42:16 +0200 |
These are interesting positions. As I would have expected most of the
move errors occur in very dynamic situations, which is where one would
expect 2ply to do a lot better than 0ply. The double/take decisions
are a bit more varied. One notices 0ply's tendency to double to early,
but again the largest differences occur in positions where a lot
depends on the next two rolls.
Christian.
On Sat, Jul 18, 2009 at 2:08 AM, boomslang<address@hidden> wrote:
>
> Thanks Zorba and Christian for your replies.
>
> I did what Zorba suggested: playing 0ply vs 0ply in a long money session (GNU
> Backgammon 0.90-mingw 20090518 crashed three times / Win XP Home edition SP
> 3) and analysing the match on 2ply NO move filter.
>
> In total 313 games were played (over 12000 moves) and the biggest errors were:
>
> MOVE ERRORS:
> -0.18
> -0.172
> -0.171
> -0.163
> -0.157
> -0.154
> -0.151
>
>
> CUBE ERRORS:
> -0.13105
> -0.128
> -0.09192
> -0.0915
> -0.07735
> -0.07571
> -0.07491
> -0.07424
>
> Here are the corresponding positions:
>
>
>
>
>
>
> MOVE ERRORS:
>
> Move number 19: boom to play 31
>
> GNU Backgammon Position ID: a3MYAwg7zwwAAw
> Match ID : cIkFAGAJiAUA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | O | | O X O O O O | 150 points
> | O | | O X O O O |
> | | | O |
> | | | |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | |
> | | | X |
> | | | X X |
> | O X | | X X X X | Rolled 31
> | O X | | X X O X X | 177 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: boom
> Pip counts: O 104, X 92
>
> * boom moves 6/3* 4/3
>
> Cube analysis
> 2-ply cubeless equity -0.07314
> 0.47771 0.10943 0.00177 - 0.52229 0.13742 0.00235
> Cubeful equities:
> 1. No double -0.04341
> 2. Double, pass +1.00000 ( +1.04341)
> 3. Double, take -0.48453 ( -0.44112)
> Proper cube action: No double, beaver (29.7%)
> Alert: very bad move ( -0.180)
>
> Rolled 31 (-0.082):
> 1. Cubeful 2-ply 20/17 4/3* Eq.: +0.09823
> 0.49661 0.15791 0.00197 - 0.50339 0.21521 0.00857
> * 2. Cubeful 2-ply 6/3* 4/3 Eq.: -0.08153 (
> -0.17976)
> 0.48036 0.09955 0.00027 - 0.51964 0.10195 0.00179
> 3. Cubeful 2-ply 8/5 4/3* Eq.: -0.08653 (
> -0.18476)
> 0.44960 0.15023 0.00129 - 0.55040 0.18816 0.00542
> 4. Cubeful 2-ply 4/3* 4/1 Eq.: -0.10149 (
> -0.19972)
> 0.47781 0.09894 0.00052 - 0.52219 0.11324 0.00185
> 5. Cubeful 2-ply 4/1 2/1 Eq.: -0.17287 (
> -0.27110)
> 0.45737 0.04512 0.00010 - 0.54263 0.08912 0.00078
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 31: boom to play 31
>
> GNU Backgammon Position ID: 7JrBAwib3YwAQA
> Match ID : QYkFAIACYAEA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg (Cube: 2)
> | O | | O O O O | 40 points
> | O | | O O O |
> | | | O |
> | | | |
> | | | |
> v| |BAR| |
> | | | |
> | O | | |
> | O | | X |
> | O X | | X X X X X | Rolled 31
> | O X X | X | X X X O X X | 44 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: boom
> Pip counts: O 125, X 93
>
> * boom moves bar/24 6/3*
> Alert: very bad move ( -0.172)
> Alert: unlucky roll! ( -0.408)
>
> Rolled 31 (-0.408):
> 1. Cubeful 2-ply bar/24 11/8 Eq.: +0.38845
> 0.64550 0.25706 0.00189 - 0.35450 0.03749 0.00117
> 2. Cubeful 2-ply bar/24 5/2 Eq.: +0.25925 (
> -0.12919)
> 0.59859 0.26720 0.00329 - 0.40141 0.06850 0.00290
> * 3. Cubeful 2-ply bar/24 6/3* Eq.: +0.21691 (
> -0.17154)
> 0.57477 0.35835 0.00519 - 0.42523 0.14897 0.00957
> 4. Cubeful 2-ply bar/24 8/5 Eq.: +0.09270 (
> -0.29574)
> 0.54372 0.26961 0.00403 - 0.45628 0.10221 0.00484
> 5. Cubeful 2-ply bar/24 4/1 Eq.: -0.24503 (
> -0.63347)
> 0.45775 0.18994 0.00284 - 0.54225 0.16215 0.00784
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 35: gnubg to play 61
>
> GNU Backgammon Position ID: tm1kAiB2dwcAIA
> Match ID : EQEHAMACgAEA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
> | X | | O O O O O X | 44 points
> | | | O O O O O | Rolled 61
> | | | O O O O |
> | | | |
> | | | |
> ^| |BAR| |
> | | | |
> | | | |
> | | | |
> | X | | X X X X X |
> | X X | | X X X X X O | 48 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom (Cube: 2)
> Pip counts: O 82, X 108
>
> * gnubg moves 24/17
> Alert: very bad move ( -0.171)
> Alert: very unlucky roll! ( -0.681)
>
> Rolled 61 (-0.681):
> 1. Cubeful 2-ply 24/18 2/1* Eq.: -0.15262
> 0.44870 0.28338 0.00776 - 0.55130 0.25796 0.01245
> * 2. Cubeful 2-ply 24/17 Eq.: -0.32407 (
> -0.17145)
> 0.41514 0.11406 0.00728 - 0.58486 0.04054 0.00077
> 3. Cubeful 2-ply 24/18 3/2 Eq.: -0.59457 (
> -0.44195)
> 0.30579 0.10745 0.00932 - 0.69421 0.05687 0.00127
> 4. Cubeful 2-ply 24/18 6/5 Eq.: -0.61006 (
> -0.45744)
> 0.29991 0.10349 0.00906 - 0.70009 0.06134 0.00142
> 5. Cubeful 2-ply 24/18 4/3 Eq.: -0.61310 (
> -0.46048)
> 0.30055 0.10194 0.00870 - 0.69945 0.05803 0.00143
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 12: gnubg to play 55
>
> GNU Backgammon Position ID: 2M4mAyCyncFBIA
> Match ID : MIEWAFAEsAIA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
> | X O | | O O O O X | 69 points
> | X O | | O O O | Rolled 55
> | | | O |
> | | | |
> | | | |
> ^| |BAR| | (Cube: 1)
> | | | |
> | | | |
> | O | | X |
> | O X X | | X X X |
> | O X X X O | | X X X O | 86 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom
> Pip counts: O 135, X 131
>
> * gnubg moves 18/13 8/3(2) 6/1*
>
> Cube analysis
> 2-ply cubeless equity -0.06393
> 0.47120 0.16824 0.00652 - 0.52880 0.17321 0.00788
> Cubeful equities:
> 1. No double -0.08317
> 2. Double, pass +1.00000 ( +1.08317)
> 3. Double, take -0.48343 ( -0.40026)
> Proper cube action: No double, beaver (27.0%)
> Alert: very bad move ( -0.163)
>
> Rolled 55 (-0.170):
> 1. Cubeful 2-ply 13/3 8/3 6/1* Eq.: -0.03332
> 0.42557 0.24365 0.00743 - 0.57443 0.27457 0.03158
> * 2. Cubeful 2-ply 18/13 8/3(2) 6/1* Eq.: -0.19647 (
> -0.16314)
> 0.43488 0.20198 0.00476 - 0.56512 0.18214 0.01075
> 3. Cubeful 2-ply 18/3 8/3 Eq.: -0.23209 (
> -0.19877)
> 0.42846 0.16874 0.00662 - 0.57154 0.16319 0.00810
> 4. Cubeful 2-ply 18/8 13/8 6/1* Eq.: -0.47014 (
> -0.43681)
> 0.37074 0.13370 0.00288 - 0.62926 0.19301 0.00970
> 5. Cubeful 2-ply 18/3 13/8 Eq.: -0.57612 (
> -0.54280)
> 0.34648 0.11117 0.00342 - 0.65352 0.20236 0.01077
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 33: boom to play 56
>
> GNU Backgammon Position ID: ljcHAwhwZxsCBg
> Match ID : cIkaAEACIAEA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O | | O O X O O | 36 points
> | O | | O O X O |
> | O | | O |
> | | | O |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | |
> | | | |
> | | | X X |
> | O X X X | | X X | Rolled 56
> | O X X X | | X X O | 36 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: boom
> Pip counts: O 111, X 143
>
> * boom moves 14/3*
>
> Cube analysis
> 2-ply cubeless equity +0.11523
> 0.54470 0.13015 0.00410 - 0.45530 0.10642 0.00200
> Cubeful equities:
> 1. No double +0.16292
> 2. Double, pass +1.00000 ( +0.83708)
> 3. Double, take -0.07888 ( -0.24180)
> Proper cube action: No double, beaver (22.4%)
> Alert: bad move ( -0.157)
>
> Rolled 56 (-0.081):
> 1. Cubeful 2-ply 9/3* 8/3 Eq.: +0.25416
> 0.55766 0.17779 0.00440 - 0.44234 0.12338 0.00717
> * 2. Cubeful 2-ply 14/3* Eq.: +0.09709 (
> -0.15707)
> 0.53016 0.14154 0.00304 - 0.46984 0.12258 0.00432
> 3. Cubeful 2-ply 14/8 10/5 Eq.: -0.08164 (
> -0.33580)
> 0.47507 0.09814 0.00212 - 0.52493 0.08416 0.00226
> 4. Cubeful 2-ply 14/8 6/1 Eq.: -0.12607 (
> -0.38023)
> 0.45919 0.09938 0.00169 - 0.54081 0.09071 0.00241
> 5. Cubeful 2-ply 14/9 10/4 Eq.: -0.12711 (
> -0.38127)
> 0.47192 0.10529 0.00243 - 0.52808 0.13054 0.00440
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 37: gnubg to play 51
>
> GNU Backgammon Position ID: 2A4Y4kLbGJkAKg
> Match ID : EYEGAEAXCAwA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
> | X O O X | | O X X O O O | 372 points
> | X O | | O X O O O | Rolled 51
> | | | X |
> | | | |
> | | | |
> ^| |BAR| |
> | | | |
> | | | |
> | | | X |
> | | | X X X |
> | O | X | X X X O O O | 385 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom (Cube: 2)
> Pip counts: O 137, X 185
>
> * gnubg moves 24/23 13/8*
> Alert: bad move ( -0.154)
>
> Rolled 51 (-0.024):
> 1. Cubeful 2-ply 11/10 9/4* Eq.: +0.51714
> 0.64203 0.47175 0.02914 - 0.35797 0.13621 0.01788
> 2. Cubeful 2-ply 24/23 9/4* Eq.: +0.42774 (
> -0.08940)
> 0.62021 0.42864 0.02798 - 0.37979 0.13009 0.00818
> 3. Cubeful 2-ply 23/22 9/4* Eq.: +0.42724 (
> -0.08990)
> 0.62078 0.42619 0.02511 - 0.37922 0.12562 0.00756
> 4. Cubeful 2-ply 9/4*/3 Eq.: +0.41276 (
> -0.10438)
> 0.60998 0.43005 0.02365 - 0.39002 0.11861 0.00681
> 5. Cubeful 2-ply 23/18 9/8* Eq.: +0.39666 (
> -0.12048)
> 0.61555 0.39804 0.02056 - 0.38445 0.11585 0.00662
> * 10. Cubeful 2-ply 24/23 13/8* Eq.: +0.36304 (
> -0.15410)
> 0.60356 0.39959 0.02250 - 0.39644 0.12419 0.00642
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 51: gnubg to play 11
>
> GNU Backgammon Position ID: 780AgMC/HRgAAA
> Match ID : AYEEAHAF2AIA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg (Cube: 2)
> | O | | X O O O | 87 points
> | O | | O O O | Rolled 11
> | | | O O |
> | | | O |
> | | | 8 |
> ^| |BAR| |
> | | | |
> | | | X X |
> | | | X X |
> | | | X X X X | X
> | | | X X X X | X 91 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom
> Pip counts: O 39, X 48
>
> * gnubg moves 9/7(2)
>
> Cube analysis
> 2-ply cubeless equity +0.13036
> 0.56710 0.00000 0.00000 - 0.43290 0.00383 0.00001
> Cubeful equities:
> 1. No double +0.33189
> 2. Double, pass +1.00000 ( +0.66811)
> 3. Double, take +0.02211 ( -0.30978)
> Proper cube action: No redouble, take (31.7%)
> Alert: bad move ( -0.151)
>
> Rolled 11 (-0.079):
> 1. Cubeful 2-ply 9/5* Eq.: +0.18450
> 0.49865 0.00000 0.00000 - 0.50135 0.02407 0.00000
> * 2. Cubeful 2-ply 9/7(2) Eq.: +0.03306 (
> -0.15144)
> 0.44945 0.00000 0.00000 - 0.55055 0.00007 0.00000
> 3. Cubeful 2-ply 9/8(2) 3/2(2) Eq.: +0.01405 (
> -0.17045)
> 0.44092 0.00000 0.00000 - 0.55908 0.00034 0.00000
> 4. Cubeful 2-ply 9/8(2) 3/1 Eq.: +0.00249 (
> -0.18201)
> 0.43589 0.00000 0.00000 - 0.56411 0.00024 0.00000
> 5. Cubeful 2-ply 3/1 3/2(2) Eq.: -0.10246 (
> -0.28696)
> 0.39022 0.00000 0.00000 - 0.60978 0.00161 0.00000
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> CUBE ERRORS:
>
> Move number 10: gnubg doubles to 2
>
> GNU Backgammon Position ID: 4HPMA0Ab24KAKA
> Match ID : MBkAALAHoAMA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
> | X O O | | O O O O | 123 points
> | X O | | O O O O |
> | X | | |
> | X | | |
> | | | |
> ^| |BAR| |
> | | | X |
> | | | X |
> | X | | X |
> | X X | | X | Cube offered at 2
> | O X X | X | X O O O | 116 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom
> Pip counts: O 130, X 153
>
> * boom rejects
>
> Alert: wrong pass ( -0.13105)!
>
> Cube analysis
> 2-ply cubeless equity +0.55940
> 0.63258 0.36115 0.00371 - 0.36742 0.06771 0.00291
> Cubeful equities:
> 1. Double, take +0.86895
> 2. Double, pass +1.00000 ( +0.13105)
> 3. No double +0.69743 ( -0.17152)
> Proper cube action: Double, take
> gnubg wins 1 point
>
>
>
>
>
>
>
>
>
>
>
> Move number 33: gnubg to play 63
>
> GNU Backgammon Position ID: 27aDAASauzsAAA
> Match ID : AQEPAOATMAsA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg (Cube: 2)
> | O O | | O O X O O | 318 points
> | O O | | O O O | Rolled 63
> | O O | | O O |
> | | | |
> | | | |
> ^| |BAR| |
> | | | |
> | | | |
> | | | X |
> | | | X X X X X X |
> | X | | X X X X X X | 358 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom
> Pip counts: O 86, X 80
>
> * gnubg moves 8/2 7/4*
> Alert: missed double ( -0.12800)!
> [bad]
> Cube analysis
> 2-ply cubeless equity +0.46748
> 0.72674 0.02903 0.00066 - 0.27326 0.01559 0.00010
> Cubeful equities:
> 1. Double, take +0.78251
> 2. Double, pass +1.00000 ( +0.21749)
> 3. No double +0.65452 ( -0.12800)
> Proper cube action: Redouble, take
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 24: gnubg doubles to 4
>
> GNU Backgammon Position ID: 2zhnAEBtayEDAg
> Match ID : ARkAAAAGAAMA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
> | O O | | O O O O O O | 96 points
> | | | O O O O |
> | | | |
> | | | |
> | | | |
> ^| |BAR| |
> | | | |
> | | | |
> | X | | X |
> | O X X | | X X X X | Cube offered at 4
> | O X X | X | X O X X X | 96 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom
> Pip counts: O 100, X 99
>
> * boom rejects
>
> Alert: wrong pass ( -0.09192)!
>
> Cube analysis
> 2-ply cubeless equity +0.53819
> 0.74112 0.15587 0.00293 - 0.25888 0.09951 0.00334
> Cubeful equities:
> 1. Double, take +0.90808
> 2. Double, pass +1.00000 ( +0.09192)
> 3. No double +0.70773 ( -0.20035)
> Proper cube action: Redouble, take
> gnubg wins 2 points
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 13: gnubg on roll, cube decision?
>
> GNU Backgammon Position ID: s20GAxDY7krAAA
> Match ID : MAEAAMAIeAQA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg
> | X O O O O | | O O O X | 140 points
> | X O | | O O O | On roll
> | O | | O |
> | | | |
> | | | |
> ^| |BAR| | (Cube: 1)
> | | | |
> | | | |
> | | | |
> | X O | | X X X X X |
> | X O | | X X X X X | 143 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom
> Pip counts: O 121, X 103
>
> * gnubg doubles
>
> Alert: wrong double ( -0.09150)!
> [bad]
> Cube analysis
> 2-ply cubeless equity +0.36845
> 0.66218 0.12628 0.00286 - 0.33782 0.08380 0.00125
> Cubeful equities:
> 1. No double +0.60972
> 2. Double, pass +1.00000 ( +0.39028)
> 3. Double, take +0.51821 ( -0.09150)
> Proper cube action: No double, take (19.0%)
> Move number 14: gnubg doubles to 2
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 9: boom on roll, cube decision?
>
> GNU Backgammon Position ID: G87gATCY85gJAg
> Match ID : cAkAAKACYAEA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X X O | | O X O O | 42 points
> | X O | | O O O |
> | | | O |
> | | | |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | |
> | O X | | |
> | O X | | X |
> | O X X | | X X O | On roll
> | O X X | | X X O | 44 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: boom
> Pip counts: O 140, X 141
>
> * boom doubles
>
> Alert: wrong double ( -0.07735)!
> [doubtful]
> Cube analysis
> 2-ply cubeless equity +0.34223
> 0.64294 0.15267 0.00636 - 0.35706 0.10134 0.00133
> Cubeful equities:
> 1. No double +0.51901
> 2. Double, pass +1.00000 ( +0.48099)
> 3. Double, take +0.44166 ( -0.07735)
> Proper cube action: No double, take (13.9%)
> Move number 10: boom doubles to 2
>
>
>
>
>
>
>
>
>
>
>
>
> Move number 11: boom on roll, cube decision?
>
> GNU Backgammon Position ID: yGfwASjYTnBAWA
> Match ID : cAkAAKAJwAUA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O | | O X O X | 154 points
> | X O | | O X |
> | X | | O |
> | | | O |
> | | | O |
> v| |BAR| | (Cube: 1)
> | O | | |
> | O | | |
> | O | | X |
> | O | | X X X | On roll
> | O X | X | X X X O O | 184 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: boom
> Pip counts: O 162, X 176
>
> * boom doubles
>
> Alert: wrong double ( -0.07571)!
> [doubtful]
> Cube analysis
> 2-ply cubeless equity +0.35890
> 0.60301 0.24697 0.02020 - 0.39699 0.10753 0.00676
> Cubeful equities:
> 1. No double +0.52364
> 2. Double, pass +1.00000 ( +0.47636)
> 3. Double, take +0.44792 ( -0.07571)
> Proper cube action: No double, take (13.7%)
> Move number 12: boom doubles to 2
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> Move number 8: boom on roll, cube decision?
>
> GNU Backgammon Position ID: xm7BASjgczMHAA
> Match ID : cAkAAMAKCAYA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | | O O O | 172 points
> | X O | | O O O |
> | X | | O |
> | | | |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | X |
> | | | X |
> | O X | | X |
> | O X X X | | X | On roll
> | O X X X | | X O O | 193 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: boom
> Pip counts: O 140, X 133
>
> * boom doubles
>
> Alert: wrong double ( -0.07491)!
> [doubtful]
> Cube analysis
> 2-ply cubeless equity +0.35248
> 0.65888 0.10077 0.00300 - 0.34112 0.06844 0.00062
> Cubeful equities:
> 1. No double +0.54791
> 2. Double, pass +1.00000 ( +0.45209)
> 3. Double, take +0.47300 ( -0.07491)
> Proper cube action: No double, take (14.2%)
> Move number 9: boom doubles to 2
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> Move number 35: gnubg to play 21
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> GNU Backgammon Position ID: bm8DAEHbZlJAIA
> Match ID : AQEFAIATIAsA
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ O: gnubg (Cube: 2)
> | O O O | | O X O O O O | 312 points
> | | | O O O O O | Rolled 21
> | | | |
> | | | |
> | | | |
> ^| |BAR| |
> | | | |
> | | | X |
> | | | X X |
> | | | X X X X X |
> | O | X | X X X X X O | 356 points
> +13-14-15-16-17-18------19-20-21-22-23-24-+ X: boom
> Pip counts: O 103, X 95
>
> * gnubg moves 8/5*
> Alert: missed double ( -0.07424)!
> [doubtful]
> Cube analysis
> 2-ply cubeless equity +0.75651
> 0.75375 0.32288 0.00967 - 0.24625 0.07824 0.00530
> Cubeful equities:
> 1. Double, pass +1.00000
> 2. Double, take +1.35756 ( +0.35756)
> 3. No double +0.92576 ( -0.07424)
> Proper cube action: Redouble, pass
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