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Open your mind
05-06-2015
, 03:37 AM
Black - Pips 103
Position 23 Variant. Black to Play 4-1
XGID=aBBaB-BC-B---a-A--cdbc-A--:3:-1:1:41:0:0:0:0:10
Sort of like this!
Mike
05-06-2015
, 10:15 AM
Code:
1. 9/5*/4 Eq.: +0,935
0,773 0,501 0,021 - 0,227 0,052 0,004 CL +1,012 CF +0,935
2. 23/22 9/5* Eq.: +0,851 ( -0,084)
0,741 0,526 0,025 - 0,259 0,096 0,008 CL +0,929 CF +0,851
Code:
1. 9/5*/4 Eq.: +1,193
0,849 0,552 0,021 - 0,151 0,028 0,002 CL +1,241 CF +1,193
2. 9/5* 8/7 Eq.: +0,961 ( -0,232)
0,779 0,539 0,023 - 0,221 0,082 0,006 CL +1,031 CF +0,961
The importance of this is shown by moving from 9 to 23:
Code:
1. 23/22 9/5* Eq.: +0,586
0,677 0,459 0,026 - 0,323 0,133 0,018 CL +0,687 CF +0,586
2. 9/5*/4 Eq.: +0,534 ( -0,052)
0,660 0,410 0,020 - 0,340 0,096 0,006 CL +0,650 CF +0,534
No shot on the outfield blot by moving white from 13w to 16:
Code:
1. 23/22 9/5* Eq.: +0,881
0,750 0,518 0,027 - 0,250 0,086 0,006 CL +0,953 CF +0,881
2. 9/5*/4 Eq.: +0,848 ( -0,034)
0,756 0,468 0,017 - 0,244 0,063 0,006 CL +0,927 CF +0,848
Combining both changes:
Code:
1. 23/22 9/5* Eq.: +0,585
0,680 0,454 0,024 - 0,320 0,136 0,019 CL +0,685 CF +0,585
2. 9/5*/4 Eq.: +0,414 ( -0,171)
0,631 0,381 0,016 - 0,369 0,108 0,010 CL +0,540 CF +0,414
PS With thanks for your open responses, and with thanks to bionic yogiman.
Last edited by yogiman; 05-06-2015 at 10:20 AM.
05-06-2015
, 12:13 PM
White - Pips 126
Black - Pips 103
Position 23 Variant. Black to Play 4-1
Unlimited game, no Jacoby, no beavers
XGID=aBBaB-BC-B---a-A--cdbc-A--:3:-1:1:41:0:0:0:0:10
The 5k rollout below confirms that lifting your blot after hitting is a 55 millipoint error.
Mike
Black - Pips 103
Position 23 Variant. Black to Play 4-1
Unlimited game, no Jacoby, no beavers
XGID=aBBaB-BC-B---a-A--cdbc-A--:3:-1:1:41:0:0:0:0:10
The 5k rollout below confirms that lifting your blot after hitting is a 55 millipoint error.
Code:
XGID=aBBaB-BC-B---a-A--cdbc-A--:3:-1:1:41:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
Pip count X: 103 O: 126 X-O: 0-0
Cube: 8, O own cube
X to play 41
1. Rollout¹ 23/22 7/3* eq:+0.7867
Player: 73.50% (G:47.96% B:1.96%)
Opponent: 26.50% (G:9.23% B:0.70%)
Confidence: ±0.0033 (+0.7834..+0.7899) - [100.0%]
2. Rollout¹ 7/6 7/3* eq:+0.7461 (-0.0406)
Player: 71.96% (G:48.99% B:1.91%)
Opponent: 28.04% (G:10.21% B:1.10%)
Confidence: ±0.0039 (+0.7421..+0.7500) - [0.0%]
3. Rollout¹ 7/3* 3/2 eq:+0.7312 (-0.0555)
Player: 73.60% (G:40.53% B:1.20%)
Opponent: 26.40% (G:5.87% B:0.39%)
Confidence: ±0.0035 (+0.7277..+0.7347) - [0.0%]
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 2025577
Moves: 3-ply, cube decisions: XG Roller
Rollout by Taper_Mike
2015-May-06
eXtreme Gammon Version: 2.10.199.2658
OpenYourMind.023.variant.xgp
05-06-2015
, 12:19 PM
05-07-2015
, 09:30 AM
Position ID: WM9GCChodwcgSA Match ID: cIkGAAAAAAAE
05-07-2015
, 05:24 PM
05-08-2015
, 04:07 AM
05-08-2015
, 09:27 AM
Code:
1. bar/24 18/13* Eq.: +0,498
0,606 0,278 0,037 - 0,394 0,140 0,013 CL +0,375 CF +0,498
2. bar/20* 6/5 Eq.: +0,366 ( -0,132)
0,582 0,253 0,031 - 0,418 0,152 0,013 CL +0,283 CF +0,366
1. Position after black has played bar/24 18/13*.
(pipnumbering is reversed)
2. Position after black has played bar/20* 6/5.
The two board positions after black's move are shown above. White's compared equity loss after black has played move 1. versus move 2. is red colored.
White rolls 41
after black plays from the bar/24 18/13*:
Code:
bar/21* 6/5 Eq.: +0,427
Code:
bar/21* 6/5* Eq.: +0,259
The equities are white's gains. In this case white has profit when black plays the right move, so the compared equity loss is negative: 0,259 – 0,427 = -0, 168
White rolls 42
Code:
bar/21* 23/21 Eq.: -0,157
Code:
bar/21* 9/7* Eq.: +0,033
White rolls 43
Code:
bar/21* 8/5 Eq.: +0,007
Code:
bar/21* 8/5* Eq.: +0,023
White rolls 44
Code:
bar/21* 9/5 6/2*(2) Eq.: +0,986
Code:
bar/21* 9/5*(2) 6/2* Eq.: +0,826
In this case both have double-hits.
White rolls 54
Code:
bar/21*/16 Eq.: -0,291
Code:
bar/21* 12/7* Eq.: +0,129
It gets very difficult for white to acquire the indispensable advanced anchor, as the bar checker is passed from the 21-point. This one is really standing out among the 4's.
White rolls 64
Code:
bar/21*/15 Eq.: -0,365
Code:
bar/21* 8/2* Eq.: -0,228
Here the checker is also passed, but 8/2* is a very bad move.
White rolls 11
Code:
bar/24 23/21* 6/5 Eq.: +0,360
Code:
bar/24 8/7* 6/5*(2) Eq.: +0,804
White can double hit and make the 5-point at once.
White rolls 22
Code:
bar/21* 9/5 Eq.: +0,212
Code:
bar/21* 9/7*/5* Eq.: +0,359
White rolls 33
Code:
bar/22 24/21* 8/5(2) Eq.: +0,278
Code:
bar/22 24/21* 8/5*(2) Eq.: +0,742
White can double hit and make the 5-point at once.
Notice that there are the lesser numbers and three big numbers.
Adding up the comparitive losses for the lesser numbers: 0,190 + 0,016 + 0,136 + 0,147 – 0,168 – 0,160 = 0,161.
Adding up the comparitive losses for the big numbers: 0,420 + 0,544 + 0,464 = 1,428.
It's clear that white's 54, 11 and 33 exclusively carry almost all the weight to tip the balance decisively towards bar/24 18/13*, and particularly the two doubles could be pathfinders over the board. But next year I will play bar/20* again.
Last edited by yogiman; 05-08-2015 at 09:32 AM.
05-08-2015
, 01:03 PM
05-09-2015
, 03:29 AM
Quote:
Nice analysis! This roll-by-roll comparison is hard work, but sometimes it is the only way to identify what is really going on.
You can get an even better measurement by weighting the equities for non-doublets twice as much as those for doublets.
Mike
You can get an even better measurement by weighting the equities for non-doublets twice as much as those for doublets.
When you use a weighted sum like this, you can divide the results by 36 to obtain the overall equity difference. Your original rollout shows that hitting on the 13pt beats hitting on the 20pt by 0.132. The portion due to the “lesser numbers” is (0.337 / 36) = 0.0094. The portion due to the “big numbers” is (1.848 / 36) = 0.0513. These two add up to 0.0607, so the rest of the difference, (0.132 – 0.0607) = 0.0713, must be due to the other rolls. A small part of this last number might also be due to differences in the strengths or seeds of the various rollouts.
Adding up the comparative losses for the lesser numbers (note that I am changing 0.136 to 0.137, for the roll of 64, correcting a typo in your post):
2 * (0.190 + 0.016 + 0.137 – 0.168) + 0.147 – 0.160 = 0.337.
Adding up the comparative losses for the big numbers:
2 * 0.420 + 0.544 + 0.464 = 1.848.
Mike
nice analysis of the analysis
i do mean sincerely, the explanation is good, as is the break down of rolls, it is lots of work.
for what ever reason the play seems very clear to me, 6/5 makes no sense. 24 18/13* is very clear to me, Funny how some plays are easy for some and difficult for others, i'm not bragging, i make horrible plays often. juist a coincidence this one wouldn't be one of them.
Last edited by TheRealFatboy; 05-09-2015 at 03:35 AM.
05-09-2015
, 01:14 PM
Here is a fun sequence. This is an unlimited game, no Jacoby, and no beavers. It opens with White playing 61-point, and Black responding with 65-down (playing two checkers down from the midpoint). White then rolls 41:
Roll 3. White to Play 4-1
White - Pips 160
Black - Pips 156
White slots his 5pt, 13/9 6/5. It would be unwise to split in the face of the 10 checkers Black has in the zone. Black’s spares are awkwardly stacked, so if White were to split from the safety of his anchor, he would be creating hitting options for Black that would help him smooth out his distribution.
Roll 4. Black to Play 4-2
White - Pips 155
Black - Pips 156
Hitting is far better than any pointing play. After that, the 2 should be played moving to the 22pt. The alternative, playing the final spare down from the midpoint, is too blotty, plus it fails to get the back checkers to where they can both see daylight.
Roll 5. White to Play 1-1
White - Pips 175
Black - Pips 150
White rolls a welcome doublet from the bar. 24/23 is better than 9/8 for the final ace. White does not want 3 checkers stuck on his 24pt. If Black hits in the outer board, White should have little trouble advancing his anchor. Besides, since White is already significantly behind in the race, getting hit will not hurt very much. Bold play is appropriate.
Roll 6. Black to Play 3-2
White - Pips 171
Black - Pips 155
Anchoring with the 3 is clear. With one blot already exposed to a double direct shot, it would be foolish to open another with the 2. Black plays 7/5, which moves the blot to the place where he wants it anyway. This also duplicates the 4 White needs on the other side of the board to extend his block.
Roll 7. White to Play 5-2
White - Pips 171
Black - Pips 150
This would be a fine problem already, but we have something even more fun coming up. Since Black is so weak and has a blot in his board, White can afford to leave the back of his prime slotted. Black’s hitting number is 6. White can duplicate this number, and bid for an advanced anchor at the same time, by playing 23/18. With the 2, White should come down from the midpoint, increasing his odds of making his 9pt. Once again, bold play is appropriate.
Roll 8. Black to Play 5-4
White - Pips 164
Black - Pips 150
WTF?!!
Now we’re having fun! The only sane way to play the 5 is down to the 8pt. After that, slotting the 4pt is better than playing to the 2pt.
At this point, White has a good double, which Black should take. Black is ahead in the race, and has an anchor on the 22pt. That’s not the best anchor, but it is an improvement that counts.
Roll 9. White to Play 6-1
White - Pips 164
Black - Pips 141
Missing a double shot is the easiest thing in the world! At least White can make a good anchor. As before, White must keep the back of his prime slotted. Creeping up to the 23pt is the best ace.
Roll 10. Black to Play 5-1
White - Pips 157
Black - Pips 141
Unlimited game, no Jacoby, no beavers
XGID=--a-AAEbD---bBa-abbbb-B---:1:1:1:51:0:0:0:0:10
Since Black rolled an ace, this must be a good roll. How should he play it?
Mike
Roll 3. White to Play 4-1
White - Pips 160
Black - Pips 156
White slots his 5pt, 13/9 6/5. It would be unwise to split in the face of the 10 checkers Black has in the zone. Black’s spares are awkwardly stacked, so if White were to split from the safety of his anchor, he would be creating hitting options for Black that would help him smooth out his distribution.
Roll 4. Black to Play 4-2
White - Pips 155
Black - Pips 156
Hitting is far better than any pointing play. After that, the 2 should be played moving to the 22pt. The alternative, playing the final spare down from the midpoint, is too blotty, plus it fails to get the back checkers to where they can both see daylight.
Roll 5. White to Play 1-1
White - Pips 175
Black - Pips 150
White rolls a welcome doublet from the bar. 24/23 is better than 9/8 for the final ace. White does not want 3 checkers stuck on his 24pt. If Black hits in the outer board, White should have little trouble advancing his anchor. Besides, since White is already significantly behind in the race, getting hit will not hurt very much. Bold play is appropriate.
Roll 6. Black to Play 3-2
White - Pips 171
Black - Pips 155
Anchoring with the 3 is clear. With one blot already exposed to a double direct shot, it would be foolish to open another with the 2. Black plays 7/5, which moves the blot to the place where he wants it anyway. This also duplicates the 4 White needs on the other side of the board to extend his block.
Roll 7. White to Play 5-2
White - Pips 171
Black - Pips 150
This would be a fine problem already, but we have something even more fun coming up. Since Black is so weak and has a blot in his board, White can afford to leave the back of his prime slotted. Black’s hitting number is 6. White can duplicate this number, and bid for an advanced anchor at the same time, by playing 23/18. With the 2, White should come down from the midpoint, increasing his odds of making his 9pt. Once again, bold play is appropriate.
Roll 8. Black to Play 5-4
White - Pips 164
Black - Pips 150
WTF?!!
Now we’re having fun! The only sane way to play the 5 is down to the 8pt. After that, slotting the 4pt is better than playing to the 2pt.
At this point, White has a good double, which Black should take. Black is ahead in the race, and has an anchor on the 22pt. That’s not the best anchor, but it is an improvement that counts.
Roll 9. White to Play 6-1
White - Pips 164
Black - Pips 141
Missing a double shot is the easiest thing in the world! At least White can make a good anchor. As before, White must keep the back of his prime slotted. Creeping up to the 23pt is the best ace.
Roll 10. Black to Play 5-1
White - Pips 157
Black - Pips 141
Unlimited game, no Jacoby, no beavers
XGID=--a-AAEbD---bBa-abbbb-B---:1:1:1:51:0:0:0:0:10
Since Black rolled an ace, this must be a good roll. How should he play it?
Mike
05-10-2015
, 09:02 AM
05-11-2015
, 01:52 PM
Problem 25. Black to Play 5-1
White - Pips 157
Black - Pips 141
Unlimited game, no Jacoby, no beavers
XGID=--a-AAEbD---bBa-abbbb-B---:1:1:1:51:0:0:0:0:10
To find the best play here, one truly needs to “open one’s mind.”
When I showed this position to a friend who holds a Grandmaster Class 3 title (awarded by the Backgammon Masters Awarding Body (BMAB)), his immediate reaction was to say that he often blunders in this sort of position. That made me feel a little better, as I failed to even consider the best play. The top play is the one Karol Szczerek found, breaking the anchor, and hitting outside!
At first, that looks a little crazy. Hitting gives up the only asset Black has managed to acquire thus far. White already has a direct shot at the two blots in Black’s board. Hitting him gives him another. After Black hits, White will hit one of the blots in Black’s board with almost any 2, 3, 4, or 5! The only rolls that miss are 66, 63, 62, and 61.
A little reflection, however, is all it takes to convince yourself that hitting is best. The key is the 16pt. As things stand, White has a double shot to make it. If White covers, Black will be primed behind a five-point block, and the game will be just about over.
Hitting mixes things up. Often Black will be forced into hitting contest. Frequently, Black will be able to advance his anchor after being hit. Other times, he may land in a backgame. And there is always the chance that White will throw a 6 from the bar. As Karol pointed out, any of these alternatives gives Black more winning opportunities than passively allowing White to complete his block.
5k XG2 Rollout – Unlimited game, no Jacoby, no beavers
The real Fatboy, Eric Peterson, asked whether slotting the 4pt was the best way to play 54 on roll 8. To see why it is, consider how to play the 5. If you don’t play 13/8, then you have to play 8/3, slotting the 3pt. But if you slot the 3pt with the 5, then the 4 has to come down from the midpoint. Otherwise, you are playing 8/4 8/3, leaving three inside blots. Two down from the midpoint is no option either. That would sacrifice the midpoint. The choice, therefore, is between 13/4 and 13/9 8/3. In this light, slotting the 4pt beats slotting the 3pt on two counts. First, it minimizes blot count at a time when a hitting war is about to erupt. Second, it slots the better point. An XGR++ eval has 13/4 on top by 13 millipoints (i.e., 0.013).
In the practice game where this position arose, I took the tutor’s advice, and made the hit. The bot promptly rolled 62, missing the shots, whereupon I luckboxed into a 21, making both my 5pt and 4pt.
You gotta love this game!
Mike
White - Pips 157
Black - Pips 141
Unlimited game, no Jacoby, no beavers
XGID=--a-AAEbD---bBa-abbbb-B---:1:1:1:51:0:0:0:0:10
To find the best play here, one truly needs to “open one’s mind.”
When I showed this position to a friend who holds a Grandmaster Class 3 title (awarded by the Backgammon Masters Awarding Body (BMAB)), his immediate reaction was to say that he often blunders in this sort of position. That made me feel a little better, as I failed to even consider the best play. The top play is the one Karol Szczerek found, breaking the anchor, and hitting outside!
At first, that looks a little crazy. Hitting gives up the only asset Black has managed to acquire thus far. White already has a direct shot at the two blots in Black’s board. Hitting him gives him another. After Black hits, White will hit one of the blots in Black’s board with almost any 2, 3, 4, or 5! The only rolls that miss are 66, 63, 62, and 61.
A little reflection, however, is all it takes to convince yourself that hitting is best. The key is the 16pt. As things stand, White has a double shot to make it. If White covers, Black will be primed behind a five-point block, and the game will be just about over.
Hitting mixes things up. Often Black will be forced into hitting contest. Frequently, Black will be able to advance his anchor after being hit. Other times, he may land in a backgame. And there is always the chance that White will throw a 6 from the bar. As Karol pointed out, any of these alternatives gives Black more winning opportunities than passively allowing White to complete his block.
5k XG2 Rollout – Unlimited game, no Jacoby, no beavers
Code:
XGID=--a-AAEbD---bBa-abbbb-B---:1:1:1:51:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
Pip count X: 141 O: 157 X-O: 0-0
Cube: 2, X own cube
X to play 51
1. Rollout¹ 22/16* eq:-0.315
Player: 34.44% (G:10.18% B:0.46%)
Opponent: 65.56% (G:22.60% B:1.65%)
Confidence: ±0.006 (-0.321..-0.310) - [100.0%]
2. Rollout¹ 8/3 6/5 eq:-0.390 (-0.075)
Player: 29.46% (G:9.13% B:0.38%)
Opponent: 70.54% (G:16.64% B:0.70%)
Confidence: ±0.006 (-0.396..-0.384) - [0.0%]
3. Rollout¹ 6/5 6/1 eq:-0.404 (-0.088)
Player: 28.76% (G:8.57% B:0.23%)
Opponent: 71.24% (G:15.96% B:0.62%)
Confidence: ±0.005 (-0.409..-0.398) - [0.0%]
4. Rollout¹ 8/3 4/3 eq:-0.422 (-0.107)
Player: 28.19% (G:7.89% B:0.25%)
Opponent: 71.81% (G:15.54% B:0.61%)
Confidence: ±0.005 (-0.427..-0.417) - [0.0%]
5. Rollout¹ 6/1 5/4 eq:-0.427 (-0.112)
Player: 28.29% (G:7.93% B:0.19%)
Opponent: 71.71% (G:16.02% B:0.59%)
Confidence: ±0.005 (-0.432..-0.422) - [0.0%]
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 24097225
Moves: 3-ply, cube decisions: XG Roller
Rollout by Taper_Mike
2015-May-08
eXtreme Gammon Version: 2.10.199.2658
61P-65D-41$-42U-11E-32$-52S-54$-C-61U-51-n-do.xgp
n[H A75 I88 P107 i112] "<=5
n[H A80 I87 P105 i111] "&e
The real Fatboy, Eric Peterson, asked whether slotting the 4pt was the best way to play 54 on roll 8. To see why it is, consider how to play the 5. If you don’t play 13/8, then you have to play 8/3, slotting the 3pt. But if you slot the 3pt with the 5, then the 4 has to come down from the midpoint. Otherwise, you are playing 8/4 8/3, leaving three inside blots. Two down from the midpoint is no option either. That would sacrifice the midpoint. The choice, therefore, is between 13/4 and 13/9 8/3. In this light, slotting the 4pt beats slotting the 3pt on two counts. First, it minimizes blot count at a time when a hitting war is about to erupt. Second, it slots the better point. An XGR++ eval has 13/4 on top by 13 millipoints (i.e., 0.013).
In the practice game where this position arose, I took the tutor’s advice, and made the hit. The bot promptly rolled 62, missing the shots, whereupon I luckboxed into a 21, making both my 5pt and 4pt.
You gotta love this game!
Mike
Last edited by Taper_Mike; 05-11-2015 at 02:01 PM.
05-14-2015
, 03:12 AM
Position ID: /7gDABDsNgkKGA Match ID: QokOAAAAAAAE