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Open your mind
05-14-2015
, 04:47 PM
05-15-2015
, 12:24 PM
Code:
move 1. 16/8 Eq.: +0,700
0,792 0,248 0,012 - 0,208 0,065 0,000 CL +0,778 CF +0,700
move 2. 10/2* Eq.: +0,575 ( -0,125)
0,778 0,202 0,008 - 0,222 0,108 0,002 CL +0,656 CF +0,575
After problem 24 you are inclined to think that a 26 double hit for white will pull the trigger, but this is fallacious. As a matter of fact a 53 for white is more detrimental for black relatively speaking:
white throws 26
after move 1:
Code:
bar/23* Eq.: -0,693
0,210 0,080 0,001 - 0,790 0,263 0,012 CL -0,774 CF -0,693
Code:
bar/23*/17* Eq.: +0,571
0,527 0,423 0,012 - 0,473 0,071 0,002 CL +0,415 CF +0,571
after move 1:
Code:
23/15* Eq.: -0,117
0,444 0,243 0,002 - 0,556 0,089 0,003 CL +0,041 CF -0,117
Code:
white does not enter Eq.: -1,634
It's clear that the difference for the two moves is a lot greater in the case of 53.
removing any gap:
Code:
1. 16/8 Eq.: +0,334
0,713 0,044 0,000 - 0,287 0,073 0,000 CL +0,398 CF +0,334
2. 10/2* Eq.: +0,281 ( -0,051)
0,719 0,044 0,000 - 0,281 0,144 0,000 CL +0,337 CF +0,281
Here with a 1-board:
Code:
1. 10/2* Eq.: +0,499
0,798 0,042 0,000 - 0,202 0,101 0,000 CL +0,538 CF +0,499
2. 16/8 Eq.: +0,475 ( -0,024)
0,782 0,041 0,000 - 0,218 0,087 0,000 CL +0,518 CF +0,475
Conclusion:
It's better not to hit, because of two equally important reasons:
– white has got a 3-board, and not being able to enter after a hit could proof fatal, not in the least because of black's blot on the 8-point
– if white is not on the bar, he not only might leave a second blot, but his homeboard can shrink from 3 points to 2 points
05-16-2015
, 07:57 PM
Here is a trio of related positions. As you go from one problem to the next, the rear checker moves forward 1 pip. Everything else stays the same.
Problem 27a. Black to Play 6-2
White - Pips 52
Black - Pips 48
Unlimited game, no Jacoby, no beavers.
XGID=-FCC--A--A--A------cacccb-:1:1:1:62:0:0:0:0:10
Problem 27b. Black to Play 6-2
White - Pips 52
Black - Pips 47
Unlimited game, no Jacoby, no beavers.
XGID=-FCC--A--A-A-------cacccb-:1:1:1:62:0:0:0:0:10
Problem 27c. Black to Play 6-2
White - Pips 52
Black - Pips 46
Unlimited game, no Jacoby, no beavers.
XGID=-FCC--A--AA--------cacccb-:1:1:1:62:0:0:0:0:10
Mike
Problem 27a. Black to Play 6-2
White - Pips 52
Black - Pips 48
Unlimited game, no Jacoby, no beavers.
XGID=-FCC--A--A--A------cacccb-:1:1:1:62:0:0:0:0:10
Problem 27b. Black to Play 6-2
White - Pips 52
Black - Pips 47
Unlimited game, no Jacoby, no beavers.
XGID=-FCC--A--A-A-------cacccb-:1:1:1:62:0:0:0:0:10
Problem 27c. Black to Play 6-2
White - Pips 52
Black - Pips 46
Unlimited game, no Jacoby, no beavers.
XGID=-FCC--A--AA--------cacccb-:1:1:1:62:0:0:0:0:10
Mike
05-18-2015
, 05:16 PM
Well done by everyone! No one was fooled by these positions. I thought by including three variants, some might err by falling into the trap of thinking there was some quiz factor. There is no quiz factor here. Playing 6/4 with the 2 is correct in all three positions. As the following rollouts show, playing 9/7 is quite a large error. The comments following the rollouts explain some of the reasons why the error is so big.
Problem 27a. Black to Play 6-2
White - Pips 52
Black - Pips 48
Unlimited game, no Jacoby, no beavers.
Problem 27b. Black to Play 6-2
White - Pips 52
Black - Pips 47
Unlimited game, no Jacoby, no beavers.
Problem 27c. Black to Play 6-2
White - Pips 52
Black - Pips 46
Unlimited game, no Jacoby, no beavers.
I wrote the following comments while looking at Problem 27b, but tailored them, for the most part, so that they apply to the other problems as well.
In all three of these positions, White is going have a head start in the bear off. His is not in a no-miss situation, but going first will give him an advantage. His 5pt is the weak spot. The first time he rolls a 5 it becomes a gap. The second time, he can play 6/1, using his “free play.” Because White has to bear off an odd number of checkers, he does not have to bear off two checkers on every roll. He has one “free play” where he can bear off just one, without adding a roll to the total needed to win the game. It is the third 5 that might cause a problem for White. If he still has a checker on his 6pt by then, he will waste half a roll. Otherwise, he is looking pretty good.
In practice, White will often need to use his “free roll” somewhere else, so he will miss more often than the foregoing paragraph describes. Nevertheless, he is still in pretty good shape.
After this roll, Black will still have one checker outside. Barring doublets, he will only bear off one checker on the next turn. White will most likely then bear off two, giving him a total of four checkers off. White will probably miss sooner or later, so Black will often catch up, but the game is still up for grabs. Black needs to be ready to play his doublets efficiently when they come.
So what about 55? Look what happens when he is lucky enough to roll this doublet. If Black plays 9/7 in any of these positions, a subsequent 55 would then bear off one checker less than Black would have gotten after playing 6/4! Scroll back up, and take a look. Moving off the 6pt now avoids the necessity of having to play 6/1 with one of the fives when 55 is the next roll.
Among non-doublets, 43, 42, and 41 stand out. After playing 9/7 on this turn, any one of them would require Black to use the 4 moving in from the 7pt on the next turn, so that he could bear off a checker with the 1, 2, or 3. The resulting position would leave Black with a checker on his 6pt, and one or more gaps on his 4pt and 5pt.
Compare this with how a 4 plays after moving 6/4 on this turn. In all three positions, the 4 would be used to bring home the last checker, 9/5, and then the small number, 1, 2, or 3, would be played bearing off a checker. One of the gaps mentioned above will have been moved to the 6pt, where it is not a gap at all!
A similar thing happens when Black next rolls 62 or 61. After playing 6/4 on this turn, a 6 on the next turn would be played coming home, 9/3, resulting in a position where a “gap” has been moved from the 4pt or 5pt to the 6pt.
I could go on. When the next roll is 53, for instance, Black is usually better off using the 5 to move 9/4 so that he can bear off from the 3pt.
The only real disadvantage to playing 6/4 occurs when Black rolls 21 or 11 on the following turn. With 21, he is stuck using the entire roll to bring home his checker on the 9pt, and cannot bear off any checkers. When he rolls 11, he can only bear off one checker instead of 3.
Mike
Problem 27a. Black to Play 6-2
White - Pips 52
Black - Pips 48
Unlimited game, no Jacoby, no beavers.
Code:
XGID=-FCC--A--A--A------cacccb-:1:1:1:62:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
Pip count X: 48 O: 52 X-O: 0-0
Cube: 2, X own cube
X to play 62
1. Rollout¹ 12/4 eq:-0.0366
Player: 41.69% (G:0.00% B:0.00%)
Opponent: 58.31% (G:0.00% B:0.00%)
Confidence: ±0.0014 (-0.0380..-0.0351) - [100.0%]
2. Rollout¹ 12/6 9/7 eq:-0.1433 (-0.1067)
Player: 37.26% (G:0.00% B:0.00%)
Opponent: 62.74% (G:0.00% B:0.00%)
Confidence: ±0.0013 (-0.1446..-0.1419) - [0.0%]
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 5613244
Moves: 3-ply, cube decisions: XG Roller
Rollout by Taper_Mike
2015-May-16
eXtreme Gammon Version: 2.10.199.2658
OpenYourMind.027a-tm.xgp
Problem 27b. Black to Play 6-2
White - Pips 52
Black - Pips 47
Unlimited game, no Jacoby, no beavers.
Code:
XGID=-FCC--A--A-A-------cacccb-:1:1:1:62:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
Pip count X: 47 O: 52 X-O: 0-0
Cube: 2, X own cube
X to play 62
1. Rollout¹ 11/5 6/4 eq:+0.1062
Player: 47.74% (G:0.00% B:0.00%)
Opponent: 52.26% (G:0.00% B:0.00%)
Confidence: ±0.0015 (+0.1047..+0.1078) - [100.0%]
2. Rollout¹ 11/5 9/7 eq:-0.0039 (-0.1101)
Player: 43.07% (G:0.00% B:0.00%)
Opponent: 56.93% (G:0.00% B:0.00%)
Confidence: ±0.0015 (-0.0054..-0.0025) - [0.0%]
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 5613244
Moves: 3-ply, cube decisions: XG Roller
Rollout by Taper_Mike
2015-May-16
eXtreme Gammon Version: 2.10.199.2658
OpenYourMind.027b-tm.xgp
Problem 27c. Black to Play 6-2
White - Pips 52
Black - Pips 46
Unlimited game, no Jacoby, no beavers.
Code:
XGID=-FCC--A--AA--------cacccb-:1:1:1:62:0:0:0:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
Pip count X: 46 O: 52 X-O: 0-0
Cube: 2, X own cube
X to play 62
1. Rollout¹ 10/4 6/4 eq:+0.1461
Player: 49.31% (G:0.00% B:0.00%)
Opponent: 50.69% (G:0.00% B:0.00%)
Confidence: ±0.0016 (+0.1446..+0.1477) - [100.0%]
2. Rollout¹ 10/4 9/7 eq:+0.0761 (-0.0700)
Player: 46.30% (G:0.00% B:0.00%)
Opponent: 53.70% (G:0.00% B:0.00%)
Confidence: ±0.0015 (+0.0746..+0.0776) - [0.0%]
¹ 5184 Games rolled with Variance Reduction.
Dice Seed: 5613244
Moves: 3-ply, cube decisions: XG Roller
Rollout by Taper_Mike
2015-May-16
eXtreme Gammon Version: 2.10.199.2658
OpenYourMind.027c-tm.xgp
I wrote the following comments while looking at Problem 27b, but tailored them, for the most part, so that they apply to the other problems as well.
In all three of these positions, White is going have a head start in the bear off. His is not in a no-miss situation, but going first will give him an advantage. His 5pt is the weak spot. The first time he rolls a 5 it becomes a gap. The second time, he can play 6/1, using his “free play.” Because White has to bear off an odd number of checkers, he does not have to bear off two checkers on every roll. He has one “free play” where he can bear off just one, without adding a roll to the total needed to win the game. It is the third 5 that might cause a problem for White. If he still has a checker on his 6pt by then, he will waste half a roll. Otherwise, he is looking pretty good.
In practice, White will often need to use his “free roll” somewhere else, so he will miss more often than the foregoing paragraph describes. Nevertheless, he is still in pretty good shape.
After this roll, Black will still have one checker outside. Barring doublets, he will only bear off one checker on the next turn. White will most likely then bear off two, giving him a total of four checkers off. White will probably miss sooner or later, so Black will often catch up, but the game is still up for grabs. Black needs to be ready to play his doublets efficiently when they come.
So what about 55? Look what happens when he is lucky enough to roll this doublet. If Black plays 9/7 in any of these positions, a subsequent 55 would then bear off one checker less than Black would have gotten after playing 6/4! Scroll back up, and take a look. Moving off the 6pt now avoids the necessity of having to play 6/1 with one of the fives when 55 is the next roll.
Among non-doublets, 43, 42, and 41 stand out. After playing 9/7 on this turn, any one of them would require Black to use the 4 moving in from the 7pt on the next turn, so that he could bear off a checker with the 1, 2, or 3. The resulting position would leave Black with a checker on his 6pt, and one or more gaps on his 4pt and 5pt.
Compare this with how a 4 plays after moving 6/4 on this turn. In all three positions, the 4 would be used to bring home the last checker, 9/5, and then the small number, 1, 2, or 3, would be played bearing off a checker. One of the gaps mentioned above will have been moved to the 6pt, where it is not a gap at all!
A similar thing happens when Black next rolls 62 or 61. After playing 6/4 on this turn, a 6 on the next turn would be played coming home, 9/3, resulting in a position where a “gap” has been moved from the 4pt or 5pt to the 6pt.
I could go on. When the next roll is 53, for instance, Black is usually better off using the 5 to move 9/4 so that he can bear off from the 3pt.
The only real disadvantage to playing 6/4 occurs when Black rolls 21 or 11 on the following turn. With 21, he is stuck using the entire roll to bring home his checker on the 9pt, and cannot bear off any checkers. When he rolls 11, he can only bear off one checker instead of 3.
Mike
Last edited by Taper_Mike; 05-18-2015 at 05:30 PM.
05-20-2015
, 02:52 AM
Position ID: mK+FCCSwuwcBSA Match ID: cAkJAAAAAAAE
05-20-2015
, 12:22 PM
Grunch.
B/23 13/9* 8/6
I prefer that to making the 4-pt now since there's a decent chance I will be able to make a 5-prime anyway.
Edit: Damn, was too anxious to answer, didn't even consider B/23 7/3*/1*.
B/23 13/9* 8/6
I prefer that to making the 4-pt now since there's a decent chance I will be able to make a 5-prime anyway.
Edit: Damn, was too anxious to answer, didn't even consider B/23 7/3*/1*.
Last edited by uberkuber; 05-20-2015 at 12:25 PM.
Reason: Damn!
05-20-2015
, 03:17 PM
05-21-2015
, 10:40 AM
Code:
1. bar/23 7/3*/1* Eq.: +0,888
0,671 0,407 0,102 - 0,329 0,093 0,006 CL +0,752 CF +0,888
2. bar/23 13/9* 7/5 Eq.: +0,646 ( -0,243)
0,638 0,280 0,039 - 0,362 0,096 0,005 CL +0,495 CF +0,646
3. bar/23 8/4 6/4 Eq.: +0,621 ( -0,267)
0,636 0,245 0,020 - 0,364 0,102 0,005 CL +0,430 CF +0,621
Also in case the number of blots is reduced, it is not wrong to blitz play.
Code:
1. bar/23 7/3*/1* Eq.: +0,328
0,553 0,257 0,022 - 0,447 0,131 0,008 CL +0,245 CF +0,328
2. bar/23 13/9*/7 Eq.: +0,273 ( -0,055)
0,559 0,184 0,011 - 0,441 0,116 0,005 CL +0,192 CF +0,273
Code:
1. bar/23 13/9*/7 Eq.: +0,680
0,651 0,245 0,020 - 0,349 0,090 0,003 CL +0,472 CF +0,680
2. bar/23 7/3*/1* Eq.: +0,645 ( -0,035)
0,631 0,307 0,029 - 0,369 0,113 0,007 CL +0,479 CF +0,645