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    1. 13/10(4)                     Eq.:  -0,165 
       0,450 0,083 0,001 - 0,550 0,103 0,003 CL  -0,121 CF  -0,165 
     
    2. 13/7(2)                      Eq.:  -0,337 ( -0,173) 
       0,416 0,082 0,001 - 0,584 0,134 0,004 CL  -0,224 CF  -0,337

Moving the back checker from the 24-point to the 22-point actually increases the value of 13/10(4):

Code:

    1. 13/10(4)                     Eq.:  +0,087
       0,521 0,097 0,002 - 0,479 0,103 0,002 CL  +0,036 CF  +0,087
    
    2. 13/7(2)                      Eq.:  -0,116 ( -0,202)
       0,484 0,110 0,002 - 0,516 0,153 0,005 CL  -0,077 CF  -0,116

This seemingly suggests that white's hitting on the 1-point is worse than semi-killing a checker on the 1-point, though four of the six 6's make a point on black's head. The reason is perhaps that white's 3's from the 19-point have become more valuable, whereas those 3's could be used to move from the 4-point to the 7-point in case of 13/10(4), with other words there is an unwelcome duplication.

Moving a white checker from the 19-point decreases the value of 13/10(4):

Code:

    1. 13/10(4)                     Eq.:  -0,336
       0,407 0,083 0,001 - 0,593 0,113 0,003 CL  -0,218 CF  -0,336
    
    2. 13/7(2)                      Eq.:  -0,448 ( -0,112)
       0,384 0,080 0,001 - 0,616 0,135 0,004 CL  -0,290 CF  -0,448

The reason is that it gives to white the opportunity to play the 6 without having to semi-kill.

Quote

03-14-2015 , 10:54 AM

#27

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,091

Moving the back checker from 24-pt to 22-pt favors even more 13/10 (4), maybe because now Black 6s are not all killed (the double-edge sword mentioned by TaperMike) since he could move the back checker before having to dump checkers from his 8-pt.

Even with 6-6, he could at least safety his straggler before having to abandon the 8-pt.

Quote

03-14-2015 , 04:31 PM

#28

yogiman

adept

Join Date: Jun 2012 Posts: 784

A very good point, but maybe it is a half-truth, viewing the result when moving the back checker to the 23-point:

Code:

    1. 13/10(4)                     Eq.:  +0,075
       0,523 0,085 0,001 - 0,477 0,092 0,002 CL  +0,039 CF  +0,075
     
     
    2. 13/7(2)                      Eq.:  -0,091 ( -0,165)
       0,489 0,088 0,001 - 0,511 0,137 0,004 CL  -0,074 CF  -0,091

For a clear surveyance:
back checker____________equity difference
24-point________________-.173
23-point________________-.165
22-point________________-.202

You would expect that the equity difference for the 22 and 23-point should be about the same. The relative value of 13/7(4) however has decreased a little bit, instead of increased. So my hypothesis is that the 23-point has the benefit of playable 6's from the back, while the 24-point has the benefit of a possible shot on a white blot, and both eventualities cancel each other. So you are not really wrong, but me possibly neither in relation to my argument for the 22-point.

Quote

03-14-2015 , 09:06 PM

#29

Robertie

old hand

Join Date: May 2004 Posts: 1,954

The 23-point is better than the 22-point.

From either point Black has 6s to escape. His 5s also play well in either case. However, the difference arrives when White rolls. If Black is on the 22-point, White's good rolls are very good, both making a 5-prime and putting Black on the bar. If Black is on the 23-point, White can point on Black or make a 5-prime, but not both.

Quote

03-15-2015 , 04:11 PM

#30

yogiman

adept

Join Date: Jun 2012 Posts: 784

Position ID: sM8OAyCYM/ggDA Match ID: UQkKAAAAAAAE

White - Pips 133

Black - Pips 169
Black to Play 4-2
Created with www.BGdiagram.com

Quote

03-15-2015 , 06:34 PM

#31

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,091

OTB I'd probably play 13/9 13/11.
13/7 would be my alternative.

Quote

03-15-2015 , 09:08 PM

#32

Robertie

old hand

Join Date: May 2004 Posts: 1,954

Nice problem. 22/18 as the 4 is out because it activates White's builders on his 6-point and 9-points. So our choice is between 13/9 13/11 and 18/14 13/11.

13/9 13/11 creates lots of builders for the 5-point and bar-point at the cost of a couple of blots. The problem then is the blot on the 18-point. White's going to hit that blot next turn with most of his 6s and 2s, after which Black won't be building anything for a while.

So 18/14 13/11 wins by default, even though it doesn't do all that much.

Quote

03-16-2015 , 05:41 PM

#33

yogiman

adept

Join Date: Jun 2012 Posts: 784

For many intermediate players the obvious move would be 22/18 13/11. But that's a big mistake.

[/CENTER]

Code:

    1. 18/14 13/11                  Eq.:  -0,095
       0,419 0,088 0,004 - 0,581 0,171 0,007 CL  -0,248 CF  -0,095
      
    2. 13/11 13/9                   Eq.:  -0,175 ( -0,080)
       0,401 0,087 0,004 - 0,599 0,201 0,009 CL  -0,319 CF  -0,175
      
    3. 22/18 13/11                  Eq.:  -0,281 ( -0,186)
       0,370 0,073 0,003 - 0,630 0,222 0,007 CL  -0,413 CF  -0,281

With thanks to the moderator for leaving room for some additional commentary.

The following variations show how the relative value of 13/11 13/9 can be somewhat decreased without altering the pipcount drastically.

Removing the builders from the white's 16-point:
[CENTER]

Code:

      
    1. 13/11 13/9                   Eq.:  -0,004
       0,450 0,100 0,004 - 0,550 0,167 0,007 CL  -0,171 CF  -0,004
      
    2. 18/14 13/11                  Eq.:  -0,019 ( -0,015)
       0,442 0,095 0,003 - 0,558 0,158 0,006 CL  -0,182 CF  -0,019
     
    3. 22/18 13/11                  Eq.:  -0,043 ( -0,039)
       0,438 0,094 0,004 - 0,562 0,173 0,005 CL  -0,204 CF  -0,043

This indicates the importance of maintaining the defensive point in the original position.

Getting two checkers from the 13 to the 11-point:

Code:

    1. 18/14 13/11                  Eq.:  -0,034
       0,437 0,094 0,004 - 0,563 0,160 0,007 CL  -0,195 CF  -0,034
     
    2. 13/9 11/9                    Eq.:  -0,086 ( -0,052)
       0,423 0,097 0,004 - 0,577 0,177 0,007 CL  -0,238 CF  -0,086

    3. 22/18 13/11                  Eq.:  -0,143 ( -0,110)
       0,414 0,092 0,004 - 0,586 0,212 0,008 CL  -0,296 CF  -0,14

This seems to indicate imo that containment of white's back checker is an issue here.

Giving an extra checker to white's 12-point:

Code:

    1. 18/14 13/11                  Eq.:  -0,197
       0,380 0,076 0,003 - 0,620 0,165 0,007 CL  -0,333 CF  -0,197
      
    2. 22/18 13/11                  Eq.:  -0,231 ( -0,034)
       0,378 0,076 0,003 - 0,622 0,196 0,007 CL  -0,368 CF  -0,231
     
    3. 13/11 13/9                   Eq.:  -0,251 ( -0,054)
       0,370 0,076 0,003 - 0,630 0,191 0,009 CL  -0,382 CF  -0,251

This shows the importance of maintaining outer board control after an eventual hit.

Conclusion:
in addition to what has been said, 18/14 13/11 is far superior because it helps contain white's back checker, could lead to a sacrifice of white's important control point, and leaves the defensive point intact.

Quote

03-17-2015 , 12:57 AM

#34

yogiman

adept

Join Date: Jun 2012 Posts: 784

Quote:

The following variations show how the relative value of 13/11 13/9 can be somewhat decreased without altering the pipcount drastically.

A big mistake of myself. I am referring ofcourse to 13/11 18/14. I don't seem to be really labour proof.

Quote

03-18-2015 , 03:13 AM

#35

yogiman

adept

Join Date: Jun 2012 Posts: 784

Position ID: bnNDAFBsXQgAPg Match ID: UYkSAAAAAAAE

White - Pips 112

Black - Pips 175
Black to Play 5-4
Created with www.BGdiagram.com

Quote

03-18-2015 , 03:55 AM

#36

Kamba

enthusiast

Join Date: Feb 2015 Posts: 93

Eeeek! I would probably play 24/20 6/1.
Moving off the 11 or 7 would seem to leave me in urgent need of throwing another 4 to get a checker out of jail. So 24/20 would be my definite first move. Rather 6/1 for me than 24/15 as it seems safer to have two of his checkers on the bar. Either way, I don't rate black's chances here.

Quote

03-18-2015 , 05:48 AM

#37

bleep69

grinder

Join Date: Sep 2008 Posts: 483

I'm also liking 24/20 6/1* the more obvious move of 6/1* 5/1 leaves us way too stuck. In fact the move I'm a fan off actually looks to be the obvious one, which makes me suspicious, but I'll stick to it.

Quote

03-18-2015 , 02:30 PM

#38

Fllecha

journeyman

Join Date: Mar 2010 Posts: 321

I escape one back man in a shot. Here the problem imo is to estricate the back men to avoid crunch position

Quote

03-18-2015 , 11:42 PM

#39

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,091

I also like 24/20 6/1* before 24/15.

Quote

03-19-2015 , 06:26 AM

#40

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

On the surface, running out seems safer than hitting inside. When you count the shots, however, hitting inside turns out to be safer. As far as losing gammons is concerned, Black is losing a ton of them already. That is true whether he hits inside or not. The best way not to lose a gammon is to win the game. So go ahead and hit! That should win more games and win more gammons.

I will be stunned if 24/20 is not part of the play.

24/20, 6/1*

Mike

Quote

03-20-2015 , 10:04 AM

#41

yogiman

adept

Join Date: Jun 2012 Posts: 784

Apologizes for the long delay. I moved the pc and had no connection for a couple of days.

In the context of the previous problems and with 83,34% QF this problem is not so very tough. As Taper_Mike remarked, there is little loss in playing "bold".

Code:

    1.24/20 6/1*                   Eq.:  -0,691
       0,333 0,084 0,004 - 0,667 0,437 0,127 CL  -0,811 CF  -0,691
     
    2. 24/15                        Eq.:  -0,849 ( -0,158)
       0,304 0,067 0,003 - 0,696 0,482 0,156 CL  -0,959 CF  -0,849
      
    3. 6/1* 5/1                     Eq.:  -0,980 ( -0,288)
       0,209 0,061 0,003 - 0,791 0,465 0,070 CL  -1,052 CF  -0,980

Quote

03-20-2015 , 10:25 AM

#42

yogiman

adept

Join Date: Jun 2012 Posts: 784

Without direct cover for the 5-point however, 24/15 is a lot better.

Code:

1. 24/15                        Eq.:  -0,629
       0,345 0,074 0,003 - 0,655 0,428 0,095 CL  -0,756 CF  -0,629
     
2. 24/20 6/1*                   Eq.:  -0,750 ( -0,121)
       0,312 0,065 0,003 - 0,688 0,447 0,109 CL  -0,865 CF  -0,750
     
3. 24/20 13/8                   Eq.:  -0,755 ( -0,125)
       0,329 0,074 0,004 - 0,671 0,464 0,153 CL  -0,880 CF  -0,755

Quote

03-21-2015 , 11:36 AM

#43

yogiman

adept

Join Date: Jun 2012 Posts: 784

Position ID: O58DAIFtjADIIw Match ID: UQkPAAAAAAAE

White - Pips 66

Black - Pips 166
Black to Play 6-3
Created with www.BGdiagram.com

Quote

03-21-2015 , 02:34 PM

#44

uberkuber

veteran

Join Date: Jul 2009 Posts: 3,091

B/16.
I surely don't want to kill a checker on the 3-pt so I eliminate 9/3. Between 22/16 and 20/14, it looks like the former offers a better coverage.

Quote

03-21-2015 , 04:48 PM

#45

Taper_Mike

adept

Join Date: Sep 2009 Posts: 1,030

I'll go with bar/16 as well. I don't think 9/3 saves enough extra gammons to make it a serious candidate. As in the previous position, Black is losing a fair amount of gammons whether he is hit or not.

More importantly, bar/16 should win more games than 9/3. It buys a direct shot on Black's next turn much more often than 9/3 does. After 9/3, Black will often get only a fly shot next turn, with perhaps a direct on the turn after that.

Note also that Black's gammon price is 0.5 in an unlimited game. If Black takes a risk that converts a lost game into a win, but which also risks losing more gammons, the break-even point comes when he loses two extra gammons for each extra win. Each extra gammon loss costs half as much as each additional regular win gains.

If I am right, therefore, that bar/16 wins more games, and that 9/3 loses fewer gammons, then the cost of leaving a blot on the 9pt is less than it might first appear.

Mike

Quote

03-21-2015 , 05:40 PM

#46

Robertie

old hand

Join Date: May 2004 Posts: 1,954

Over the board, Bar/16 looks automatic. I don't think I would waste more than a second or two on the play.

Bar/22 9/3 kills a checker and gives up the outfield. The sequence: White hits and Black fans occurs less than 25% of the time. The rest of the time I'm happy I made the obvious move. I'm losing a lot of gammons from here after any play, so let's assume we won't get hit next turn and play to win.

Quote

03-21-2015 , 07:35 PM

#47

bleep69

grinder

Join Date: Sep 2008 Posts: 483

Annoyingly, on mobile the diagram is not showing up for me. Glad you are back in action Yogi.

I agree with Robertie.

Quote

03-22-2015 , 06:19 AM

#48

yogiman

adept

Join Date: Jun 2012 Posts: 784

White - Pips 66

Black - Pips 166

Code:

    1. bar/16                       Eq.:  -1,131 
       0,215 0,000 0,000 - 0,785 0,612 0,025 CL  -1,207 CF  -1,131 
      
    2. bar/22 9/3                   Eq.:  -1,240 ( -0,110) 
       0,161 0,000 0,000 - 0,839 0,605 0,013 CL  -1,295 CF  -1,240 
      
    3. bar/22 20/14                 Eq.:  -1,257 ( -0,126) 
       0,179 0,000 0,000 - 0,821 0,652 0,023 CL  -1,318 CF  -1,257

bar/16 is even far better when the outfield checker does not need to be killed:

White - Pips 66

Black - Pips 167

Code:

    1. bar/16                       Eq.:  -1,135
       0,218 0,000 0,000 - 0,782 0,612 0,033 CL  -1,210 CF  -1,135
     
    2. bar/22 10/4                  Eq.:  -1,219 ( -0,084)
       0,184 0,000 0,000 - 0,816 0,633 0,016 CL  -1,282 CF  -1,219
     
    3. bar/22 20/14                 Eq.:  -1,274 ( -0,138)
       0,179 0,000 0,000 - 0,821 0,666 0,028 CL  -1,335 CF  -1,274

The following two positions show how the relative value of bar/16 decreases, when the gammon threat is diminished.

Killing one checker:

White - Pips 66

Black - Pips 147

Code:

    1. bar/16                       Eq.:  -1,089
       0,194 0,000 0,000 - 0,806 0,531 0,015 CL  -1,157 CF  -1,089
    
    2. bar/22 9/3                   Eq.:  -1,147 ( -0,058)
       0,144 0,000 0,000 - 0,856 0,478 0,007 CL  -1,197 CF  -1,147
      
    3. bar/22 20/14                 Eq.:  -1,191 ( -0,102)
       0,158 0,000 0,000 - 0,842 0,547 0,014 CL  -1,246 CF  -1,191

Killing two checkers:

White - Pips 66

Black - Pips 128

Code:

    1. bar/16                       Eq.:  -0,987
       0,177 0,000 0,000 - 0,823 0,396 0,009 CL  -1,052 CF  -0,987
      
    2. bar/22 9/3                   Eq.:  -0,989 ( -0,002)
       0,130 0,000 0,000 - 0,870 0,293 0,002 CL  -1,035 CF  -0,989
    
    3. bar/22 20/14                 Eq.:  -1,068 ( -0,081)
       0,139 0,000 0,000 - 0,861 0,389 0,007 CL  -1,117 CF  -1,068

It should be mentioned that by killing checkers black's containment power is also diminished, which would be in favour of 9/3. As the equity difference between the two non-killing moves bar/16 and bar/22 20/14 changes just slightly, I am inclined to conclude that this factor is of lesser significance.

Quote

03-23-2015 , 07:19 AM

#49

yogiman

adept

Join Date: Jun 2012 Posts: 784

Position ID: jGs2gwCYEQbsTA Match ID: cIkSAAAAAAAE

White - Pips 133

Black - Pips 229
Black to Play 5-4
Created with www.BGdiagram.com

Quote

03-23-2015 , 07:42 AM

#50

Kamba

enthusiast

Join Date: Feb 2015 Posts: 93

OTB I would play bar/16 without too much thought.

Basically just trying to waste a bit of time until he moves off my 7 point and hoping to hit once he has collapsed a bit. I think its still a bit too early to start trying to fill my home by moving 9/5 with no spare checkers close behind, so happy to get hit again now and start moving toward home when he's squashed up a bit (which should be very soon i would guess).

I actually rate black's chances here. When I'm in the position white is in here, I always seem to get whipped!

Quote

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