Code:
23/18 6/3 Eq.: +0,996
0,683 0,376 0,065 - 0,317 0,047 0,002 CL +0,758 CF +0,996
12/7 6/3 Eq.: +0,958 ( -0,038)
0,670 0,376 0,066 - 0,330 0,050 0,001 CL +0,731 CF +0,958
8/3 7/4* Eq.: +0,829 ( -0,168)
0,651 0,396 0,084 - 0,349 0,084 0,007 CL +0,692 CF +0,829
This is meant to be an obvious=obvious problem, though you are free to disagree.
Because this is a backgame position I have done 1296 trials, like with most positions in this post. There is barely any difference between 23/18 and 12/7, but as a general rule (e.g. 44,66) it is wise to play from the back (see Modern Backgammon, Robertie). The cubeless difference between playing safe and hitting loose is relatively small, so it is not so easy to judge by the naked eye.
Ofcourse it gets worse with a better 3-board. 22w to 20:
Code:
23/18 6/3 Eq.: +0,893
0,645 0,362 0,065 - 0,355 0,054 0,002 CL +0,660 CF +0,893
8/3 7/4* Eq.: +0,676 ( -0,217)
0,597 0,364 0,082 - 0,403 0,098 0,008 CL +0,535 CF +0,676
Here the cubeless difference is 0.12, which supports and facilitates an analysis of the former position.
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Position after 23/18 6/3:
As a matter of fact, if black plays safe and white subsequently throws a 4, he is pretty much out of the grave:
White has played 64:
Code:
Cube analysis
Rollout cubeless equity +0,539
Cubeful equities:
1. Double, take +0,820
2. Double, pass +1,000 ( +0,180)
3. No double +0,794 ( -0,026)
Proper cube action: Double, take
White has played 54:
Code:
Cube analysis
Rollout cubeless equity +0,480
Cubeful equities:
1. Double, take +0,695
2. Double, pass +1,000 ( +0,305)
3. No double +0,693 ( -0,002)
Proper cube action: Double, take
The position was initially too good to double, but black has barely a double in these cases.
Whereas, if white doesn't throw a 4, the position will still be too good to double:
White has played 51:
Code:
Cube analysis
Rollout cubeless equity +0,790
Cubeful equities:
1. Double, pass +1,000
2. Double, take +1,376 ( +0,376)
3. No double +0,991 ( -0,009)
Proper cube action: Double, pass
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This brings up the question how bad it is if, after 7/4*, black's blot is hit. White has played 41 after black's 8/3 7/4*, and black is on the bar:
Code:
Cube analysis
Rollout cubeless equity +0,266
Cubeful equities:
1. No double +0,333
2. Double, pass +1,000 ( +0,667)
3. Double, take +0,195 ( -0,138)
Proper cube action: No double, take
Well, very bad. Black had an equity of almost 1,0 in the original position, and this had dropped to 0,27. White, having the better board, gets a chance to start a whole new game from the back.
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By the way, black's many blots are of no concern. 13 to 12:
Code:
23/18 6/3 Eq.: +1,004
0,682 0,374 0,065 - 0,318 0,044 0,001 CL +0,759 CF +1,004
8/3 7/4* Eq.: +0,827 ( -0,177)
0,645 0,388 0,081 - 0,355 0,077 0,004 CL +0,677 CF +0,827
With three blots on the bar a white backlash is unlikely.
The 7-point seems to be of strategic value:
Black to Play 5-4
Code:
8/4* 8/3 Eq.: +0,859
0,664 0,399 0,083 - 0,336 0,082 0,007 CL +0,721 CF +0,859
23/18 7/3 Eq.: +0,845 ( -0,014)
0,639 0,350 0,061 - 0,361 0,061 0,002 CL +0,625 CF +0,845
It is important for priming purposes, and blocking 6s, as is made clear by the drop in relative equity difference when moving the 1w-point to 2:
Black to Play 5-4
Code:
23/18 7/3 Eq.: +0,769
0,627 0,335 0,032 - 0,373 0,075 0,004 CL +0,541 CF +0,769
8/4* 8/3 Eq.: +0,685 ( -0,085)
0,622 0,369 0,043 - 0,378 0,097 0,008 CL +0,550 CF +0,685
The original equity difference is 0,17.
The 6-point pile makes hitting loose also less desirable. Moving the pile to the 8-point.
Code:
23/20 8/3 Eq.: +1,008
0,692 0,364 0,060 - 0,308 0,050 0,002 CL +0,756 CF +1,008
8/3 7/4* Eq.: +0,931 ( -0,078)
0,688 0,405 0,078 - 0,312 0,075 0,006 CL +0,778 CF +0,931
23/18 6/3 Eq.: +0,896 ( -0,112)
0,665 0,327 0,047 - 0,335 0,060 0,002 CL +0,642 CF +0,896
There is little cubeless difference, so hitting loose has moved up. If everything goes well, priming gets a lot easier now.
Another factor is that white still has an opportunity to make the 5w-point in case black has managed to make the 3 and 4-points. See the following position:
Black to Play 4-2
Code:
13/9 6/4 Eq.: +1,042
0,701 0,407 0,076 - 0,299 0,048 0,002 CL +0,836 CF +1,042
8/4 7/5* Eq.: +0,960 ( -0,082)
0,687 0,429 0,091 - 0,313 0,070 0,006 CL +0,817 CF +0,960
With black's position hitting loose is only (slightly) profitable when white has no homeboard, which I think is pretty unthinkable at this stage:
Code:
8/3 7/4* Eq.: +1,055
0,672 0,445 0,109 - 0,328 0,048 0,002 CL +0,849 CF +1,055
23/18 6/3 Eq.: +0,993 ( -0,062)
0,655 0,409 0,084 - 0,345 0,039 0,001 CL +0,764 CF +0,993
Or, when there is more ammo and a better spread of builders:
Code:
8/3 7/4* Eq.: +1,216
0,758 0,470 0,095 - 0,242 0,044 0,002 CL +1,035 CF +1,216
23/20 8/3 Eq.: +1,136 ( -0,080)
0,735 0,411 0,068 - 0,265 0,035 0,001 CL +0,913 CF +1,136
If white hits back, he can easily do so in return, and he will even be contented if he manages to create a 4-prime.
Conclusion:
In a situation like this black should never hit loose, unless he has a good spread of builders.