As a matter of fact this problem was meant as a dummy, so the QF caused confusion instead of guidance. The obvious move was meant to be 18/17*/13.
White - Pips 174
Black - Pips 110
Code:
1. 18/17*/13 Eq.: +0,561
0,662 0,376 0,018 - 0,338 0,041 0,001 CL +0,676 CF +0,561
2. 11/10*/6 Eq.: +0,508 ( -0,053)
0,658 0,340 0,015 - 0,342 0,046 0,001 CL +0,625 CF +0,508
3. 18/13 Eq.: +0,399 ( -0,162)
0,661 0,233 0,009 - 0,339 0,047 0,001 CL +0,517 CF +0,399
Contrary to our expectations, getting a nice 3-point board for white doesn't change the relative value of hitting an awful lot:
White - Pips 180
Black - Pips 110
Code:
1. 18/17*/13 Eq.: +0,268
0,560 0,351 0,016 - 0,440 0,063 0,001 CL +0,421 CF +0,268
2. 18/13 Eq.: +0,131 ( -0,137)
0,560 0,236 0,009 - 0,440 0,070 0,002 CL +0,293 CF +0,131
3. 11/10*/6 Eq.: +0,131 ( -0,137)
0,533 0,305 0,013 - 0,467 0,082 0,002 CL +0,300 CF +0,131
See how 11/10*/6 has decreased in value. This is because one reason for hitting is to keep white from building an extra homeboard point, which will be more powerful with a straight homeboard (this in reply to Kamba's question, though I am still an aspiring guru). The other reason being to generate more gammons, which is in Taper_Mike's pipeline.
Reducing the pipdifference by moving the 1-point to the 13-point leads to a strong relative value decrease:
White - Pips 174
Black - Pips 134
Code:
1. 18/17*/13 Eq.: +0,541
0,702 0,267 0,013 - 0,298 0,040 0,001 CL +0,643 CF +0,541
2. 18/13 Eq.: +0,498 ( -0,043)
0,726 0,177 0,008 - 0,274 0,045 0,001 CL +0,592 CF +0,498
The reason being that white has a worse timing for a backgame, which means that white sooner will have to give up a backgame point before black is compelled to leave a shot. Besides again, because of a smaller pipdifference less gammons will be generated.
Creating a 4-point block by removing the 1-point makes hitting rather arbitrary:
White - Pips 174
Black - Pips 124
Code:
1. 11/10*/6 Eq.: +0,591
0,712 0,286 0,014 - 0,288 0,033 0,000 CL +0,689 CF +0,591
2. 18/14 11/10* Eq.: +0,570 ( -0,021)
0,712 0,268 0,013 - 0,288 0,035 0,000 CL +0,669 CF +0,570
3. 11/10* 11/7 Eq.: +0,568 ( -0,024)
0,705 0,281 0,015 - 0,295 0,037 0,000 CL +0,669 CF +0,568
4. 18/17*/13 Eq.: +0,567 (-0,024)
0,696 0,298 0,015 - 0,304 0,034 0,000 CL +0,671 CF +0,567
5. 18/13 Eq.: +0,542 ( -0,049)
0,733 0,190 0,008 - 0,267 0,030 0,000 CL +0,634 CF +0,542
This in spite of a somewhat better backgame timing than in the previous position. Now there is a greater probability that white has to give up his 4-point instead of his 2-point, and black will have more shot chances in case this happens.
Here is the original problem, with the 4-point moved to the 3-point:
White - Pips 176
Black - Pips 112
Code:
1. 18/17*/13 Eq.: +0,445
0,615 0,358 0,026 - 0,385 0,039 0,001 CL +0,576 CF +0,445
2. 11/10*/6 Eq.: +0,409 ( -0,036)
0,613 0,331 0,022 - 0,387 0,038 0,000 CL +0,541 CF +0,409
3. 18/13 Eq.: +0,405 ( -0,040)
0,652 0,250 0,012 - 0,348 0,039 0,001 CL +0,526 CF +0,405
In the original problem hitting has an advantage of 0.16 , and now it is 0.04. That is ofcourse because a 23 backgame needs a better timing than a 24 backgame, and as the pipdifference is about equal this shows imo that the extra gammons are a minor factor.
A pipdifference of 40 seems to be a hitting threshold with this type of backgame:
White - Pips 143
Black - Pips 110
Code:
1. 18/13 Eq.: +0,398
0,691 0,167 0,007 - 0,309 0,054 0,001 CL +0,500 CF +0,398
2. 18/17*/13 Eq.: +0,354 ( -0,044)
0,644 0,237 0,008 - 0,356 0,054 0,001 CL +0,479 CF +0,354
White - Pips 143
Black - Pips 120
Code:
1. 18/17*/13 Eq.: +0,730
0,783 0,253 0,011 - 0,217 0,025 0,001 CL +0,804 CF +0,730
2. 18/13 Eq.: +0,714 ( -0,016)
0,820 0,147 0,004 - 0,180 0,017 0,000 CL +0,775 CF +0,714
To make matters very simple I propose the following gross pipdifferences for the different types of backgames (and I hope I will be corrected). Don't hit below the
given pipdifference, in case the front backgame point is 5:
30, if 4:
40, if 3:
60, if 2:
90.