In my first post regarding position 129 I ended with a couple of questions, lets explore the answers
The first question was what to play if the hit on the five has to come from the 8 point instead of the 6 point. This hit risk getting two blots hit. Even though the blot on the 8 is fairly safe on the first roll—only 53 will hit both blots—the odds are that if red gets hit on their 5 point again that blot on the 8 will stay there another roll giving blue another shot at it. (If red is hit there are only 9 rolls that cover the blot, red must have a 5 to cover but 56 does not work because red would have to come in with the 5). Here is the position
Pip counts: Blue 158, Red 180
Position ID: 4PPgASHgM/iAUA Match ID: cIkVAAAAAAAA
#  Ply  Move  Equity  

1  R  bar/20 8/5*  0.105  


2  R  bar/20 6/3  0.146 ( 0.041)  


3  R  bar/20 13/10  0.169 ( 0.063)  


4  R  bar/20 24/21  0.180 ( 0.075)  

So the loose hit on the 5 point is still the way to go, but the equity difference between this and the second best is much less than it was in the original scenario. The other point I find interesting here is that the safer play of bar/20 24/21 is in fourth place. All of the better plays leaves blue more shots. This is one of those positions where it seems that having more checkers back is better because red needs time to build a blockade and establish a better home board. Once again if we look at the criteria given on page 69 more checkers back leads to bolder play.
Suppose red rolls 41 instead of 51 in the above position. Then the question is should red use the 1 to hit or to make the 20? If red does hit they will have a good chance of making the 20 the next time.
#  Ply  Move  Equity  

1  R  bar/20  0.132  


•  2  R  bar/21 6/5*  0.196 ( 0.064)  


3  R  bar/21 24/23  0.366 ( 0.234)  


4  R  bar/24 13/9  0.378 ( 0.246)  

Based on the 648 game rollout bar/20 looks like the best choice, but the hit is not out of the question (given the standard errors on this one a longer rollout would be needed for a definitive answer).
Here is another position that was developed from 129
Pip counts: Blue 158, Red 208
Position ID: 4PPgASHgDD5gSQ Match ID: cIkMAAAAAAAA
This addresses a position similar to the one above, the question is whether it red should hit the blot on the five one again or whether the roll would better be played to make two points in blue’s home board?
#  Ply  Move  Equity  

1  R  bar/22 6/5*  0.002  


•  2  R  bar/21  0.041 ( 0.039)  


3  R  bar/22 23/22  0.079 ( 0.077)  


4  R  bar/24 13/10  0.165 ( 0.164)  


5  0  bar/24 21/18  0.267 ( 0.265)  
0.446 0.084 0.002 – 0.554 0.200 0.008  
0ply cubeful prune [expert] 
The above rollout is based on 1296 games, the bar/22 6/5* play is once again the best, but only by a little. (Note that this position has been corrected since the original post, thanks Timothy for pointing out the error)
I happen to run into very similar positions playing a match online earlier today, and because of my study of this position I repeated the loose hit on the 5 with a great deal more confidence that I had in the past.