As for the rule with [11] and making the 4pt it is definitely not obvious to most people. 31P-31P-11? 31P-65R-11? A containment position like this one: XGID=-a---BD-C----B-A---B--cAc-:1:1:1:11:0:0:3:0:10? How about bringing home a holding game with blots involved: XGID=-a-b-BDaB-B-dD--Aabbb-----:0:0:1:11:0:0:3:0:10? I have endless examples that confuse me so I figure they might confuse other people too.
My error rate is far too high to make any claims to wisdom here, but this particular type is not one that I often get wrong. I compensate this by making every other type of stupidity. In any case, here has been my reasoning for the most part:
With one checker to hold back, the bar point is not much better than the 4 if at all, and the 4 brings the advantage of another point for the opponent to fan if hit, and improving the board, which is nearly always a good thing.
In the containment position:
       
 
        
 | | White is Player 2
score: 0
pip: 36 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-a---BD-C----B-A---B--cAc-:1:1:1:11:0:0:3:0:10 |
| Blue to play 11 |
| 1. | XG Roller++ | 6/4(2) | eq: +0.051 |
| Player:
Opponent: | 52.29% (G:0.00% B:0.00%)
47.71% (G:17.35% B:1.21%) | |
|
| 2. | XG Roller++ | 19/16 6/5 | eq: -0.060 (-0.111) |
| Player:
Opponent: | 49.47% (G:0.00% B:0.00%)
50.53% (G:21.02% B:1.74%) | |
|
| 3. | XG Roller++ | 19/18 19/17 6/5 | eq: -0.070 (-0.121) |
| Player:
Opponent: | 49.13% (G:0.00% B:0.00%)
50.87% (G:21.37% B:1.66%) | |
|
| 4. | XG Roller++ | 19/17 15/14 6/5 | eq: -0.105 (-0.156) |
| Player:
Opponent: | 48.30% (G:0.00% B:0.00%)
51.70% (G:22.72% B:1.86%) | |
|
| 5. | XG Roller++ | 19/18 8/7(2) 6/5 | eq: -0.126 (-0.177) |
| Player:
Opponent: | 47.89% (G:0.00% B:0.00%)
52.11% (G:23.19% B:2.27%) | |
|
eXtreme Gammon Version: 2.10
Making the 4 is clearly better than the bar, no? There is no large benefit of shots avoided, and the defense's best chance is to speed-build the board so that each time the blot is hit, there will be more chances he will stay out of action.
As to the second one:
     
   
| | White is Player 2
score: 0
pip: 182 | Unlimited Game
Jacoby Beaver | pip: 138
score: 0
Blue is Player 1 |
|
| XGID=-a-b-BDaB-B-dD--Aabbb-----:0:0:1:11:0:0:3:0:10 |
| Blue to play 11 |
| 1. | XG Roller++ | 16/14 8/7*(2) | eq: +0.787 |
| Player:
Opponent: | 66.33% (G:22.55% B:1.10%)
33.67% (G:5.15% B:0.19%) | |
|
| 2. | XG Roller++ | 16/15 8/7*(2) 6/5 | eq: +0.784 (-0.004) |
| Player:
Opponent: | 66.07% (G:23.13% B:1.16%)
33.93% (G:5.33% B:0.21%) | |
|
| 3. | XG Roller++ | 10/9(2) 8/7*(2) | eq: +0.769 (-0.018) |
| Player:
Opponent: | 65.90% (G:22.84% B:1.13%)
34.10% (G:5.35% B:0.21%) | |
|
| 4. | XG Roller++ | 6/4(2) | eq: +0.741 (-0.047) |
| Player:
Opponent: | 66.90% (G:18.58% B:0.85%)
33.10% (G:5.04% B:0.19%) | |
|
| 5. | XG Roller++ | 16/13 6/5 | eq: +0.679 (-0.108) |
| Player:
Opponent: | 66.39% (G:16.45% B:0.57%)
33.61% (G:4.91% B:0.17%) | |
|
eXtreme Gammon Version: 2.10
My first choice was 16/15 8/7(2) 6/5. Maybe with serious stakes at hand, I might be inclined to play it safe, but that was my first instinct. It hits a blot, doesn't let him settle down on my bar (which would make bringing the rest home a little riskier) takes half the opp's role, and the two remaining aces are best served with 16/15 and 6/5. One can argue there's also the issue of slightly duped 3s, but it is a minor factor if at all.
In any case, as I said, I make more than enough bonehead moves to keep my head low, very low, and maybe even a few of this type too, just fewer.