Great problem! I liked David Presser's analysis the best. Here is some more bot info.
Close White's board and take a look at how far down 8/4* drops in the rankings.
  White is Player 1
score: 0 pip: 70  Unlimited Game Jacoby  pip: 92 score: 0
Blue is Player 2  
XGID=BBAaBBABBAbbccbb:0:0:1:31:0:0:1:0:10 
Blue to play 31 
1.  XG Roller++  9/8 9/6  eq: 0.570 
 Player: Opponent:  33.20% (G:0.68% B:0.01%) 66.80% (G:7.78% B:0.07%)  

2.  XG Roller++  11/10 11/8  eq: 0.590 (0.020) 
 Player: Opponent:  39.09% (G:0.92% B:0.02%) 60.91% (G:19.33% B:0.14%)  

3.  XG Roller++  11/8 3/2  eq: 0.664 (0.094) 
 Player: Opponent:  33.57% (G:0.61% B:0.01%) 66.43% (G:12.59% B:0.11%)  

4.  XG Roller++  13/12 11/8  eq: 0.683 (0.113) 
 Player: Opponent:  34.27% (G:0.82% B:0.02%) 65.73% (G:12.88% B:0.11%)  

5.  XG Roller++  8/5 3/2  eq: 0.714 (0.144) 
 Player: Opponent:  30.53% (G:0.47% B:0.01%) 69.47% (G:8.58% B:0.06%)  

6.  XG Roller++  13/12 8/5  eq: 0.759 (0.189) 
 Player: Opponent:  29.79% (G:0.61% B:0.01%) 70.21% (G:9.11% B:0.08%)  

7.  XG Roller++  13/10 11/10  eq: 0.810 (0.240) 
 Player: Opponent:  34.88% (G:0.89% B:0.02%) 65.12% (G:20.62% B:0.13%)  

8.  XG Roller++  8/4*  eq: 0.937 (0.367) 
 Player: Opponent:  36.77% (G:1.10% B:0.02%) 63.23% (G:33.13% B:0.38%)  

eXtreme Gammon Version: 2.10
Give White a sixprime as well as a bit of timing, and the bot won't give the time of day to any play besides 9/8 9/6 (though 11/10 11/8 might still win by a nose at DMP).
  White is Player 1
score: 0 pip: 82  Unlimited Game Jacoby  pip: 92 score: 0
Blue is Player 2  
XGID=BBAaBBABBAbbbccb:0:0:1:31:0:0:1:0:10 
Blue to play 31 
1.  XG Roller++  9/8 9/6  eq: 0.213 
 Player: Opponent:  41.03% (G:0.96% B:0.02%) 58.97% (G:6.63% B:0.10%)  

2.  XG Roller++  8/5 3/2  eq: 0.358 (0.145) 
 Player: Opponent:  37.44% (G:0.72% B:0.01%) 62.56% (G:8.17% B:0.16%)  

3.  XG Roller++  11/8 3/2  eq: 0.359 (0.146) 
 Player: Opponent:  38.90% (G:0.80% B:0.01%) 61.10% (G:10.09% B:0.19%)  

4.  XG Roller++  13/12 8/5  eq: 0.384 (0.171) 
 Player: Opponent:  37.58% (G:1.06% B:0.02%) 62.42% (G:7.44% B:0.08%)  

5.  XG Roller++  13/12 11/8  eq: 0.434 (0.221) 
 Player: Opponent:  38.97% (G:1.22% B:0.02%) 61.03% (G:11.56% B:0.32%)  

6.  XG Roller++  11/10 11/8  eq: 0.443 (0.231) 
 Player: Opponent:  41.63% (G:1.42% B:0.03%) 58.37% (G:18.67% B:0.27%)  

7.  XG Roller++  13/10 11/10  eq: 0.602 (0.389) 
 Player: Opponent:  38.38% (G:1.11% B:0.02%) 61.62% (G:18.04% B:0.33%)  

8.  XG Roller++  11/8 2/1  eq: 0.707 (0.494) 
 Player: Opponent:  32.62% (G:0.67% B:0.01%) 67.38% (G:12.47% B:0.36%)  

9.  XG Roller++  8/4*  eq: 0.713 (0.501) 
 Player: Opponent:  38.72% (G:2.08% B:0.04%) 61.28% (G:30.71% B:0.76%)  

10.  XG Roller++  8/5 2/1  eq: 0.765 (0.553) 
 Player: Opponent:  29.43% (G:0.37% B:0.01%) 70.57% (G:7.35% B:0.10%)  

eXtreme Gammon Version: 2.10
Now let's take a look at some smaller changes. Suppose we give White a spare on the 6pt so that 66 doesn't expose a blot.
  White is Player 2
score: 0 pip: 77  Unlimited Game Jacoby  pip: 92 score: 0
Blue is Player 1  
XGID=BBAaBBABBAcbcdb:0:0:1:31:0:0:1:0:10 
Blue to play 31 
1.  XG Roller++  9/8 9/6  eq: 0.350 
 Player: Opponent:  37.68% (G:0.91% B:0.01%) 62.32% (G:7.00% B:0.13%)  

2.  XG Roller++  11/10 11/8  eq: 0.435 (0.085) 
 Player: Opponent:  40.80% (G:1.20% B:0.02%) 59.20% (G:17.68% B:0.30%)  

3.  XG Roller++  11/8 3/2  eq: 0.452 (0.101) 
 Player: Opponent:  36.81% (G:0.82% B:0.01%) 63.19% (G:11.33% B:0.20%)  

4.  XG Roller++  13/12 11/8  eq: 0.493 (0.142) 
 Player: Opponent:  37.08% (G:1.10% B:0.02%) 62.92% (G:11.33% B:0.24%)  

5.  XG Roller++  8/5 3/2  eq: 0.521 (0.170) 
 Player: Opponent:  34.17% (G:0.54% B:0.01%) 65.83% (G:7.71% B:0.15%)  

6.  XG Roller++  8/4*  eq: 0.556 (0.205) 
 Player: Opponent:  40.78% (G:1.45% B:0.03%) 59.22% (G:28.12% B:0.69%)  

7.  XG Roller++  13/12 8/5  eq: 0.569 (0.219) 
 Player: Opponent:  33.53% (G:0.73% B:0.01%) 66.47% (G:7.03% B:0.09%)  

8.  XG Roller++  13/10 11/10  eq: 0.574 (0.223) 
 Player: Opponent:  38.07% (G:1.00% B:0.02%) 61.93% (G:16.92% B:0.27%)  

eXtreme Gammon Version: 2.10
What about just shifting one checker from White's 3pt to her 4pt? Someone might want to do a full rollout for this one:
  White is Player 2
score: 0 pip: 75  Unlimited Game Jacoby  pip: 92 score: 0
Blue is Player 1  
XGID=BBAaBBABBAbbddb:0:0:1:31:0:0:1:0:10 
Blue to play 31 
1.  XG Roller++  9/8 9/6  eq: 0.338 
 Player: Opponent:  37.43% (G:0.97% B:0.02%) 62.57% (G:6.13% B:0.10%)  

2.  XG Roller++  11/10 11/8  eq: 0.338 (0.000) 
 Player: Opponent:  42.32% (G:1.19% B:0.02%) 57.68% (G:15.93% B:0.27%)  

3.  XG Roller++  8/4*  eq: 0.373 (0.034) 
 Player: Opponent:  43.17% (G:2.40% B:0.07%) 56.83% (G:25.82% B:0.61%)  

eXtreme Gammon Version: 2.10