It's clear to cover with the ace and then to choose between splitting and bringing one more checker down with 3. Among all Slot(5pt)Slot(5pt)31 sequences 51$51$31 presents the most difficult choice. I'd guess this is the reason this position was chosen for the tutorial.
The simple summary is as follows: it's correct to split with 3 except when your opening move was 41$, where it's best to bring a checker down. The only exception to this rule is the OP where splitting and bringing a checker down are essentially tied. Positions 41$51$31 and 21$21$31 are covered in Backgammon Openings as A141 and A143, respectively.
  White is Player 2
score: 0 pip: 161  Unlimited Game Jacoby Beaver  pip: 161 score: 0
Blue is Player 1  
XGID=bADDdDddaB:0:0:1:31:0:0:3:0:10 
Blue to play 31 
1.  Rollout^{1}  24/21 6/5  eq: +0.191 
 Player: Opponent:  54.57% (G:15.39% B:0.76%) 45.43% (G:12.27% B:0.49%)  Conf.: ± 0.003 (+0.188...+0.194)  [88.4%] Duration: 14 hours 45 minutes 

2.  Rollout^{1}  13/10 6/5  eq: +0.188 (0.003) 
 Player: Opponent:  54.19% (G:17.38% B:0.94%) 45.81% (G:13.28% B:0.70%)  Conf.: ± 0.004 (+0.185...+0.192)  [11.6%] Duration: 13 hours 31 minutes 

3.  Rollout^{1}  8/5 6/5  eq: +0.175 (0.016) 
 Player: Opponent:  53.83% (G:17.13% B:0.92%) 46.17% (G:13.41% B:0.66%)  Conf.: ± 0.004 (+0.171...+0.178)  [0.0%] Duration: 12 hours 03 minutes 

4.  Rollout^{1}  24/23 8/5  eq: +0.163 (0.028) 
 Player: Opponent:  53.70% (G:16.62% B:0.81%) 46.30% (G:13.25% B:0.58%)  Conf.: ± 0.003 (+0.160...+0.166)  [0.0%] Duration: 13 hours 06 minutes 

5.  Rollout^{2}  24/20*  eq: +0.119 (0.072) 
 Player: Opponent:  52.50% (G:14.30% B:0.77%) 47.50% (G:11.16% B:0.52%)  Conf.: ± 0.008 (+0.111...+0.128)  [0.0%] Duration: 4 hours 44 minutes 


^{1} 62208 Games rolled with Variance Reduction. Moves and cube decisions: 3ply Using version 1
^{2} 10368 Games rolled with Variance Reduction. Moves and cube decisions: 3ply Using version 1

eXtreme Gammon Version: 2.10
  White is Player 2
score: 0 pip: 164  Unlimited Game Jacoby Beaver  pip: 164 score: 0
Blue is Player 1  
XGID=bADCAdDacdaB:0:0:1:31:0:0:3:0:10 
Blue to play 31 
1.  Rollout^{1}  24/21 6/5  eq: +0.183 
 Player: Opponent:  54.46% (G:15.58% B:0.88%) 45.54% (G:13.22% B:0.60%)  Conf.: ± 0.004 (+0.179...+0.187)  [100.0%] Duration: 2 hours 20 minutes 

2.  Rollout^{1}  13/10 6/5  eq: +0.167 (0.016) 
 Player: Opponent:  53.99% (G:17.19% B:0.98%) 46.01% (G:14.31% B:0.83%)  Conf.: ± 0.004 (+0.163...+0.171)  [0.0%] Duration: 2 hours 10 minutes 

3.  Rollout^{2}  24/20*  eq: +0.104 (0.079) 
 Player: Opponent:  52.17% (G:15.68% B:1.00%) 47.83% (G:12.82% B:0.70%)  Conf.: ± 0.010 (+0.094...+0.114)  [0.0%] Duration: 49 minutes 46 seconds 


^{1} 20736 Games rolled with Variance Reduction. Dice Seed: 76008645 Moves: 3ply, cube decisions: XG Roller
^{2} 5184 Games rolled with Variance Reduction. Dice Seed: 76008645 Moves: 3ply, cube decisions: XG Roller

Rollout by Taper_Mike 2012Jul11 eXtreme Gammon Version: 2.03 21$21$31tm.xgp [E N16 H79] "<=20*5 
eXtreme Gammon Version: 2.10
  White is Player 2
score: 0 pip: 164  Unlimited Game Jacoby Beaver  pip: 162 score: 0
Blue is Player 1  
XGID=bADCAdDacdaB:0:0:1:13:0:0:3:0:10 
Blue to play 13 
1.  Rollout^{1}  13/10 6/5  eq: +0.221 
 Player: Opponent:  55.15% (G:18.17% B:1.10%) 44.85% (G:13.83% B:0.77%)  Conf.: ± 0.005 (+0.217...+0.226)  [100.0%] Duration: 1 hour 32 minutes 

2.  Rollout^{1}  24/21 6/5  eq: +0.209 (0.012) 
 Player: Opponent:  55.07% (G:16.51% B:0.99%) 44.93% (G:13.27% B:0.62%)  Conf.: ± 0.005 (+0.204...+0.214)  [0.0%] Duration: 1 hour 41 minutes 

3.  Rollout^{2}  24/23 8/5  eq: +0.148 (0.074) 
 Player: Opponent:  53.51% (G:17.06% B:0.90%) 46.49% (G:14.06% B:0.65%)  Conf.: ± 0.008 (+0.139...+0.156)  [0.0%] Duration: 33 minutes 27 seconds 

4.  Rollout^{2}  8/5 6/5  eq: +0.146 (0.075) 
 Player: Opponent:  53.21% (G:18.08% B:1.12%) 46.79% (G:14.24% B:0.78%)  Conf.: ± 0.008 (+0.138...+0.154)  [0.0%] Duration: 31 minutes 36 seconds 


^{1} 15552 Games rolled with Variance Reduction. Dice Seed: 89190316 Moves: 3ply, cube decisions: XG Roller
^{2} 5184 Games rolled with Variance Reduction. Dice Seed: 89190316 Moves: 3ply, cube decisions: XG Roller

Rollout by Igor Erovenko 2015Jan06 eXtreme Gammon Version: 2.10 41$21$31ie.xgp [N E12 C74 A75] "<=15*5 
eXtreme Gammon Version: 2.10
  White is Player 2
score: 0 pip: 161  Unlimited Game Jacoby Beaver  pip: 162 score: 0
Blue is Player 1  
XGID=bADCAdDddaB:0:0:1:31:0:0:3:0:10 
Blue to play 31 
1.  Rollout^{1}  13/10 6/5  eq: +0.276 
 Player: Opponent:  56.26% (G:18.51% B:1.04%) 43.74% (G:13.15% B:0.76%)  Conf.: ± 0.008 (+0.267...+0.284)  [100.0%] Duration: 43 minutes 03 seconds 

2.  Rollout^{1}  24/21 6/5  eq: +0.243 (0.033) 
 Player: Opponent:  55.84% (G:16.39% B:0.86%) 44.16% (G:12.67% B:0.59%)  Conf.: ± 0.008 (+0.234...+0.251)  [0.0%] Duration: 46 minutes 23 seconds 

3.  Rollout^{1}  8/5 6/5  eq: +0.199 (0.077) 
 Player: Opponent:  54.30% (G:18.10% B:0.91%) 45.70% (G:13.57% B:0.72%)  Conf.: ± 0.008 (+0.191...+0.207)  [0.0%] Duration: 41 minutes 00 second 


^{1} 5184 Games rolled with Variance Reduction. Dice Seed: 58039970 Moves: 3ply, cube decisions: XG Roller

Rollout by Taper_Mike 2012Jul30 41$51$31tm.xgp [N E33 a77] "<=5 
eXtreme Gammon Version: 2.10
  White is Player 2
score: 0 pip: 164  Unlimited Game Jacoby Beaver  pip: 161 score: 0
Blue is Player 1  
XGID=bADDdDacdaB:0:0:1:13:0:0:3:0:10 
Blue to play 13 
1.  Rollout^{1}  24/21 6/5  eq: +0.176 
 Player: Opponent:  54.17% (G:15.58% B:0.93%) 45.83% (G:13.05% B:0.53%)  Conf.: ± 0.008 (+0.168...+0.184)  [100.0%] Duration: 35 minutes 18 seconds 

2.  Rollout^{1}  13/10 6/5  eq: +0.142 (0.034) 
 Player: Opponent:  53.09% (G:17.17% B:1.02%) 46.91% (G:14.10% B:0.73%)  Conf.: ± 0.008 (+0.134...+0.150)  [0.0%] Duration: 33 minutes 00 second 

3.  Rollout^{1}  24/23 8/5  eq: +0.130 (0.046) 
 Player: Opponent:  53.02% (G:16.61% B:0.85%) 46.98% (G:13.86% B:0.60%)  Conf.: ± 0.008 (+0.123...+0.138)  [0.0%] Duration: 33 minutes 10 seconds 

4.  Rollout^{1}  8/5 6/5  eq: +0.129 (0.047) 
 Player: Opponent:  52.84% (G:16.95% B:0.98%) 47.16% (G:14.15% B:0.68%)  Conf.: ± 0.008 (+0.121...+0.137)  [0.0%] Duration: 30 minutes 07 seconds 

5.  Rollout^{1}  24/20*  eq: +0.091 (0.085) 
 Player: Opponent:  51.71% (G:15.29% B:1.02%) 48.29% (G:12.47% B:0.61%)  Conf.: ± 0.009 (+0.082...+0.099)  [0.0%] Duration: 54 minutes 35 seconds 


^{1} 5184 Games rolled with Variance Reduction. Dice Seed: 89190316 Moves: 3ply, cube decisions: XG Roller

Rollout by Igor Erovenko 2015Jan06 eXtreme Gammon Version: 2.10 51$21$31ie.xgp [E N34 C46 A47 H85] "<=5 
eXtreme Gammon Version: 2.10
  White is Player 2
score: 0 pip: 164  Unlimited Game Jacoby  pip: 159 score: 0
Blue is Player 1  
XGID=bAECdDacdaB:0:0:1:13:0:0:1:0:10 
Blue to play 13 
1.  XG Roller++  24/21 6/5  eq: +0.199 
 Player: Opponent:  54.38% (G:16.34% B:0.90%) 45.62% (G:12.29% B:0.48%)  

2.  XG Roller++  13/10 6/5  eq: +0.149 (0.049) 
 Player: Opponent:  52.95% (G:17.65% B:1.04%) 47.05% (G:13.75% B:0.68%)  

3.  XG Roller++  8/5 6/5  eq: +0.105 (0.094) 
 Player: Opponent:  51.89% (G:16.77% B:0.98%) 48.11% (G:14.04% B:0.65%)  

4.  XG Roller++  24/20*  eq: +0.070 (0.128) 
 Player: Opponent:  51.13% (G:14.94% B:0.91%) 48.87% (G:12.33% B:0.57%)  

5.  XG Roller++  24/23 8/5  eq: +0.070 (0.129) 
 Player: Opponent:  51.30% (G:16.07% B:0.84%) 48.70% (G:14.07% B:0.62%)  

eXtreme Gammon Version: 2.10
  White is Player 2
score: 0 pip: 161  Unlimited Game Jacoby Beaver  pip: 159 score: 0
Blue is Player 1  
XGID=bAECdDddaB:0:0:1:13:0:0:3:0:10 
Blue to play 13 
1.  Rollout^{1}  24/21 6/5  eq: +0.216 
 Player: Opponent:  54.83% (G:16.85% B:0.82%) 45.17% (G:12.30% B:0.48%)  Conf.: ± 0.005 (+0.211...+0.222)  [100.0%] Duration: 1 hour 02 minutes 

2.  Rollout^{1}  13/10 6/5  eq: +0.203 (0.013) 
 Player: Opponent:  54.25% (G:18.62% B:0.93%) 45.75% (G:13.21% B:0.69%)  Conf.: ± 0.006 (+0.198...+0.209)  [0.0%] Duration: 56 minutes 38 seconds 


^{1} 10368 Games rolled with Variance Reduction. Dice Seed: 44214296 Moves: 3ply, cube decisions: XG Roller

Rollout by Igor Erovenko 2014Jan11 eXtreme Gammon Version: 2.10 31P53P41ie.xgp [N E13 S29 D35 U36] "<=10*5 
eXtreme Gammon Version: 2.10