Before getting into 4th roll positions let's take a look at what we are dealing with.
      
 
         
 | | White is Player 2
score: 0
pip: 47 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-aa---EBB----D----------B-:0:0:1:41:0:0:3:0:10 |
| Blue to play 41 |
eXtreme Gammon Version: 2.03
What does 61P do? Besides the obvious, making bar point, it blocks 5s and 6s. This often means White will have to play these numbers from the midpoint. Since she already unloaded one checker on the 1st roll this is not part of her plan. In Advanced Backgammon Robertie argues that Blue has an attacking position and not priming. This is wrong. As modern bots show, Blue's primary plan is priming. Although 61P-structure is not very effective in holding two checkers back, White does not feel comfortable with third man back. If Blue succeeds in making 4pt or 5pt, White will feel very uncomfortable whether she has 2 or 3 men back. If Blue rolls 41, hitting both (K) is not of his game plan, since checker on ace point cannot be part of a prime. It could be correct under certain conditions. More on that later.
L (13/8) and S(24/23, 13/9) both help Blue's game plan. Both bring another man down creating new rolls that make his 5pt or 4pt without breaking his 8pt. After S, however 9pt blot is exposed to 11 numbers that both hit and partially escape one checker. Moreover, split back men may come under attack and he simply may not have a chance to take advantage of his new point making numbers. Although Blue doesn't mind making 9pt if he rolls a 4 after he is missed, there is a cost attached to it--after covering 9pt he will have a set of stripped points with a stack on 6pt and two men still back. In other words his flexibility will suffer. With that said it should be easy to see that if Blue has given a choice, he should prefer L to S. In fact, S wasn't correct in any of 55 or so positions I rolled out.
What about U (24/20, 24/23)? Quality of this play will depend on amount of power in range and White's own game plan. More on that later.
We all know that on 2nd roll it is correct to hit both with 41 after our opponent split with X1. We are in need to stop him from doing anything useful next roll since we can't do much ourselves, so we hit. Not all double hits are created equal though. Double hit is less effective after 51 than after 21 and lesser than after 41. If we don't hit she will have more numbers to make key points after 41S, less after 21 and less after 51. Another important reason double hit is much stronger after 41S and 21S than after 51 is that extra blot itself. With some luck it can be picked up.
With this information in mind let's look at our 4th roll positions.
21S-61P-11N-41
Easy one. K is correct. White has to many numbers (to count) to improve her position. You simply cannot leave her alone. Two extra blots make this decision particularly easy.
    
| | White is Player 2
score: 0
pip: 160 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-aa---EBB---dDa--abcb---B-:0:0:1:14:0:0:3:0:10 |
| Blue to play 14 |
| 1. | Rollout1 | 6/2* 2/1* | eq: -0.418 |
| Player:
Opponent: | 39.68% (G:12.51% B:0.59%)
60.32% (G:18.20% B:1.06%) | Conf.: ± 0.009 (-0.427...-0.410) - [100.0%]
Duration: 13 minutes 37 seconds |
|
| 2. | Rollout1 | 24/23 6/2* | eq: -0.439 (-0.021) |
| Player:
Opponent: | 39.80% (G:10.91% B:0.56%)
60.20% (G:19.06% B:1.03%) | Conf.: ± 0.008 (-0.448...-0.431) - [0.0%]
Duration: 14 minutes 39 seconds |
|
| 3. | Rollout1 | 24/23 13/9 | eq: -0.478 (-0.060) |
| Player:
Opponent: | 38.73% (G:11.31% B:0.49%)
61.27% (G:19.32% B:1.05%) | Conf.: ± 0.009 (-0.487...-0.470) - [0.0%]
Duration: 12 minutes 55 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 75109221
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.03
21S-61P-31P-41
How about now? OK, K is not part of Blue's game plan, but White has 13 numbers to make her 7pt or 4pt. Moreover, She has a blot on 11pt. Does the benefit outweigh the risk of sending our 3rd man back? It turns out it doesn't. If Blue plays K White's aces send a third man back behind a growing prime--the risk is big. If Blue just plays L (13/8), White's aces are lesser evil. Yes, she will make bar point with 41 and 61, but that will cost her the 8pt. Another thing to look at is her 6s. Although 6x make her dance with at least one checker, most of White's 6s are not very useful for her front game anyway. Therefore, benefit of 6x from the bar is reduced.
 
| | White is Player 2
score: 0
pip: 160 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-aa---EBB---dDa--b-db---B-:0:0:1:41:0:0:3:0:10 |
| Blue to play 41 |
| 1. | Rollout1 | 13/8 | eq: -0.262 |
| Player:
Opponent: | 43.85% (G:12.52% B:0.56%)
56.15% (G:17.72% B:0.86%) | Conf.: ± 0.008 (-0.270...-0.254) - [100.0%]
Duration: 11 minutes 28 seconds |
|
| 2. | Rollout1 | 6/2* 2/1* | eq: -0.306 (-0.044) |
| Player:
Opponent: | 42.91% (G:12.62% B:0.46%)
57.09% (G:18.23% B:0.99%) | Conf.: ± 0.008 (-0.314...-0.297) - [0.0%]
Duration: 13 minutes 25 seconds |
|
| 3. | Rollout1 | 24/23 13/9 | eq: -0.330 (-0.068) |
| Player:
Opponent: | 42.57% (G:11.79% B:0.52%)
57.43% (G:18.58% B:0.91%) | Conf.: ± 0.008 (-0.338...-0.322) - [0.0%]
Duration: 12 minutes 26 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 75109221
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.03
21S-61P-42P-41
She now has 14 numbers to make her bar point or 5pt. Also if she is left alone her 6s are better now than in previous position. Is it enough to swing it? Maybe--5k rollout is inconclusive--but probably not. White's 6s and 1s are better if left alone, but Blue is in less danger to be primed in comparing to previous position. The sum of above factors shifts considerably toward K though. Question: How do you play in a similar position 41S-61P-42P-41?
| | White is Player 2
score: 0
pip: 158 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-aa---EBB---dDa--b-d-b--B-:0:0:1:41:0:0:3:0:10 |
| Blue to play 41 |
| 1. | Rollout1 | 13/8 | eq: -0.233 |
| Player:
Opponent: | 44.79% (G:13.00% B:0.58%)
55.21% (G:18.41% B:0.91%) | Conf.: ± 0.008 (-0.241...-0.225) - [72.2%]
Duration: 1 hour 35 minutes |
|
| 2. | Rollout1 | 6/2* 2/1* | eq: -0.237 (-0.004) |
| Player:
Opponent: | 44.50% (G:13.60% B:0.50%)
55.50% (G:18.14% B:1.06%) | Conf.: ± 0.009 (-0.245...-0.228) - [27.7%]
Duration: 1 hour 56 minutes |
|
| 3. | Rollout1 | 24/23 24/20 | eq: -0.248 (-0.015) |
| Player:
Opponent: | 44.92% (G:11.83% B:0.61%)
55.08% (G:18.91% B:0.71%) | Conf.: ± 0.008 (-0.256...-0.240) - [0.1%]
Duration: 1 hour 50 minutes |
|
| 4. | Rollout1 | 24/23 13/9 | eq: -0.258 (-0.025) |
| Player:
Opponent: | 44.64% (G:12.54% B:0.63%)
55.36% (G:19.35% B:0.99%) | Conf.: ± 0.008 (-0.266...-0.251) - [0.0%]
Duration: 1 hour 46 minutes |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 75109221
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.03
21S-61P-41P-41
"Backgammon is a simple game. Make points, hit blots and jump primes!" Walter trice.
OK, K is not an option here. Blue doesn't need to prevent White from making new points, nor there is a blot sitting around. S is not good either, as we now know. U and L are left. Blue needs both to start those checkers moving and bring more help down from the midpoint. The benefit from couple extra numbers to make 4pt or 5pt is not big enough. Move those back checkers. Odds are there won't be safer opportunity to do it than now.
| | White is Player 2
score: 0
pip: 159 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-aa---EBB---dD---bbe----B-:0:0:1:14:0:0:3:0:10 |
| Blue to play 14 |
| 1. | Rollout1 | 24/23 24/20 | eq: -0.033 |
| Player:
Opponent: | 49.22% (G:11.96% B:0.50%)
50.78% (G:13.33% B:0.47%) | Conf.: ± 0.008 (-0.041...-0.025) - [100.0%]
Duration: 13 minutes 06 seconds |
|
| 2. | Rollout1 | 13/8 | eq: -0.082 (-0.049) |
| Player:
Opponent: | 47.67% (G:13.76% B:0.50%)
52.33% (G:14.36% B:0.70%) | Conf.: ± 0.007 (-0.090...-0.075) - [0.0%]
Duration: 11 minutes 51 seconds |
|
| 3. | Rollout1 | 24/23 13/9 | eq: -0.129 (-0.095) |
| Player:
Opponent: | 46.93% (G:13.32% B:0.51%)
53.07% (G:15.51% B:0.71%) | Conf.: ± 0.009 (-0.137...-0.120) - [0.0%]
Duration: 12 minutes 07 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 75109221
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.03
21S-61P-64P-41
I posted it to trick you. Sorry......NOT. Yes, White is more equipped to attack you now than in previous position. But Sitting back is still bad. She may roll 31 and point on Blue's head, but if she does so he will have his checkers split now --one on the ace and one on the bar. This is not a likely scenario, but I thought I should point it out. More often she will hit lose and he will hit back sending that 3rd checker back I was talking about in the beginning. What type of game plan does white have? Priming! U (24/20, 24/23) will be correct in many other similar structure positions. Question: How do you play 61P-61P-21S-41? and 61P-61P-41S-41?
| | White is Player 2
score: 0
pip: 154 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-aa---EBB---cD---cbe----B-:0:0:1:41:0:0:3:0:10 |
| Blue to play 41 |
| 1. | Rollout1 | 24/23 24/20 | eq: -0.132 |
| Player:
Opponent: | 47.37% (G:11.55% B:0.50%)
52.63% (G:16.07% B:0.54%) | Conf.: ± 0.007 (-0.139...-0.125) - [100.0%]
Duration: 12 minutes 13 seconds |
|
| 2. | Rollout1 | 13/8 | eq: -0.163 (-0.031) |
| Player:
Opponent: | 45.97% (G:13.02% B:0.47%)
54.03% (G:15.63% B:0.78%) | Conf.: ± 0.007 (-0.171...-0.156) - [0.0%]
Duration: 11 minutes 38 seconds |
|
| 3. | Rollout1 | 6/2* 2/1* | eq: -0.199 (-0.067) |
| Player:
Opponent: | 44.81% (G:13.05% B:0.36%)
55.19% (G:15.98% B:0.82%) | Conf.: ± 0.008 (-0.207...-0.191) - [0.0%]
Duration: 13 minutes 13 seconds |
|
| 4. | Rollout1 | 24/20 6/5 | eq: -0.214 (-0.082) |
| Player:
Opponent: | 45.95% (G:11.42% B:0.51%)
54.05% (G:17.97% B:0.88%) | Conf.: ± 0.008 (-0.222...-0.206) - [0.0%]
Duration: 14 minutes 08 seconds |
|
| 5. | Rollout1 | 13/9 6/5 | eq: -0.229 (-0.097) |
| Player:
Opponent: | 45.61% (G:11.97% B:0.54%)
54.39% (G:18.50% B:1.56%) | Conf.: ± 0.009 (-0.238...-0.221) - [0.0%]
Duration: 14 minutes 35 seconds |
|
| 6. | Rollout1 | 24/23 13/9 | eq: -0.265 (-0.133) |
| Player:
Opponent: | 44.21% (G:11.78% B:0.49%)
55.79% (G:18.13% B:0.83%) | Conf.: ± 0.008 (-0.273...-0.257) - [0.0%]
Duration: 11 minutes 59 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 75109221
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.03
21S61P-66D-41
Best for last! Did anyone even consider the best play? Ok, I admit, I didn't. What is going on here? white has 13 men in the zone. Any type of splitting is just wrong. So, he is a gazillion pips behind in the race and has an opportunity to slot while duplicating almost all numbers that would make key points on another side anyway. Doesn't sound like he is risking much. What about K 6/2*/1*? Well, it doesn't exactly help his case here. She will reenter and he will have same problem. Against a weaker opponent slot is especially effective. It will give him a chance to make a big error an almost every roll. He may decide not to hit and make a home board point just to find out several rolls later that he is on the wrong side of priming battle.
| | White is Player 2
score: 0
pip: 140 | Unlimited Game
Jacoby Beaver | pip: 160
score: 0
Blue is Player 1 |
|
| XGID=-aa---EBB----Da--cde----B-:0:0:1:41:0:0:3:0:10 |
| Blue to play 41 |
| 1. | Rollout1 | 13/9 6/5 | eq: -0.171 |
| Player:
Opponent: | 48.01% (G:11.82% B:0.58%)
51.99% (G:20.54% B:2.07%) | Conf.: ± 0.010 (-0.180...-0.161) - [100.0%]
Duration: 12 minutes 49 seconds |
|
| 2. | Rollout1 | 13/12 13/9 | eq: -0.216 (-0.045) |
| Player:
Opponent: | 45.56% (G:12.07% B:0.59%)
54.44% (G:19.05% B:1.59%) | Conf.: ± 0.009 (-0.224...-0.207) - [0.0%]
Duration: 10 minutes 04 seconds |
|
| 3. | Rollout1 | 6/2* 2/1* | eq: -0.225 (-0.055) |
| Player:
Opponent: | 45.14% (G:11.99% B:0.47%)
54.86% (G:18.06% B:1.23%) | Conf.: ± 0.008 (-0.234...-0.217) - [0.0%]
Duration: 11 minutes 44 seconds |
|
| 4. | Rollout1 | 13/12 6/2* | eq: -0.249 (-0.079) |
| Player:
Opponent: | 45.19% (G:11.39% B:0.53%)
54.81% (G:19.35% B:1.65%) | Conf.: ± 0.009 (-0.258...-0.240) - [0.0%]
Duration: 12 minutes 23 seconds |
|
| 5. | Rollout1 | 24/23 6/2* | eq: -0.253 (-0.082) |
| Player:
Opponent: | 44.91% (G:10.62% B:0.50%)
55.09% (G:19.68% B:1.00%) | Conf.: ± 0.009 (-0.262...-0.244) - [0.0%]
Duration: 12 minutes 34 seconds |
|
| 6. | Rollout1 | 13/8 | eq: -0.259 (-0.089) |
| Player:
Opponent: | 44.42% (G:11.54% B:0.52%)
55.58% (G:19.10% B:1.31%) | Conf.: ± 0.008 (-0.267...-0.251) - [0.0%]
Duration: 9 minutes 06 seconds |
|
| |
1 5184 Games rolled with Variance Reduction.
Dice Seed: 75109221
Moves and cube decisions: 3-ply
|
eXtreme Gammon Version: 2.03