In the future I will make sure these have the bottom player on roll at all times but on this first run I forgot as it came up OtB and then I copied and pasted position ids from there. I will also work on the formatting as I think it would appear a lot crisper than it's presented here but I got tired of fiddling with the HTML. First, we have the original position where the top player on roll is cubing. It's a straightforward position for the most part yet I'm surprised at how often people will drop these.
The race is even if this was to somehow turn into a race. That's not the likely path down which this game will lead, but it's always worth noting. The doubler's big advantage stems from his stronger home board combined with three blots his shooting at. Dissecting his immediate rolls we see only [52 55] miss completely. Looking further we note [11 22 33 44 31 41 61 43 63 64], a full 16 numbers, hit both blots and on top of that another 10 numbers (33 listed both cases) [33 66 51 53 54 65] both hit and cover the blot on the ace point. Of the only rolls unlisted so far we 21 which is your basic hitting dud, 32 in the same ballpark, 42 which is a little better because it splits the back men while hitting the important blot, gaining the most in the race, depriving your opponent the opportunity of covering that blot, and slotting the best anchor, and 62, another dud.
So we see as the taker we love any of our opponent's misses of which there are 3, and he has basically 8 other numbers that aren't so hot. (he'd happily reroll if given the choice) Even in the scenarios where he rolls one of his better numbers this game is far from over. He has only a two (possibly three) point board and that checker of his hanging on his ace point will sometimes be your savior. You do lose a lot of gammons, over 30%, but that is compensated by the games you're able to get a hold on the position and turn it around. Remember when you consider dropping a cube like this, if you don't already have a man on the bar it's faaaaaaaaaaaaaaaaaaaaaaaaaaaaaaar more often a take than a drop.
          
   
         
 |  is Player 2
score: 0
pip: 149 | | Money session | pip: 144
score: 0
 is Player 1 |
|
| XGID=-b---AE-C---bDbA-cAcb---a-:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 62.16% (G: 31.57% B: 1.63%) |
| Opponent Winning Chances: | 37.84% (G: 9.35% B: 0.70%) |
| Double/Take |
| Player Winning Chances: | 62.53% (G: 32.38% B: 1.68%) |
| Opponent Winning Chances: | 37.47% (G: 9.72% B: 0.75%) |
| |
| Cubeless Equities |
| No Double: | +0.475 |
| Double: | +0.973 |
| |
| Cubeful Equities |
| No Double: | +0.604 (-0.040) |
| Double/Take: | +0.644 |
| Double/Drop: | +1.000 (+0.356) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.020 (+0.584...+0.624) |
| Confidence Double: | ± 0.028 (+0.616...+0.672) |
| |
| Double Decision confidence: | 98.9% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 05 minutes |
Modified Position #1
Here I've lifted the blot from the cuber's ace point assuming the addition of a diversified builder/attacker for the higher inner board points will more than compensate for the loss of 4 pips. The blot on the ace in the original position was a weakness even though it was pips. Put it almost anywhere else as I'll show in the following examples and having 15 checkers to play with has a higher equity than the original position.
| is Player 2
score: 0
pip: 153 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-b---AE-C---bDbA-cAcc-----:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 64.75% (G: 30.53% B: 1.89%) |
| Opponent Winning Chances: | 35.25% (G: 7.68% B: 0.51%) |
| Double/Take |
| Player Winning Chances: | 64.74% (G: 31.58% B: 2.06%) |
| Opponent Winning Chances: | 35.26% (G: 7.84% B: 0.55%) |
| |
| Cubeless Equities |
| No Double: | +0.537 |
| Double: | +1.094 |
| |
| Cubeful Equities |
| No Double: | +0.713 (-0.084) |
| Double/Take: | +0.797 |
| Double/Drop: | +1.000 (+0.203) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.018 (+0.695...+0.731) |
| Confidence Double: | ± 0.028 (+0.770...+0.825) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 57 minutes 34 seconds |
Modified Position #2
Here I've undiversified the spare by stacking it on the 6pt. (yes, 'stacking' is used very loosely) This is still a clear improvement over the blotted ace point and also inferior to having it as a diversified builder as in our previous example. Its equity lies rightfully so between the original position and modified position #1 which has the highest equity of all the positions.
| is Player 2
score: 0
pip: 154 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-b---AE-C---bDbA-cAdb-----:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 63.91% (G: 28.92% B: 1.75%) |
| Opponent Winning Chances: | 36.09% (G: 8.38% B: 0.53%) |
| Double/Take |
| Player Winning Chances: | 63.95% (G: 29.97% B: 1.84%) |
| Opponent Winning Chances: | 36.05% (G: 8.33% B: 0.58%) |
| |
| Cubeless Equities |
| No Double: | +0.496 |
| Double: | +1.016 |
| |
| Cubeful Equities |
| No Double: | +0.650 (-0.059) |
| Double/Take: | +0.709 |
| Double/Drop: | +1.000 (+0.291) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.020 (+0.630...+0.669) |
| Confidence Double: | ± 0.031 (+0.678...+0.740) |
| |
| Double Decision confidence: | 99.9% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 01 minute |
Modified Position #3
We continue moving what was the blotted ace point checker around the board, losing pips in the process, and see that it's still more useful as part of the offense than dangling to be shot at immediately on the ace point regardless of what the race is. Here it's stacked on the 8pt.
| is Player 2
score: 0
pip: 156 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-b---AE-C---bDbA-dAcb-----:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 63.57% (G: 27.08% B: 1.73%) |
| Opponent Winning Chances: | 36.43% (G: 8.37% B: 0.54%) |
| Double/Take |
| Player Winning Chances: | 63.63% (G: 28.22% B: 1.88%) |
| Opponent Winning Chances: | 36.37% (G: 8.54% B: 0.63%) |
| |
| Cubeless Equities |
| No Double: | +0.470 |
| Double: | +0.964 |
| |
| Cubeful Equities |
| No Double: | +0.630 (-0.032) |
| Double/Take: | +0.662 |
| Double/Drop: | +1.000 (+0.338) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.020 (+0.609...+0.650) |
| Confidence Double: | ± 0.031 (+0.632...+0.693) |
| |
| Double Decision confidence: | 95.7% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 07 minutes |
Modified Position #4
Here we've dropped a full 10 pips from the original position and it's still better to have that checker in play. You also may be noticing around this point that the ND/D decision has become borderline even though the equity is higher than in the original position. This is also due to the hit and cover numbers making a 3pt board in our original position. That blot added more volatility to the position.
| is Player 2
score: 0
pip: 159 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-b---AE-C---bDcA-cAcb-----:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 63.43% (G: 26.23% B: 1.58%) |
| Opponent Winning Chances: | 36.57% (G: 8.31% B: 0.51%) |
| Double/Take |
| Player Winning Chances: | 63.39% (G: 27.00% B: 1.79%) |
| Opponent Winning Chances: | 36.61% (G: 8.31% B: 0.55%) |
| |
| Cubeless Equities |
| No Double: | +0.459 |
| Double: | +0.934 |
| |
| Cubeful Equities |
| No Double: | +0.633 |
| Double/Take: | +0.633 (0.000) |
| Double/Drop: | +1.000 (+0.367) |
| |
| Best Cube action: No Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.010 (+0.623...+0.643) |
| Confidence Double: | ± 0.015 (+0.618...+0.647) |
| |
| Double Decision confidence: | 51.6% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 2 hours 32 minutes |
Modified Position #5
Spare clear back to the midpoint now and as one would suspect, no real change from having it on either the 11pt or the 13pt.
| is Player 2
score: 0
pip: 161 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-b---AE-C---cDbA-cAcb-----:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 63.41% (G: 25.85% B: 1.62%) |
| Opponent Winning Chances: | 36.59% (G: 8.51% B: 0.52%) |
| Double/Take |
| Player Winning Chances: | 63.46% (G: 27.10% B: 1.83%) |
| Opponent Winning Chances: | 36.54% (G: 8.65% B: 0.61%) |
| |
| Cubeless Equities |
| No Double: | +0.453 |
| Double: | +0.932 |
| |
| Cubeful Equities |
| No Double: | +0.628 (-0.004) |
| Double/Take: | +0.632 |
| Double/Drop: | +1.000 (+0.368) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
5184 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.010 (+0.618...+0.638) |
| Confidence Double: | ± 0.015 (+0.617...+0.647) |
| |
| Double Decision confidence: | 68.4% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 3 hours 40 minutes |
Modified Position #6
In modified position #6 we toss a real scare into the position, we've reverted to the original position but split the back checkers. While this is a clear improvement it isn't that big of an improvement. Since threes are already duped to hit it doesn't add any hitters/double hitters. What it does do is gain on shots to the blot you'd like to hit most gaining you the most ground in the race, lifting your opponent's slotted 5pt, and also slotting your best anchor should a hitting exchange ensue you can enter and anchor on that point killing your opponent's counterplay. This is only a guess, but I think if most people were shown all these positions this is one of the ones they'd incorrectly pass.
 
| is Player 2
score: 0
pip: 148 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-aa--AE-C---bDbA-cAcb---a-:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 64.08% (G: 32.29% B: 1.60%) |
| Opponent Winning Chances: | 35.92% (G: 8.23% B: 0.52%) |
| Double/Take |
| Player Winning Chances: | 64.45% (G: 32.99% B: 1.72%) |
| Opponent Winning Chances: | 35.55% (G: 8.17% B: 0.56%) |
| |
| Cubeless Equities |
| No Double: | +0.533 |
| Double: | +1.098 |
| |
| Cubeful Equities |
| No Double: | +0.694 (-0.098) |
| Double/Take: | +0.792 |
| Double/Drop: | +1.000 (+0.208) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.021 (+0.673...+0.714) |
| Confidence Double: | ± 0.029 (+0.762...+0.821) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 54 minutes 46 seconds |
Modified Position #7
Now we leave the back men split and lift the blot from the ace point and we still have a take! That seems like two big improvements and before studies of this sort I think I would have let this one go. It reinforces the idea that your opponent only has a two point board and you have no men in the air yet. There's a lot of scare factor but you have plenty of counterplay being up in the race, all your checkers in play, and your opponent only having a two point board.
| is Player 2
score: 0
pip: 152 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-aa--AE-C---bDbA-cAcc-----:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 67.20% (G: 31.53% B: 1.96%) |
| Opponent Winning Chances: | 32.80% (G: 7.01% B: 0.44%) |
| Double/Take |
| Player Winning Chances: | 67.25% (G: 32.41% B: 2.20%) |
| Opponent Winning Chances: | 32.75% (G: 7.11% B: 0.48%) |
| |
| Cubeless Equities |
| No Double: | +0.604 |
| Double: | +1.230 |
| |
| Cubeful Equities |
| No Double: | +0.796 (-0.145) |
| Double/Take: | +0.942 |
| Double/Drop: | +1.000 (+0.058) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.026 (+0.771...+0.822) |
| Confidence Double: | ± 0.033 (+0.908...+0.975) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 56 minutes 13 seconds |
Modified Position #8
Back to the blot on the ace point and now we split the back checkers to the 22pt instead of the earlier 23pt. What is going on here is should be obvious to you. Before twos were something you didn't want to see, now with the back checkers split to the 22pt you've diversified your numbers and have a much more powerful position. [11 22 33 44 21 31 41 61 32 42 62 43 63 64] or 24 numbers now hit two blots as opposed to 'only' 16 in the original position. The rest of the non hitting numbers still play quite well with the hit and covers or hit and make another inside point etc...
| is Player 2
score: 0
pip: 147 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-a-a-AE-C---bDbA-cAcb---a-:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 66.71% (G: 35.67% B: 1.91%) |
| Opponent Winning Chances: | 33.29% (G: 7.73% B: 0.51%) |
| Double/Take |
| Player Winning Chances: | 66.68% (G: 36.94% B: 1.93%) |
| Opponent Winning Chances: | 33.32% (G: 8.06% B: 0.56%) |
| |
| Cubeless Equities |
| No Double: | +0.628 |
| Double: | +1.272 |
| |
| Cubeful Equities |
| No Double: | +0.804 (-0.188) |
| Double/Take: | +0.992 |
| Double/Drop: | +1.000 (+0.008) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
2592 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.014 (+0.790...+0.818) |
| Confidence Double: | ± 0.020 (+0.971...+1.012) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 78.7% |
| |
| Duration: 1 hour 49 minutes |
Modified Position #9
Modified Position #9 reaffirms what we thought when comparing the split from the 23pt to the 22pt. The overriding factor is that the 22pt split is the strongest because it gives good twos to play. There are other minor changes that could still be made to our original position but I'm capped out for now.
| is Player 2
score: 0
pip: 146 | | Money session | pip: 144
score: 0
is Player 1 |
|
| XGID=-a--aAE-C---bDbA-cAcb---a-:0:0:-1:00:0:0:0:0:10 |
| on roll, cube action? |
| Analyzed in Rollout |
| No Double |
| Player Winning Chances: | 64.80% (G: 33.14% B: 1.66%) |
| Opponent Winning Chances: | 35.20% (G: 8.12% B: 0.61%) |
| Double/Take |
| Player Winning Chances: | 65.05% (G: 34.00% B: 1.75%) |
| Opponent Winning Chances: | 34.95% (G: 8.18% B: 0.68%) |
| |
| Cubeless Equities |
| No Double: | +0.557 |
| Double: | +1.140 |
| |
| Cubeful Equities |
| No Double: | +0.710 (-0.122) |
| Double/Take: | +0.832 |
| Double/Drop: | +1.000 (+0.168) |
| |
| Best Cube action: Double / Take |
| |
| Rollout details |
1296 Games rolled with Variance Reduction.
Dice Seed: 1296
Moves and cube decisions: 3 ply |
| |
| Confidence No Double: | ± 0.020 (+0.690...+0.730) |
| Confidence Double: | ± 0.029 (+0.803...+0.861) |
| |
| Double Decision confidence: | 100.0% |
| Take Decision confidence: | 100.0% |
| |
| Duration: 1 hour 00 minute |