                       |
| ||||
| XGID=aABBBBC-----b---bc-cCb-b--:1:-1:1:23:0:0:3:0:10 | |||||
Variant 1 (White's 3pt blot is gone -- now a 6pt spare) | |||||
| 1. | Rollout1 | 6/1 | eq: +0.879 | |||
| ||||||
| 2. | Rollout1 | 20/15 | eq: +0.644 (-0.235) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller | ||||||
 |
| ||||
| XGID=aABBBBC-----b---bc-bCb-ba-:1:-1:1:32:0:0:3:0:10 | |||||
Variant 2 (White's 3pt blot is on her 1pt) | |||||
| 1. | Rollout1 | 6/1 | eq: +0.945 | |||
| ||||||
| 2. | Rollout1 | 20/15 | eq: +0.875 (-0.070) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller | ||||||
Consider Variants 1 and 2 above (side by side, if your window is wide). These are the same as the original PBA-article position that David posted (see rollout below), except that White's 3pt checker has been moved.
Unfortunately, some players don't pay attention unless they see a contrasting results that swings which move is better (i.e., it happens to cross the zero threshold). But IMO they should. For purposes of improving one's intuition about the impact of a factor or factors in a position, there is as much to learn from a play that goes from +.140 to +.236 (original vs Variant 1) as there is from a play that goes from (say) –.050 to +.046, and there is as much to learn from a play that goes from +.140 to +.070 (original vs Variant 2) as there is from a play that goes from (say) +.035 to –.035.
Doc BG, the author of the PBA article, stated: "White's imperfect board is a key factor in mitigating the risk of White's ace shot." Doc BG is both right and astute to point out this valuable criterion! If the blot alone doesn't exist, the margin moves by a whopping .096. Conversely, if the location of the blot is worsened, the margin moves the other way by .070.
An idiomatic expression that applies fairly well is: "Don't throw the baby out with the bath water."
For the remaining diagrams in this post, except for one, I'll leave White's blot where it is (on her 3pt).
|
| ||||
| XGID=aABBBBC-----b---bc-bCbab--:1:-1:1:32:0:0:3:0:10 | |||||
ORIGINAL Position | |||||
| 1. | Rollout1 | 6/1 | eq: +0.911 | |||
| ||||||
| 2. | Rollout1 | 20/15 | eq: +0.771 (-0.140) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 95623456 Moves: 3-ply, cube decisions: XG Roller | ||||||
The original position is shown above. If Blue covers with 6/1, he will subsequently crack his board with 14 numbers (as many have noted). If Blue runs with 20/15 (and White fans), he will crack next roll with only 1 number (though he will also fail to close his board with an additional 20 numbers).
Next, consider Variant 3 below, where White's (three-stack on the) 8pt has been backed up to her 11pt. I believe that some players, even in modern times (or dare I say "especially" in modern times?), would get Blue's play wrong OTB.
Compared to the original position (above), after Blue closes his board he has (19.5 – 14 =) 5.5 additional cracking numbers (counting the status-quo 66 as a half-number). Clearly, the correct count is important; a comparison of the rollout results (above vs below) suggest that each cracking number affects the checker play margin by .037 (in this position).
 |
| ||||
| XGID=aABBBBC-----b-c-b--bCbab--:1:-1:1:32:0:0:3:0:10 | |||||
Variant 3 (White owns 11pt instead of 8pt) | |||||
| 1. | Rollout1 | 20/15 | eq: +0.850 | |||
| ||||||
| 2. | Rollout1 | 6/1 | eq: +0.786 (-0.063) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller | ||||||
But WAIT! Do you remember Doc BG's comment? "White's imperfect board is a key factor in mitigating the risk of White's ace shot." Let's duplicate Variant 4, except for White's board. And we won't even perfect it. All we'll do is to get rid of White's 3pt blot (the same way we did in Variant 1 compared to the Original). The 19.5 cracking numbers (the ones that I suspect some readers may declare would have correctly led them to the running play in Variant 4) still exist in Variant 5 below, and yet Blue should NOT run.
|
| ||||
| XGID=aABBBBC-----b-c-b--cCb-b--:1:-1:1:32:0:0:3:0:10 | |||||
Variant 4 (same as Var. 3 above, except White has no 3pt blot) | |||||
| 1. | Rollout1 | 6/1 | eq: +0.715 | |||
| ||||||
| 2. | Rollout1 | 20/15 | eq: +0.664 (-0.051) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller | ||||||
If you endeavored to study the margin difference of .096 between Variant 1 and the original position (even though it didn't toggle the better play), you were better equipped to predict (or intuit) the margin difference of .114 between Variant 3 and Variant 4, and therefore better equipped to choose the better play in each position.
Giving White the 3pt with 11/3 (instead of taking away the blot with 3/6) creates an even bigger contrast with Variant 3. (According to the rollout, not shown, 6/1 is best by .200 when White owns her 3pt, which means the swing in margin increases to .251.)
Next, you are about to witness a pair of positions with a startling contrast. (Necessarily, the roll is changed from 32 to 41, but it doesn't materially affect the problem.) The two positions can be viewed side by side, if your window is wide.
Variant 5 is the same as the original checker position (two diagrams ago), except White's 9pt is nudged back to her 10pt. Variant 6 is the same as Variant 5 except White's 13pt is nudged forward to her 12pt. In short, the only difference between the two positions below is 13/12(2).
 |
| ||||
| XGID=aABBBBC-----b--b-c-bCbab--:1:-1:1:41:0:0:3:0:10 | |||||
Variant 5 (White owns her 13pt) | |||||
| 1. | Rollout1 | 6/1 | eq: +0.865 | |||
| ||||||
| 2. | Rollout1 | 20/16 6/5 | eq: +0.757 (-0.108) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 95623456 Moves: 3-ply, cube decisions: XG Roller | ||||||
|
| ||||
| XGID=aABBBBC------b-b-c-bCbab--:1:-1:1:41:0:0:3:0:10 | |||||
Variant 6 (White owns her 12pt) | |||||
| 1. | Rollout1 | 20/16 6/5 | eq: +0.678 | |||
| ||||||
| 2. | Rollout1 | 6/1 | eq: +0.623 (-0.055) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller | ||||||
The two positions above look nearly identical, but the cracked-number count (after Blue's 6/1) is 16 vs 21 numbers. The difference is that 44 is blocked solely in Variant 5, whereas all sevens (61 52 43) are blocked solely in Variant 6.
Finally, Variant 7 (below) is an offshoot of Variant 6. The checker position is exactly the same but the roll has been changed back to 32. So what? The cracked-number count is still 21.
The problem is that that the roll of 32 is miles worse than the roll of 41. After 32E (20/18 6/3) is played below, the 18pt checker is still partially trapped and the blocked numbers (5s, 3s and 1s) are annoyingly duplicated. On the following roll, 11 numbers (vs 1) still crack, and only 5 numbers (vs 11) close the board. As a consequence, the partial-running play goes from +.055 to –.223!
Variant 7 is included in order to demonstrate that it can also be worthwhile to take into account residual cracking, though it is an extreme case.
Nack
|
| ||||
| XGID=aABBBBC------b-b-c-bCbab--:1:-1:1:32:0:0:3:0:10 | |||||
Variant 7 (Roll is 32 instead of 41) | |||||
| 1. | Rollout1 | 6/1 | eq: +0.623 | |||
| ||||||
| 2. | Rollout1 | 20/18 6/3 | eq: +0.400 (-0.223) | |||
| ||||||
| 1 5184 Games rolled with Variance Reduction. Dice Seed: 51521755 Moves: 3-ply, cube decisions: XG Roller | ||||||