A few days ago, Neil posted an XG 4-ply rollout of 65R-54S-62, which will be integrated into this post.
Timothy Chow wrote: Now I'm curious to see money rollouts for 65R-43Z-54 and 65R-52S-64. Anybody already done these?
The second of those (65R-52S-64) seems obvious to me, but I rolled out the first (65R-43Z-54) plus some related positions. I've only had time to do 1k or 2k Snowie truncated rollouts (which are faster and a lot more reliable than 1k full rollouts). Perhaps these will spark the curiosity of someone who has more available CPU and he'll do long full rollout(s) of the close position(s).
I am covering positions (for money) where the following occurs on rolls 1, 2 and 3 of the game:
(1) Blue runs with 65.
(2) White makes a common split response with a 4, 3 or 2.
(3) Blue rolls an 8, 9 or 10, with a choice of running or hitting inside from the midpoint.
Those six positions are diagrammed below with the result in nacbracs, followed by "tr" (for truncated). In the one case where a full rollout (Neil's, 7k) has been done, it is also included. When no rollout has been done, "ev" (for evaluation) follows the brackets.
On the third roll, when Blue rolls an 8, it is best to use 53 for the rollout instead of 62, because Blue has more options: the result conveys more useful information. Likewise with 54 versus 63. Nevertheless, I have included the twin situations (with 62 instead of 53, and with 63 instead of 54) as right-hand diagrams, for reference. [That is, the results captioned in the right-hand diagrams feed from the results captioned in the left-hand diagrams.]
Note that the one full result we have likes running by 17 (compared to hitting) more than the trunc result. Part may be due to variance (7k full, 1k trunc), but let's say that 10 of the 17 is due to a trunc bias. That suggests that perhaps all the H/R (or R/H) margins should be adjusted by about 10 (i.e., .010) -- running is a bit better than the truncs indicate.
To get the most out of this post, you can test yourself by covering the caption beneath each diagram (or scroll just far enough that it is not quite revealed), choose your play, then compare your answer to the result shown in the caption. Sometimes a third play is better than running or hitting.
Nactation key: R = Run, H = Hit, P = Point, S = Split (Up and down), K = Kill (hit twice).
Error sizes are listed in thousandths. For example, [H P12 R20] would mean that H (hit) is best, P (point) is -.012, and R (run) is -.020.
Nactation key: R = Run, H = Hit, P = Point, S = Split (Up and down), K = Kill (hit twice).
Error sizes are listed in thousandths. For example, [R H77 P98] means that R (run) is best, H (hit) is -.077, and P (point) is -.098.
Which plays did you get wrong? Were there plays that you thought should have been close but weren't? Vice versa?
For reference, below are the second roll position equivalents, where Blue has not yet run with 65. (All results are full rollouts of at least 5k.)
Conclusion: For money, when Blue has run with 65, White has split with a 4, 3 or 2, and Blue rolls an 8, 9 or 10, running is better than hitting (though making a point is better than either with 53). Exception: 65R-43S-62 (or 53), hitting is better than running.
If Blue hasn't run with 65 (i.e., the second roll positions), he should hit from the midpoint (even better than making a point).
What other conclusions can you make from comparing two or more of the (left-hand) position results?
Nack
