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54D 33
Posted By: Nack Ballard In Response To: 54D 33 (Timothy Chow)
Date: Wednesday, 11 November 2009, at 9:02 p.m.
36-ing Technique (54D-33) For 54D-33 (money), the long Gnu rollout you know about is [E B6 A16 C16] rounded. I also have a long Snowie rollout, [E B1 A16 C25]. The bot average is [E B4 A16 C21].
[Nacbrac translation: Error sizes are in thousandths. So, E (Each, 24/21(2) 6/3(2)) is best, B (Both, 24/21(2) 13/10(2)) is -.004, A (Attack, 8/5(2) 6/3(2)) is -.016, and C (Cross, 24/21(2) 8/5(2)) is -.021.]
Below is a method of comparing plays that I call “36-ing.” It employs the Dice 36 function of Snowie to display the equities of each of White’s rolls after she opens with 54D and Black replies with each of the plays you addressed: 33B, 33E and 33C. [Please forgive my inexperience creating HTML tables: the header dots are space fillers and I don't know how to right-align columns.]
Each of the first three columns not counting the Roll column) are derived from separate Dice 36 punches on Snowie 1-ply. (3-ply is more accurate but often buggy; 1-ply is good enough for our purposes.) [Perhaps similar data is derivable from Gnu's temperature map; I haven’t checked.]
Equities, shown in thousandths, have been cut in half (and rounded towards zero) for doublets; e.g., if White rolls 44 after Black has played E, her equity is .143, but this is cut in half and the decimal point omitted, producing the upper left table entry of 71.
The purpose of the table is to compare not only the strengths but also the swings of the rolls. The three right-hand columns show the difference between the rolls’ equities for two given plays. For example, in the 44 row under “E-B” (E minus B), the difference is shown for White rolling double 4s. For this case, White is better off by 28 (i.e., .028) versus E rather than B, which conversely means that Black is better off by 28 having played B (emerging with the 10pt in front of White’s 20pt anchor) rather than E (with his 3pt behind the anchor). On the other hand, C easily beats both E and B (by 143 and 115 respectively, even after being cut in half for the doublet factor) because it prevents White’s 24pt checkers from moving.
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Roll.... .E..... .B..... .C............. E-B... E-C... B-C 44 71 43 -72 28 143 115 66 49 43 57 6 -8 -14 33 25 -1 21 26 4 -22 11 -12 -2 -19 -10 7 17 41 -104 -102 -121 -2 17 19 43 -112 -116 7 4 -105 -123 31 -131 -112 -154 -19 23 42 65 -134 -142 -151 8 17 9 64 -139 -126 -160 13 21 34 21 -153 -155 -190 2 37 35 22 -80 -30 -22 -50 -58 -8 54 -168 -186 -233 18 65 47 62 -190 -180 -217 -10 27 37 63 -192 -188 -224 4 32 36 61 -198 -196 7 2 -191 -203 55 -108 -98 -120 -10 12 22 42 -218 -146 -140 -72 -78 -6 51 -222 -258 -307 36 85 59 53 -255 -230 -277 -25 22 47 52 -257 -261 7 4 -250 -268 32 -278 -265 -284 -13 6 19
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Obviously, Black loses a lot if he plays C (instead of B or E) and gets hit. The far right two columns of the 43, 61 and 52 rows of the table show how much at a glance: they’re the only negative three-digit numbers. (Of the three rolls, 43 costs C the least because White can blotlessly make her 5pt when she can’t hit, and 52 costs C the most because there is otherwise no constructive use for the roll.) Most of the time that White rolls a non-7, Black’s superior 5pt or zone-boosting 10pt (made by the C or B play) gains over the 3pt (made by E); however, the cost of White’s 7s (with Black's comeback 5s duplicated) is enough to put C solidly behind B and E overall.
Combing through the right-hand columns can provide insights you might not easily conjure on your own. For example, White's roll of 42 best isolate's the strength of Black's E play: relatively, B loses 72 and C loses 78. Making the 3pt prevents White from splitting with a 2; if she covers her 9pt with the 4, she has to either play 8/6 (stripping her 8pt and stacking six checkers on her 6pt) or break her midpoint. Her least of evils is 24/20 13/7, but clearly White suffers for being finessed out of her 9pt.
I hope that helps (or is at least interesting). Primarily in this post, rather than “solve” the 54D-33 play decision, I'm demonstrating a method by which you can examine rolls in detail and build that into more general conclusions about the plays. To gain further insights, you can create similar tables for related positions (e.g., 51$-33, where C tops A, B and E, or 41$-33 where E and C are suddenly tied, or 52D-33 where C, B and E are close though A crushes them all) and cross-compare. In writing pages for my books, I sometimes resort to 36-ing when the explanation for some play being preferable in one position and not another might otherwise elude me.
Nack
- 54D 33
Timothy Chow -- Wednesday, 11 November 2009, at 2:58 a.m.
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