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Qarey Quiz -- Summary

Posted By: Nack Ballard
Date: Monday, 16 July 2018, at 4:59 a.m.

Kudos to Steven Carey for his admirable work ethic. (I knew what he was doing but I didn't want to give it away.) I've analyzed all these positions before, and written on some, but I've done little exploration of match score cusps. Steven's rollouts he posted are surely just the tip of the iceberg, as he must have tried many other rollouts in the quest to find cusps (or the best cusps).

All his rollouts represented below are 46k trials if result is close (else only 3k), 3-ply checker, 4-ply cube. Nacbracs are in red. The first nacbracs is always at -11-11 (what might be considered a "normal" match score). The second nacbracs, where the result is very tied (second best play is within .000, .001 or .002), is at the score listed.

By nacbracs implication, I've rounded to three decimals. I'm mostly not good enough to make use of the fourth decimal place; it only clutters my brain.

The fourth column is included only for completeness, and you would probably do well to ignore it. The value is knowing that at the score it is a "cusp," not in knowing which play happens to be a tiny bit better.

For example, look at row 1: At a normal score, P (Point, 9/5 6/5) beats @ (anchor 24/20 23/20) by .013, whereas the plays are tied if the score is adjusted to –5–9 ("need 5, need 9").

.....–11–11 score..........................Cusp score

.....43Z-61P-41 [P @13]............ –5–9 [P @1]
.....41S-21S-43 [@ P74]............–11–6 [@ P1]
.....43S-42P-31 [@ P45]............–11–6 [P=@]
.....54S-42P-31 [P @9].............–10–11 [@ P1]
.....62S-31P-61 [B P76].............–11–4 [B=P]
.....52S-51S-42 [@ P28]............–11–6 [P @1]
.....52S-66P-31 [@ P68]............–11–4 [@ P1]
.....41S-31P-21 [P @22]............–5–11 [P @1]
.....41S-42P-21 [P @20]............–11–3 [@ P1]
.....41S-62H-54 [H @28]...........–4–11 [@ H2]
.....62S-54S-42 [@ P11]............–11–6 [P @2]
.....42P-65R-53 [S P11]..............–9–3 [S=P]
.....31P-65R-61 [P E28].............–3–11 [P E1]
.....43D-31P-65 [R P9]...............–9–11 [R=P]
.....43D-42P-65 [P R47].............–3–11 [R=P]
.....31P-54D-32 [S D10 $10].......–9–7 [S=$ D2 Z11]

Nactation Key: @ (or B) = anchor, D = Down, E = Each, H = Hit, P = Point, R = Run, S = Split, $ = Slot, Z = reverse split. Explanation of nacbracs.

In case anyone was confused, (#2) 41S-21S-43 was mismarked "41S-61P-43," and (#9) 41S-42P-21 was mismarked "31S-42P-21" in the answer posts.

Nack