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A Go endgame database consists of optimal game values and moves for every legal arrangement of no more than S pieces on an N by N board. This paper describes methods for constructing such databases when 1 < N ≤ 5 and S = N 2 . When cycles of plies with lengths greater than 4 are encountered, two rules, one allowing cycles and the other disallowing them, are implemented. Observations and knowledge are obtained for these endgames, which may elucidate the fundamental properties of the popular game Go. First, the optimal game values are different when N is even and odd, regardless of whether the repetition of positions is allowed. When N is odd, the first player can occupy the whole board, while this is not the case when N is even. Second, allowing cycles makes the first and second players equal in strength when N is even, whereas the first player always dominates when N is odd. Using the state-of-the-art open-source deep learning Go engine KataGo to correctly solve a given position as an indicator, factors affecting level of difficulty are found, including the distributions of the optimal game values among all legal plies and the cardinality and values of the true optimal plies. A simple formula is designed that works on more than 10% of the positions so that positions with a given level of difficulty can be found with a high probability.
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BACKGROUND: The need for patients to wear compression stockings after varicose vein surgery and the duration of compressions tocking therapy has been debated. This study isa meta-analysis of randomized controlled trials (RCTs) to determine the optimal duration of compression stocking therapy after endovenous thermal ablation (ETA) of the great saphenous vein. METHODS: The PubMed, Embase, and Cochrane Library databases were searched before January 2019. Individual effect sizes were standardized, and a meta-analysis was conducted to calculate the pooled effect size by using a random effects model. The primary outcome was the severity of pain in the postoperative period. Secondary outcomes were quality of life (QoL), leg volume, bruising scores, consumptionof analgesic agents, recovery time off work, satisfaction, and the incidence rates of postoperative complications including paresthesia and phlebitis. RESULTS: Five RCTsinvolving775 patients were reviewed. The long-duration (1-2 weeks) group significantly reduced postoperative pain at 1 week (mean difference [MD] 1.19; 95% confidence interval [CI]: 0.58-1.80) and recovery time off work (MD: 1.01 day, 95% CI: 0.06-1.96)when compared with the short-duration (24-48â¯h) group. However, the mean pain scores at 2 (0.1; 95% CI: 0-0.2) and 6 weeks postoperatively (-0.3; 95% CI: -1.09-0.49) did not differ significantly between the two groups. Moreover, the incidence rates of complication, paresthesia, and phlebitis did not differ significantly between the short-duration and long-duration groups. CONCLUSION: The use of compression therapy for a long time (1-2 weeks) is better than short-term (24-48â¯h) use in terms of postoperative pain at 1 week and recovery off work. Hence, we recommend the prescription of 1-week compression stocking therapy after ETA in routine clinical practice. However, the available evidence is of variable quality, further well-structured RCTs with improved standardization of compression treatment, types of stockings, and target populations are warranted.