LOS+Table

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After a tournament between two engines is over one can deduct the likelihood of superiority of one engine over the other by consulting the following table. The first column gives the score difference (wins - losses), the next columns give the LOS for a certain number of games. The table was calculated for a draw ratio of 32%.

=Table=
 * ~  ||~ 10 ||~ 50 ||~ 100 ||~ 200 ||~ 500 ||~ 1000 ||
 * ~ 0 ||= 50.00% ||= 50.00% ||= 50.00% ||= 50.00% ||= 50.00% ||= 50.00% ||
 * ~ 1 ||= 64.51% ||= 56.77% ||= 54.81% ||= 53.41% ||= 52.16% ||= 51.53% ||
 * ~ 2 ||= 77.22% ||= 63.34% ||= 59.55% ||= 56.80% ||= 54.32% ||= 53.06% ||
 * ~ 3 ||= 86.95% ||= 69.55% ||= 64.16% ||= 60.14% ||= 56.46% ||= 54.58% ||
 * ~ 4 ||= 93.43% ||= 75.24% ||= 68.57% ||= 63.40% ||= 58.58% ||= 56.09% ||
 * ~ 5 ||= 97.14% ||= 80.32% ||= 72.73% ||= 66.57% ||= 60.68% ||= 57.60% ||
 * ~ 6 ||= 98.95% ||= 84.71% ||= 76.60% ||= 69.63% ||= 62.75% ||= 59.10% ||
 * ~ 7 ||= 99.68% ||= 88.40% ||= 80.14% ||= 72.55% ||= 64.78% ||= 60.58% ||
 * ~ 8 ||= 99.93% ||= 91.41% ||= 83.34% ||= 75.33% ||= 66.77% ||= 62.05% ||
 * ~ 9 ||= 99.99% ||= 93.80% ||= 86.19% ||= 77.96% ||= 68.72% ||= 63.50% ||
 * ~ 10 ||= 100.00% ||= 95.64% ||= 88.69% ||= 80.41% ||= 70.61% ||= 64.93% ||
 * ~ 11 ||=  ||= 97.02% ||= 90.85% ||= 82.69% ||= 72.45% ||= 66.34% ||
 * ~ 12 ||=  ||= 98.01% ||= 92.68% ||= 84.80% ||= 74.23% ||= 67.73% ||
 * ~ 13 ||=  ||= 98.71% ||= 94.23% ||= 86.72% ||= 75.95% ||= 69.09% ||
 * ~ 14 ||=  ||= 99.19% ||= 95.50% ||= 88.48% ||= 77.60% ||= 70.43% ||
 * ~ 15 ||=  ||= 99.50% ||= 96.54% ||= 90.06% ||= 79.19% ||= 71.74% ||
 * ~ 16 ||=  ||= 99.71% ||= 97.37% ||= 91.48% ||= 80.71% ||= 73.02% ||
 * ~ 17 ||=  ||= 99.83% ||= 98.03% ||= 92.74% ||= 82.16% ||= 74.27% ||
 * ~ 18 ||=  ||= 99.91% ||= 98.55% ||= 93.85% ||= 83.54% ||= 75.49% ||
 * ~ 19 ||=  ||= 99.95% ||= 98.94% ||= 94.82% ||= 84.85% ||= 76.68% ||
 * ~ 20 ||=  ||= 99.97% ||= 99.24% ||= 95.67% ||= 86.08% ||= 77.84% ||
 * ~ 21 ||=  ||= 99.99% ||= 99.46% ||= 96.41% ||= 87.25% ||= 78.96% ||
 * ~ 22 ||=  ||= 99.99% ||= 99.62% ||= 97.03% ||= 88.35% ||= 80.05% ||
 * ~ 23 ||=  ||= 100.00% ||= 99.74% ||= 97.57% ||= 89.38% ||= 81.11% ||
 * ~ 24 ||=  ||=   ||= 99.82% ||= 98.02% ||= 90.34% ||= 82.12% ||
 * ~ 25 ||=  ||=   ||= 99.88% ||= 98.40% ||= 91.23% ||= 83.11% ||
 * ~ 26 ||=  ||=   ||= 99.92% ||= 98.71% ||= 92.07% ||= 84.06% ||
 * ~ 27 ||=  ||=   ||= 99.95% ||= 98.97% ||= 92.84% ||= 84.97% ||
 * ~ 28 ||=  ||=   ||= 99.97% ||= 99.18% ||= 93.55% ||= 85.85% ||
 * ~ 29 ||=  ||=   ||= 99.98% ||= 99.36% ||= 94.21% ||= 86.69% ||
 * ~ 30 ||=  ||=   ||= 99.99% ||= 99.50% ||= 94.81% ||= 87.50% ||
 * ~ 31 ||=  ||=   ||= 99.99% ||= 99.61% ||= 95.36% ||= 88.27% ||
 * ~ 32 ||=  ||=   ||= 100.00% ||= 99.70% ||= 95.86% ||= 89.01% ||
 * ~ 33 ||=  ||=   ||=   ||= 99.77% ||= 96.32% ||= 89.71% ||
 * ~ 34 ||=  ||=   ||=   ||= 99.82% ||= 96.74% ||= 90.38% ||
 * ~ 35 ||=  ||=   ||=   ||= 99.87% ||= 97.11% ||= 91.02% ||
 * ~ 36 ||=  ||=   ||=   ||= 99.90% ||= 97.45% ||= 91.62% ||
 * ~ 37 ||=  ||=   ||=   ||= 99.93% ||= 97.76% ||= 92.20% ||
 * ~ 38 ||=  ||=   ||=   ||= 99.95% ||= 98.03% ||= 92.74% ||
 * ~ 39 ||=  ||=   ||=   ||= 99.96% ||= 98.28% ||= 93.26% ||
 * ~ 40 ||=  ||=   ||=   ||= 99.97% ||= 98.50% ||= 93.74% ||
 * ~ 41 ||=  ||=   ||=   ||= 99.98% ||= 98.69% ||= 94.20% ||
 * ~ 42 ||=  ||=   ||=   ||= 99.98% ||= 98.86% ||= 94.63% ||
 * ~ 43 ||=  ||=   ||=   ||= 99.99% ||= 99.02% ||= 95.04% ||
 * ~ 44 ||=  ||=   ||=   ||= 99.99% ||= 99.15% ||= 95.42% ||
 * ~ 45 ||=  ||=   ||=   ||= 99.99% ||= 99.27% ||= 95.78% ||
 * ~ 46 ||=  ||=   ||=   ||= 100.00% ||= 99.37% ||= 96.11% ||
 * ~ 47 ||=  ||=   ||=   ||=   ||= 99.46% ||= 96.42% ||
 * ~ 48 ||=  ||=   ||=   ||=   ||= 99.54% ||= 96.72% ||
 * ~ 49 ||=  ||=   ||=   ||=   ||= 99.61% ||= 96.99% ||
 * ~ 50 ||=  ||=   ||=   ||=   ||= 99.67% ||= 97.24% ||
 * ~ 51 ||=  ||=   ||=   ||=   ||= 99.72% ||= 97.47% ||
 * ~ 52 ||=  ||=   ||=   ||=   ||= 99.76% ||= 97.69% ||
 * ~ 53 ||=  ||=   ||=   ||=   ||= 99.80% ||= 97.89% ||
 * ~ 54 ||=  ||=   ||=   ||=   ||= 99.83% ||= 98.08% ||
 * ~ 55 ||=  ||=   ||=   ||=   ||= 99.86% ||= 98.25% ||
 * ~ 56 ||=  ||=   ||=   ||=   ||= 99.88% ||= 98.41% ||
 * ~ 57 ||=  ||=   ||=   ||=   ||= 99.90% ||= 98.56% ||
 * ~ 58 ||=  ||=   ||=   ||=   ||= 99.92% ||= 98.69% ||
 * ~ 59 ||=  ||=   ||=   ||=   ||= 99.93% ||= 98.82% ||
 * ~ 60 ||=  ||=   ||=   ||=   ||= 99.94% ||= 98.93% ||
 * ~ 61 ||=  ||=   ||=   ||=   ||= 99.95% ||= 99.03% ||
 * ~ 62 ||=  ||=   ||=   ||=   ||= 99.96% ||= 99.13% ||
 * ~ 63 ||=  ||=   ||=   ||=   ||= 99.97% ||= 99.22% ||
 * ~ 64 ||=  ||=   ||=   ||=   ||= 99.97% ||= 99.29% ||
 * ~ 65 ||=  ||=   ||=   ||=   ||= 99.98% ||= 99.37% ||
 * ~ 66 ||=  ||=   ||=   ||=   ||= 99.98% ||= 99.43% ||
 * ~ 67 ||=  ||=   ||=   ||=   ||= 99.99% ||= 99.49% ||
 * ~ 68 ||=  ||=   ||=   ||=   ||= 99.99% ||= 99.54% ||
 * ~ 69 ||=  ||=   ||=   ||=   ||= 99.99% ||= 99.59% ||
 * ~ 70 ||=  ||=   ||=   ||=   ||= 99.99% ||= 99.64% ||
 * ~ 71 ||=  ||=   ||=   ||=   ||= 99.99% ||= 99.68% ||
 * ~ 72 ||=  ||=   ||=   ||=   ||= 100.00% ||= 99.71% ||
 * ~ 73 ||=  ||=   ||=   ||=   ||=   ||= 99.74% ||
 * ~ 74 ||=  ||=   ||=   ||=   ||=   ||= 99.77% ||
 * ~ 75 ||=  ||=   ||=   ||=   ||=   ||= 99.80% ||
 * ~ 76 ||=  ||=   ||=   ||=   ||=   ||= 99.82% ||
 * ~ 77 ||=  ||=   ||=   ||=   ||=   ||= 99.84% ||
 * ~ 78 ||=  ||=   ||=   ||=   ||=   ||= 99.86% ||
 * ~ 79 ||=  ||=   ||=   ||=   ||=   ||= 99.88% ||
 * ~ 80 ||=  ||=   ||=   ||=   ||=   ||= 99.89% ||
 * ~ 81 ||=  ||=   ||=   ||=   ||=   ||= 99.91% ||
 * ~ 82 ||=  ||=   ||=   ||=   ||=   ||= 99.92% ||
 * ~ 83 ||=  ||=   ||=   ||=   ||=   ||= 99.93% ||
 * ~ 84 ||=  ||=   ||=   ||=   ||=   ||= 99.94% ||
 * ~ 85 ||=  ||=   ||=   ||=   ||=   ||= 99.94% ||
 * ~ 86 ||=  ||=   ||=   ||=   ||=   ||= 99.95% ||
 * ~ 87 ||=  ||=   ||=   ||=   ||=   ||= 99.96% ||
 * ~ 88 ||=  ||=   ||=   ||=   ||=   ||= 99.96% ||
 * ~ 89 ||=  ||=   ||=   ||=   ||=   ||= 99.97% ||
 * ~ 90 ||=  ||=   ||=   ||=   ||=   ||= 99.97% ||
 * ~ 91 ||=  ||=   ||=   ||=   ||=   ||= 99.98% ||
 * ~ 92 ||=  ||=   ||=   ||=   ||=   ||= 99.98% ||
 * ~ 93 ||=  ||=   ||=   ||=   ||=   ||= 99.98% ||
 * ~ 94 ||=  ||=   ||=   ||=   ||=   ||= 99.98% ||
 * ~ 95 ||=  ||=   ||=   ||=   ||=   ||= 99.99% ||
 * ~ 96 ||=  ||=   ||=   ||=   ||=   ||= 99.99% ||
 * ~ 97 ||=  ||=   ||=   ||=   ||=   ||= 99.99% ||
 * ~ 98 ||=  ||=   ||=   ||=   ||=   ||= 99.99% ||
 * ~ 99 ||=  ||=   ||=   ||=   ||=   ||= 99.99% ||
 * ~ 100 ||=  ||=   ||=   ||=   ||=   ||= 99.99% ||
 * ~ 101 ||=  ||=   ||=   ||=   ||=   ||= 99.99% ||
 * ~ 102 ||=  ||=   ||=   ||=   ||=   ||= 100.00% ||

=Forum Posts=
 * [|Likelihood of superiority] by Marco Costalba, CCC, November 15, 2009
 * [|LOS calculation: Does the same result is always the same?] by Marco Costalba, CCC, October 01, 2012
 * [|LOS (again)] by Ed Schröder, CCC, October 30, 2012
 * [|Fast LOS estimation] by Gary, CCC, February 18, 2013
 * [|LOS] by BB+, OpenChess Forum, March 31, 2013
 * [|Type I error in LOS based early stopping rule] by Kai Laskos, CCC, August 06, 2013

=References= =What links here?= include page="LOS Table" component="backlinks" limit="20"
 * Up one level**