Home * Engine Testing * Match Statistics * LOS Table

After a tournament between two engines is over one can deduct the likelihood of superiority ^[1] 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 ^[2]

References

1. ^ Likelihood of superiority by Marco Costalba, CCC, November 15, 2009
2. ^ Type I and type II errors from Wikipedia

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