Table 1.

Summary results for our comparison of algorithms

Algorithm	Round-Robin average	% Best score	Worst-case score	Replicator dynamic	Group-1 Tourney	Group-2 Tourney	Rank summary min–mean–max
S++	1, 1, 1	2, 1, 2	1, 1, 1	1, 1, 1	1, 1, 2	1, 1, 1	1–1.2–2
Manipulator	3, 2, 3	4, 3, 8	5, 2, 4	6, 4, 3	5, 3, 3	5, 2, 2	2–3.7–8
Bully	3, 2, 1	3, 2, 1	7, 13, 20	7, 3, 2	6, 2, 1	6, 3, 5	1–4.8–20
S++/simple	5, 4, 4	8, 5, 9	4, 6, 10	10, 2, 6	8, 4, 6	9, 4, 6	2–6.1–10
S	5, 5, 8	6, 7, 10	3, 3, 8	5, 5, 8	7, 5, 9	7, 5, 9	3–6.4–10
Fict. play	2, 8, 14	1, 6, 10	2, 8, 16	3, 12, 15	2, 8, 12	4, 9, 14	1–8.1–16
MBRL-1	6, 6, 10	5, 4, 7	8, 7, 14	11, 11, 13	9, 7, 10	8, 7, 10	4–8.5–14
EEE	11, 8, 7	14, 9, 5	9, 4, 2	14, 10, 9	13, 9, 8	13, 10, 8	2–9.1–14
MBRL-2	14, 5, 5	13, 8, 6	19, 5, 3	18, 9, 4	18, 6, 5	18, 6, 4	3–9.2–19
Mem-1	6, 9, 13	7, 10, 21	6, 9, 17	2, 6, 10	3, 10, 17	2, 8, 15	2–9.5–21
M-Qubed	14, 20, 4	15, 20, 3	15, 19, 5	17, 19, 5	17, 21, 4	16, 21, 3	3–13.2–21
Mem-2	9, 11, 20	9, 11, 22	13, 17, 22	4, 13, 19	4, 13, 25	3, 12, 20	3–13.7–25
Manip-Gf	11, 11, 21	12, 12, 19	12, 11, 19	9, 7, 20	12, 14, 20	11, 13, 21	7–14.2–21
WoLF-PHC	17, 11, 13	18, 14, 14	18, 14, 18	16, 14, 14	16, 11, 11	15, 11, 11	11–14.2–18
QL	17, 17, 7	19, 19, 4	17, 18, 7	19, 18, 7	19, 20, 7	19, 18, 7	4–14.4–20
gTFT	11, 14, 22	11, 15, 20	11, 16, 23	8, 8, 22	10, 16, 21	10, 15, 22	8–15.3–23
EEE/simple	20, 15, 11	20, 17, 12	20, 10, 9	20, 16, 11	24, 15, 14	20, 16, 13	9–15.7–24
Exp3	19, 23, 11	16, 23, 15	16, 23, 6	15, 23, 12	15, 25, 13	17, 25, 12	6–17.2–25
CJAL	24, 14, 14	25, 14, 13	24, 12, 15	24, 17, 16	20, 12, 16	22, 14, 16	12–17.3–25
WSLS	9, 17, 24	10, 16, 24	10, 20, 24	12, 20, 24	11, 17, 24	12, 17, 25	9–17.6–25
GIGA-WoLF	14, 19, 23	17, 18, 23	14, 15, 21	13, 15, 23	14, 18, 22	14, 19, 23	13–18.1–23
WMA	21, 21, 15	21, 21, 16	22, 21, 12	22, 21, 17	21, 19, 15	23, 20, 17	12–19.2–23
Stoch. FP	21, 21, 15	22, 22, 17	23, 22, 11	23, 22, 18	25, 24, 18	25, 22, 18	11–20.5–25
Exp3/simple	21, 24, 16	23, 24, 18	21, 24, 13	21, 24, 21	22, 22, 19	21, 23, 19	13–20.9–24
Random	24, 25, 25	24, 25, 25	25, 25, 25	25, 25, 25	23, 23, 23	24, 24, 24	23–24.4–25

This summary gives the relative rank of each algorithm with respect to each of the six performance metrics we considered, at each game length. A lower rank indicates higher performance. For each metric, the algorithms are ranked in 100-round, 1000-round, and 50,000-round games, respectively. For example, the 3-tuple 3, 2, 1 indicates the algorithm was ranked 3rd, 2nd, and 1st in 100, 1000, and 50,000-round games, respectively. More detailed results and explanations are given in Supplementary Note 3