The most played game: a drawing line
The most played game in the TWIC database (issues 920 to 1438, containing about 1.8 million tournament games) is the following one, which appears 111 times. I add also a variation of the same (a change in move order) that is the second most played game (87 times). A couple of variations ending a move earlier or a move later also are amongst the most played games, with 38 and 39 repetitions respectively.
[FEN ""]
1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.O-O Nxe4 5.d4 Nd6 6.dxe5 Nxb5 7.a4 Nbd4 8.
Nxd4 Nxd4 ( 8...d5 9.exd6 Nxd4 10.Qxd4 Qxd6 11.Qe4+ Qe6 12.Qd4 Qd6 13.Qe4+
Qe6 14.Qd4 Qd6 {2nd most played game, 87 times} ) 9.Qxd4 d5 10.exd6 Qxd6
11.Qe4+ Qe6 12.Qd4 Qd6 13.Qe4+ Qe6 14.Qd4 {15th most played game, 38 times
} 14...Qd6 {Most played game, 111 times} ( 14...Qd6 15.Qe4+ {14th most
played game, 39 times} ) 1/2-1/2
How I found the answer
In case anyone is interested, I used a custom made script to parse the games in pgn format and extract the movetext section (the section containing the actual moves and result).
After saving the results as a dataframe in R, I grouped the data by the column movetext (equal games are grouped together), calculated the number of times for each game and sorted in decreasing order:
games <- mdata %>% group_by(movetext) %>%
summarise(n_times = n()) %>% arrange(desc(n_times))
And I only took into account the games where there was at least one move by each of the players. Otherwise, the most played game would be "0-1", black wins because white didn't show up, followed by "1.e4 1-0", white wins because black didn't show up.
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" in SE.