Carlton has won 16 Grand Finals.
Although Essendon has also won 16 premierships, it has won only 14 grand finals in this achievement. The premierships of 1897 and 1924 were decided by a round robin finals series and no grand final was played in those years.
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Someone may correct me, but I believe Essendon has that trophy. 24consecutive games. Not sure on the date - I was in high school when it happened - so 1997???maybe...?!