It was acknowledged forty years after the release of "Tumbling Dice" that Miller played the last part of the song, right as the coda begins, because Watts was having trouble with it. "Tumbling Dice" was the only Rolling Stones song where Watts overdubbed a second drum track over the original, creating a bigger sound. In a retrospective article shortly after Watts' death, Ben Sisario wrote for The New York Times that Watts' backbeat gave "Tumbling Dice" a "languid strut".
The song's lyrical structure is irregular. While many songs have the same number of lines for the verse or chorus, the first verse of "Tumbling Dice" has eight, the second six, and the third two lines. The song's first chorus has two lines, the second has three, and the third has twelve lines. At the beginning of each chorus, the piano, bass and drums drop out and the backing vocals sing "you got to roll me" as the guitar plays the song's signature guitar figure. The third chorus leads into the song's coda. Slowly, the band's rhythm section works its way back into the song. The coda includes a call and response with the backing vocals singing "you got to roll me" as Jagger and Richards respond by singing "keep on rollin'."
"Tumbling Dice" appears on Stones' compilations and live albums, including the 1977 double album Love You Live, Shine a Light (2006), and Hyde Park Live. The song is included on several "From the Vault" archive releases, including Hampton Coliseum – Live In 1981 (2014) and L.A. Forum – Live In 1975 (2014). A unique, live version of the song was recorded for Stripped, the 1995 CD that documented part of the Voodoo Lounge Tour but did not appear on that album or on the 2016 re-release CD, Totally Stripped. The recording crossfades from a backstage vocal rehearsal of the song on solo piano to an onstage performance of the song. The backstage rehearsal portion was recorded at the Paradiso, Amsterdam, on 26 or 27 May 1995, and the live performance at the Olympia, Paris, on 3 July 1995. This recording appears on the 1996 "Wild Horses" (live) single and the Rarities 1971–2003 album.
Several critics complimented the tempo and groove of the single. Music critic Jack Garner asserted in a review for Courier News that the song featured a "marvellous tempo". Shipley felt the song has an "irresistible singalong energy", describing the "breakdown and buildup into the final 'you got to roll me' refrain" as "sublime". Critic Bill Janovitz described "Tumbling Dice" in his 2014 book Rocks Off as the "Holy Grail of grooves".
The lyrics of "Tumbling Dice" were well received by critics. Barsocchini considered its lyrics to be "provocative". Garner agreed, stating in a review for Courier News that the lyrics contained "wonderfully sexy double entendre[s]".
Credits per Margotin and Guesdon.
The opening line of Ronstadt’s version varied significantly from the Rolling Stones. Their version begins with:
The single's B-side, "I Never Will Marry", charted concurrently on the country charts of both the US (number 8) and Canada (number 16), and reached number 30 and 39 on the corresponding Adult Contemporary charts.
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