Learn English – “Broken the duck”? Is this a common idiom/phrase

Searching for the phrase "duck and dive" in the Corpus of Contemporary American English (COCA) turns up zero references.

For the period (1990-2012) that COCA covers, "duck and dive" would appear to not be used in American English at all.

Garrison Keillor doesn't know, and online sources are all rather contradictory (the game is variously said to have originated in Germany, Ireland, Sweden, and the U.S.) and dubious. So the best answer may well be that origin of the Minnesota name is lost to history, and any answers will be speculative.

I noticed, however, that of all the variants played in different countries— le facteur ("the postman"), plumpsack (lit. "the plump sack"), 수건 돌리기 (loosely, "towel whirl")— only the Swedish name is similar to the English: Anka Anka Gås (i.e. duck duck goose). Digging around a bit more, I did find a site which referred to the Swedish game by a different name: Anka Anka Grå Anka, which happens to translate to duck duck grey duck. An alternative, Anka, Anka, Gråttanka, is attested to on Reddit.

Now, this name is vanishingly rare on the Internet compared to Anka Anka Gås (4 vs 27,000 Google.se results). Nevertheless, Minnesota has the largest concentration of ethnic Swedes in the U.S.— its most common surnames to this day are Scandinavian, and I could certainly envision a scenario where a regional or dialectic name of the game was transplanted by immigrants to became the prevalent usage in the new country even as it faded in the old. The Swedish community was fairly isolated until the turn of the 20th century but has been economically quite successful since.