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Historically, out of the 182 times that they have contended, the Chicago Bears have taken 93 of those games, and 84 have gone to the Pack. Six of those games resulted in a tie (yea, a tie, remember those?), one of which was zip to zip.
The Packers and the Bears can also be attributed to the first teams ever who had players removed from the game for poor sportsman-like conduct. In 1924, the Bears' Frank Hanney and Packers’ Walter Voss were ejected for throwing punches.
We need only look back to the beginning to see how this type of precedent was set.
George Halas and Curly Lambeau used to regularly engage in heckling and taunting that would nowadays be ground for fines. According to an article in the Chicago Tribune, dozens of players stated that "Halas' demeanor would transform from professional to possessed after kickoff."
Despite all this, everyone needs someone to hate, and without a rival, you have no rivalry.
Behind closed doors during the Great Depression, the Green Bay Packers actually issued a loan to Halas and the Chicago Bears when payroll expenses could not be met. Rather than let the franchise go for broke, the Packers helped them out in order to continue with what would become a historic rivalry.