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Equity And Earnings Per Share (IBG LLC Ownership of Member Interests) (Details)
Dec. 31, 2018
shares
Ownership Percentage 100.00%
Membership Interests 413,792,672
IBG Inc [Member]  
Ownership Percentage 18.10%
Membership Interests 75,100,955
Holdings [Member]  
Ownership Percentage 81.90%
Membership Interests 338,691,717