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GOODWILL, INTANGIBLE ASSETS, NET, AND DIGITAL ASSETS HELD - Goodwill by segment (Details) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended 7 Months Ended
Sep. 30, 2022
Jun. 30, 2022
Jun. 30, 2023
Jun. 30, 2022
Dec. 31, 2022
Goodwill          
Balance at beginning of the period     $ 3,122.8    
Changes in foreign currency exchange rates     15.6    
Balance at end of the period     3,138.4   $ 3,122.8
Impairment   $ (460.1)   $ (460.1)  
Deferred tax benefit     17.3 142.3  
Carrying value of investments     294.2   253.2
Cboe Digital          
Goodwill          
Adjustment $ 0.8        
Impairment $ (0.8) (460.1)      
Options          
Goodwill          
Balance at beginning of the period     305.8    
Balance at end of the period     305.8   305.8
North American Equities          
Goodwill          
Balance at beginning of the period     2,000.8    
Changes in foreign currency exchange rates     3.6    
Balance at end of the period     2,004.4   2,000.8
Europe and Asia Pacific          
Goodwill          
Balance at beginning of the period     549.0    
Changes in foreign currency exchange rates     12.0    
Balance at end of the period     561.0   549.0
Global FX          
Goodwill          
Balance at beginning of the period     267.2    
Balance at end of the period     267.2   $ 267.2
Digital          
Goodwill          
Impairment   460.1      
Deferred tax benefit   116.2      
Decrease in carrying value   343.9   343.9  
Carrying value of investments   220.0   $ 220.0  
Intangible asset impairment   $ 0.0      
Futures          
Goodwill          
Balance at end of the period     $ 0.0