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GOODWILL, INTANGIBLE ASSETS, NET, AND DIGITAL ASSETS HELD - Goodwill by segment (Details) - USD ($)
$ in Millions
 3 Months Ended 7 Months Ended 9 Months Ended
Sep. 30, 2022
Jun. 30, 2022
Dec. 31, 2022
Sep. 30, 2023
Sep. 30, 2022
Goodwill          
Balance at beginning of the period       $ 3,122.8  
Changes in foreign currency exchange rates       2.1  
Balance at end of the period     $ 3,122.8 3,124.9  
Impairment $ (0.8)       $ (460.9)
Deferred tax benefit       6.9 $ 146.8
Carrying value of investments     253.2 342.6  
Cboe Digital          
Goodwill          
Adjustment 0.8        
Impairment $ (0.8)        
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       (0.4)  
Balance at end of the period     2,000.8 2,000.4  
Europe and Asia Pacific          
Goodwill          
Balance at beginning of the period       549.0  
Changes in foreign currency exchange rates       2.5  
Balance at end of the period     549.0 551.5  
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      
Carrying value of investments   220.0      
Intangible asset impairment   $ 0.0      
Futures          
Goodwill          
Balance at end of the period       $ 0.0