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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
Mar. 31, 2023
Sep. 30, 2022
Jun. 30, 2022
Mar. 31, 2022
Dec. 31, 2022
Goodwill          
Balance at beginning of the period $ 3,122.8        
Changes in foreign currency exchange rates 5.6        
Balance at end of the period 3,128.4       $ 3,122.8
Deferred tax benefit 10.6     $ 17.8  
Carrying value of investments 269.7       253.2
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 0.2        
Balance at end of the period 2,001.0       2,000.8
Europe and Asia Pacific          
Goodwill          
Balance at beginning of the period 549.0        
Changes in foreign currency exchange rates 5.4        
Balance at end of the period 554.4       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    
Carrying value of investments     220.0    
Intangible asset impairment     $ 0.0    
Futures          
Goodwill          
Balance at end of the period $ 0.0