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Segments - Schedule of Disaggregation of Revenue (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
Sep. 30, 2025
Jun. 30, 2025
Mar. 31, 2025
Sep. 30, 2024
Jun. 30, 2024
Mar. 31, 2024
Sep. 30, 2025
Sep. 30, 2024
Segment Reporting Information [Line Items]                
Gross revenue $ 1,176.9     $ 909.2     $ 2,991.4 $ 2,443.6
General and administrative expenses:                
Revaluation of contingent liabilities (2.8)     1.5     (7.4) 3.9
Depreciation and amortization expense [1] (85.8)     (51.6)     (199.4) (143.1)
Professional expenses (35.3)     (9.4)     (69.1) (29.0)
Advertising and marketing expenses (7.7)     (6.2)     (21.5) (14.5)
Loss on extinguishment of debt (9.2)     0.0     (12.3) 0.0
Interest income 17.5     9.7     49.1 20.1
Other income (expense), net (1.4)     (1.5)     (5.6) 0.3
Gain on investments in securities 0.0     10.8     0.0 21.6
Change in TRA liability (0.2)     (289.4)     2.0 (294.2)
Interest expense (60.8)     (18.3)     (128.7) (34.5)
Income tax benefit (expense) (27.1)     280.5     (33.6) 280.9
Net income 33.4 $ 41.1 $ 19.5 72.2 $ 54.5 $ 28.5 94.0 155.2
Depreciation and amortization expenses of equipment 19.4     14.1     53.1 39.0
Reportable Segment                
Segment Reporting Information [Line Items]                
Network fees (587.7)     (544.1)     (1,620.3) (1,494.2)
Other costs of sales (exclusive of depreciation of equipment under lease) (160.2)     (97.8)     (392.6) (262.5)
General and administrative expenses:                
Employee and other general and administrative expenses (158.5)     (98.0)     (385.6) (267.5)
Equity-based compensation expense (15.9)     (14.4)     (58.4) (52.1)
Rent, office, occupancy and equipment expenses (14.0)     (5.8)     (28.8) (15.8)
Revaluation of contingent liabilities 2.8     (1.5)     7.4 (3.9)
Depreciation and amortization expense (85.8)     (51.6)     (199.4) (143.1)
Professional expenses (35.3)     (9.4)     (69.1) (29.0)
Advertising and marketing expenses (7.7)     (6.2)     (21.5) (14.5)
Loss on extinguishment of debt (9.2)     0.0     (12.3) 0.0
Interest income 17.5     9.7     49.1 20.1
Other income (expense), net (1.4)     (1.5)     (5.6) 0.3
Gain on investments in securities 0.0     10.8     0.0 21.6
Change in TRA liability (0.2)     (289.4)     2.0 (294.2)
Interest expense (60.8)     (18.3)     (128.7) (34.5)
Income tax benefit (expense) (27.1)     280.5     (33.6) 280.9
Net income 33.4     72.2     94.0 155.2
Payments-based revenue                
Segment Reporting Information [Line Items]                
Gross revenue 1,058.0     806.8     2,682.2 2,217.7
Payments-based revenue | Reportable Segment                
Segment Reporting Information [Line Items]                
Gross revenue 1,058.0     806.8     2,682.2 2,217.7
Subscription and other revenue                
Segment Reporting Information [Line Items]                
Gross revenue 118.9     102.4     309.2 225.9
Subscription and other revenue | Reportable Segment                
Segment Reporting Information [Line Items]                
Gross revenue $ 118.9     $ 102.4     $ 309.2 $ 225.9
[1] Depreciation and amortization expense includes depreciation of equipment under lease of $19.4 million and $53.1 million for the three and nine months ended September 30, 2025, respectively, and $14.1 million and $39.0 million for the three and nine months ended September 30, 2024, respectively.