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Summary of Significant Accounting Policies - Schedule of Impact of Topic 606 (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 12 Months Ended
Dec. 31, 2018
Sep. 30, 2018
Jun. 30, 2018
Mar. 31, 2018
Dec. 31, 2017
Sep. 30, 2017
Jun. 30, 2017
Mar. 31, 2017
Dec. 31, 2018
Dec. 31, 2017
Dec. 31, 2016
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                      
Revenues, net $ 643,422 $ 619,586 $ 584,985 $ 585,500 $ 609,991 $ 577,877 $ 541,237 $ 520,433 $ 2,433,492 [1] $ 2,249,538 $ 1,831,546
Expenses:                      
Merchant commissions                 0 [1] 113,133 104,345
Processing                 487,695 [1] 429,613 355,414
Selling                 182,593 [1] 170,717 131,443
General and administrative                 389,172 [1] 387,694 283,625
Depreciation and amortization                 274,609 [1] 264,560 203,256
Other operating expense (income), net                 8,725 [1] 61 (690)
Operating income 284,738 281,090 264,783 260,087 240,012 232,637 216,043 195,068 1,090,698 [1] 883,760 754,153
Total other (income) expense                 (4,427) [1] (9,830) 111,234
Income before income taxes                 1,095,125 [1] 893,590 642,919
Provision for income taxes                 283,642 [1] 153,390 190,534
Net income $ 302,000 $ 157,694 $ 176,852 $ 174,937 $ 282,696 $ 202,823 $ 130,987 $ 123,693 $ 811,483 [1],[2] $ 740,200 [2] $ 452,385 [2]
Basic earnings per share (in usd per share) $ 3.45 $ 1.78 $ 1.98 $ 1.95 $ 3.15 $ 2.23 $ 1.42 $ 1.34 $ 9.14 [1] $ 8.12 $ 4.89
Diluted earnings per share (in usd per share) $ 3.33 $ 1.71 $ 1.91 $ 1.88 $ 3.05 $ 2.18 $ 1.39 $ 1.31 $ 8.81 [1] $ 7.91 $ 4.75
Calculated under Revenue Guidance in Effect before Topic 606                      
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                      
Revenues, net [1]                 $ 2,545,449    
Expenses:                      
Merchant commissions [1]                 126,849    
Processing [1]                 474,732    
Selling [1]                 187,912    
General and administrative [1]                 389,172    
Depreciation and amortization [1]                 274,609    
Other operating expense (income), net [1]                 8,725    
Operating income [1]                 1,083,450    
Total other (income) expense [1]                 (4,427)    
Income before income taxes [1]                 1,087,877    
Provision for income taxes [1]                 281,599    
Net income [1]                 $ 806,278    
Basic earnings per share (in usd per share) [1]                 $ 9.08    
Diluted earnings per share (in usd per share) [1]                 $ 8.75    
Accounting Standards Update 2014-09 | Impact of ASC 606                      
New Accounting Pronouncements or Change in Accounting Principle [Line Items]                      
Revenues, net [1]                 $ 111,957    
Expenses:                      
Merchant commissions [1]                 126,849    
Processing [1]                 (12,963)    
Selling [1]                 5,319    
General and administrative [1]                 0    
Depreciation and amortization [1]                 0    
Other operating expense (income), net [1]                 0    
Operating income [1]                 (7,248)    
Total other (income) expense [1]                 0    
Income before income taxes [1]                 (7,248)    
Provision for income taxes [1]                 (2,043)    
Net income [1]                 $ (5,205)    
[1] Reflects the impact of the Company's adoption of Accounting Standards Update 2014-09, Revenue from Contracts with Customers (Topic 606) ("ASC 606") and related cost capitalization guidance, which was adopted by the Company on January 1, 2018 using the modified retrospective transition method. The adoption of ASC 606 resulted in an adjustment to retained earnings in our consolidated balance sheet for the cumulative effect of applying the standard, which included costs incurred to obtain a contract, as well as presentation changes in our statements of income, including the classification of certain amounts previously classified as merchant commissions and processing expense net with revenues. As a result of the application of the modified retrospective transition method, the Company's prior period results within its Form 10-K and quarterly reports on Form 10-Q will not be restated to reflect ASC 606.
[2] Reflects the impact of the Company's adoption of Accounting Standards Update 2016-18, Statement of Cash Flows (Topic 230), which was adopted by the Company on January 1, 2018 and applied retrospectively to results for 2017. The adoption of Topic 230 resulted in the statement of cash flows presenting the changes in the total of cash, cash equivalents and restricted cash. As a result, the Company will no longer present transfers between cash and cash equivalents and restricted cash in the statement of cash flows.