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Quarterly Results of Operations (Unaudited) - Schedule of Quarterly Financial Information (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended 12 Months Ended
Sep. 30, 2023
Jun. 30, 2023
Mar. 31, 2023
Dec. 31, 2022
Sep. 30, 2022
Jun. 30, 2022
Mar. 31, 2022
Dec. 31, 2021
Sep. 30, 2021
Jun. 30, 2021
Mar. 31, 2021
Dec. 31, 2020
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Quarterly Financial Information Disclosure [Abstract]                              
Revenues $ 75,250 $ 77,055 $ 71,517 $ 69,968 $ 71,378 $ 70,714 $ 63,692 $ 61,836 $ 54,941 $ 57,860 $ 44,059 $ 38,398 $ 293,790 $ 267,620 $ 195,258
Income (loss) from operations 5,644 15,515 13,427 16,898 17,960 20,507 17,081 15,911 3,617 18,507 9,841 6,583 51,484 71,459 38,548
Net income (loss) attributable to RCIHH stockholders $ 2,191 $ 9,085 $ 7,732 $ 10,238 $ 10,612 $ 13,902 $ 10,952 $ 10,575 $ 2,300 $ 12,302 $ 6,091 $ 9,643 $ 29,246 $ 46,041 $ 30,336
Earnings per share                              
Basic (in dollars per share) $ 0.23 $ 0.96 $ 0.83 $ 1.11 $ 1.15 $ 1.48 $ 1.15 $ 1.12 $ 0.26 $ 1.37 $ 0.68 $ 1.07 $ 3.13 $ 4.91 $ 3.37
Diluted (in dollars per share) $ 0.23 $ 0.96 $ 0.83 $ 1.11 $ 1.15 $ 1.48 $ 1.15 $ 1.12 $ 0.26 $ 1.37 $ 0.68 $ 1.07 $ 3.13 $ 4.91 $ 3.37
Weighted average shares used in computing earnings per share                              
Basic (in shares) 9,417,166 9,430,225 9,265,781 9,230,258 9,249,864 9,389,675 9,489,085 9,407,519 8,999,910 8,999,910 8,999,910 9,019,088 9,335,983 9,383,445 9,004,744
Diluted (in shares) 9,417,166 9,430,225 9,265,781 9,230,258 9,249,864 9,389,675 9,489,085 9,407,519 8,999,910 8,999,910 8,999,910 9,019,088 9,335,983 9,383,445 9,004,744
Dividends per share declared and paid (in dollars per share) $ 0.06 $ 0.06 $ 0.06 $ 0.05 $ 0.05 $ 0.05 $ 0.05 $ 0.04 $ 0.04 $ 0.04 $ 0.04 $ 0.04 $ 0.23 $ 0.19 $ 0.16