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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, 2024
Jun. 30, 2024
Mar. 30, 2024
Dec. 31, 2023
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, 2024
Sep. 30, 2023
Sep. 30, 2022
Quarterly Financial Information Disclosure [Abstract]                              
Revenues $ 73,234 $ 76,180 $ 72,283 $ 73,907 $ 75,250 $ 77,055 $ 71,517 $ 69,968 $ 71,378 $ 70,714 $ 63,692 $ 61,836 $ 295,604 $ 293,790 $ 267,620
Income (loss) from operations 3,519 (2,536) 4,657 13,165 5,644 15,515 13,427 16,898 17,960 20,507 17,081 15,911 18,805 51,484 71,459
Net income (loss) attributable to RCIHH stockholders $ 244 $ (5,233) $ 774 $ 7,226 $ 2,191 $ 9,085 $ 7,732 $ 10,238 $ 10,612 $ 13,902 $ 10,952 $ 10,575 $ 3,011 $ 29,246 $ 46,041
Earnings (loss) per share                              
Basic (in dollars per share) $ 0.03 $ (0.56) $ 0.08 $ 0.77 $ 0.23 $ 0.96 $ 0.83 $ 1.11 $ 1.15 $ 1.48 $ 1.15 $ 1.12 $ 0.33 $ 3.13 $ 4.91
Diluted (in dollars per share) $ 0.03 $ (0.56) $ 0.08 $ 0.77 $ 0.23 $ 0.96 $ 0.83 $ 1.11 $ 1.15 $ 1.48 $ 1.15 $ 1.12 $ 0.33 $ 3.13 $ 4.91
Weighted average shares used in computing earnings per share                              
Basic (in shares) 9,006,014 9,278,921 9,350,292 9,367,151 9,417,166 9,430,225 9,265,781 9,230,258 9,249,864 9,389,675 9,489,085 9,407,519 9,250,245 9,335,983 9,383,445
Diluted (in shares) 9,006,014 9,278,921 9,350,292 9,367,151 9,417,166 9,430,225 9,265,781 9,230,258 9,249,864 9,389,675 9,489,085 9,407,519 9,250,245 9,335,983 9,383,445
Dividends per share declared and paid (in dollars per share) $ 0.07 $ 0.06 $ 0.06 $ 0.06 $ 0.06 $ 0.06 $ 0.06 $ 0.05 $ 0.05 $ 0.05 $ 0.05 $ 0.04 $ 0.25 $ 0.23 $ 0.19