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Supplemental Pro Forma Information on Prior Year Business Acquisition - Schedule of Unaudited Pro Forma Combined Results of Operations (Details) - Baby Dolls-Chicas Locas - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Business Acquisition [Line Items]
Pro forma revenues	$ 72,283	$ 77,292	$ 146,190	$ 154,424
Pro forma net income attributable to RCIHH common stockholders	$ 774	$ 8,303	$ 8,000	$ 17,213
Pro forma earnings per share – basic (in dollars per share)	$ 0.08	$ 0.88	$ 0.85	$ 1.83
Pro forma earnings per share – diluted (in dollars per share)	$ 0.08	$ 0.88	$ 0.85	$ 1.83
Pro forma weighted average shares used in computing earnings per share - basic (in shares)	9,350,292	9,430,225	9,358,768	9,430,241
Pro forma weighted average shares used in computing earnings per share - diluted (in shares)	9,350,292	9,430,225	9,358,768	9,430,241

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