Acquisitions and Dispositions - Schedule of Unaudited Pro Forma Combined Results of Operations (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended	9 Months Ended
Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Business Combination and Asset Acquisition [Abstract]
Pro forma revenues	$ 70,714	$ 64,407	$ 197,968	$ 155,184
Pro forma net income attributable to RCIHH common stockholders	$ 13,931	$ 13,745	$ 34,876	$ 29,252
Pro forma earnings per share – basic (in dollars per share)	$ 1.48	$ 1.45	$ 3.70	$ 3.08
Pro forma earnings per share – diluted (in dollars per share)	$ 1.48	$ 1.45	$ 3.70	$ 3.08
Pro forma weighted average number of common shares outstanding - basic (in shares)	9,389,675	9,499,910	9,428,461	9,506,373
Pro forma weighted average number of common shares outstanding - diluted (in shares)	9,389,675	9,499,910	9,428,461	9,506,373

Pro forma basic earnings per share or earnings per unit, which is commonly presented in initial public offerings based on the terms of the offering.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 855
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 1.B.3)
-URI https://asc.fasb.org/extlink&oid=122134661&loc=d3e463720-122850

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 10
-Section S99
-Paragraph 7
-Subparagraph (SAB Topic 1.B.2)
-URI https://asc.fasb.org/extlink&oid=126898705&loc=d3e5934-122674

+ Details

Name:	us-gaap_BasicEarningsPerShareProForma
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The pro forma net Income or Loss for the period as if the business combination or combinations had been completed at the beginning of a period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(3)
-URI https://asc.fasb.org/extlink&oid=79982066&loc=d3e1392-128463

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(2)
-URI https://asc.fasb.org/extlink&oid=79982066&loc=d3e1392-128463

+ Details

Name:	us-gaap_BusinessAcquisitionsProFormaNetIncomeLoss
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The pro forma revenue for a period as if the business combination or combinations had been completed at the beginning of the period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(2)
-URI https://asc.fasb.org/extlink&oid=79982066&loc=d3e1392-128463

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 805
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (h)(3)
-URI https://asc.fasb.org/extlink&oid=79982066&loc=d3e1392-128463

+ Details

Name:	us-gaap_BusinessAcquisitionsProFormaRevenue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- References

No definition available.

+ Details

Name:	us-gaap_BusinessCombinationAndAssetAcquisitionAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Pro forma diluted earnings per share, which is commonly presented in initial public offerings.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 205
-SubTopic 10
-Section S99
-Paragraph 7
-Subparagraph (SAB Topic 1.B.2)
-URI https://asc.fasb.org/extlink&oid=126898705&loc=d3e5934-122674

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 855
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 1.B.3)
-URI https://asc.fasb.org/extlink&oid=122134661&loc=d3e463720-122850

+ Details

Name:	us-gaap_DilutedEarningsPerShareProForma
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The weighted average number of shares or units and dilutive common stock or unit equivalents outstanding in the calculation of proforma diluted earnings per share (earnings per unit), which is commonly presented in initial public offerings based on the terms of the offering.

+ References

No definition available.

+ Details

Name:	us-gaap_ProFormaWeightedAverageSharesOutstandingDiluted
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The weighted average number of shares (units) outstanding in the calculation of pro forma basic earnings per share (earnings per unit), which is commonly presented in initial public offerings based on the terms of the offering.

+ References

No definition available.

+ Details

Name:	us-gaap_WeightedAverageBasicSharesOutstandingProForma
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration