Related Party Transactions, Revenue from Transactions with Related Parties (Details) - USD ($)	3 Months Ended	6 Months Ended
Jun. 30, 2023	Jun. 30, 2022	Jun. 30, 2023	Jun. 30, 2022	Dec. 31, 2022
Related Party Transaction [Abstract]
Investment income	$ 32,120	$ 9,274	$ 63,309	$ 14,213
Commission revenue	436,373	449,664	903,645	953,403
Gabelli Funds, LLC [Member]
Related Party Transaction [Abstract]
Affiliated investments	1,499,337		1,499,337		$ 2,259,801
Investment income	$ 25,203	$ 3,213	$ 49,495	$ 3,422
Investment, Type [Extensible Enumeration]	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember	mghl:USTreasuryMoneyMarketFundMember
Affiliated Entities [Member] \| Commissions [Member]
Related Party Transaction [Abstract]
Commission revenue	$ 276,349	$ 262,525	$ 605,420	$ 537,420
Revenue percentage	63.00%	58.00%	67.00%	56.00%

Indicates type of investment. Includes, but is not limited to, common stock, preferred stock, convertible security, fixed income security, government security, option purchased, warrant, loan participation and assignment, commercial paper, bankers' acceptance, certificates of deposit, short-term security, repurchase agreement, and other investment company.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480524/946-210-50-6

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
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-URI https://asc.fasb.org//1943274/2147480524/946-210-50-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.12-12A(Column A)(Footnote 2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-2

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 6
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-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-6

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.12-12(Column A)(Footnote 2)(i))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.12-12(Column C)(Footnote 5))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-1

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
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-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-3

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
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-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-3

Reference 9: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 6
-Subparagraph (SX 210.12-14(Column F)(Footnote 7))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-6

Reference 10: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 320
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.12-12A(Column C)(Footnote 4))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480032/946-320-S99-2

+ Details