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RETIREMENT PLANS - Narrative (Details)	6 Months Ended
	Apr. 13, 2025 healthcarePlan definedBenefitPensionPlan	Jan. 01, 2022 USD ($)
Retirement Benefits [Abstract]
Number of sponsored defined benefit pension plans | definedBenefitPensionPlan	2
Number of postretirement health care plans | healthcarePlan	2
Minimum required contribution for retirement plans | $		$ 0

X

- Definition

Minimum required contribution for retirement plans

+ References

No definition available.

+ Details

Name:	jack_MinimumRequiredContributionForRetirementPlans
Namespace Prefix:	jack_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Number Of Defined Benefit Pension Plans Sponsored

+ References

No definition available.

+ Details

Name:	jack_NumberOfDefinedBenefitPensionPlansSponsored
Namespace Prefix:	jack_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Postretirement Medical Plan, Number Sponsored

+ References

No definition available.

+ Details

Name:	jack_PostretirementMedicalPlanNumberSponsored
Namespace Prefix:	jack_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

X

- References

No definition available.

+ Details

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