Revenues are recognized when control of the promised goods or services is transferred to our customers in an amount that reflects the consideration we expect to be entitled to in exchange for those goods or services. Sales and other taxes we collect concurrent with revenue-producing activities are excluded from revenue. Incidental items that are immaterial in the context of the contract are recognized as expense.

The following tables present our revenues disaggregated by contract duration for the three and nine month periods ended October 2, 2022, and October 3, 2021, respectively. Long-term and short-term contracts consist of our contracts with customers with terms greater than one year and less than or equal to one year, respectively.

(a)	Other revenues primarily include sales of single-day tickets and short-term transactional sales for which we have the right to invoice.

Long-term Contracts

Our long-term contracts consist of season passes that have a duration more than twelve months, consisting of season passes purchased by customers in the year preceding the operating season to which they relate, sponsorship contracts, and international agreements with third parties. We recently shifted our product offering from season passes to annual passes, which expire on the first anniversary of purchase. Annual passes are categorized as short-term contracts as described below under “Short-Term Contracts and Other”. We earn season pass revenue pursuant to our customers purchasing a season pass for a fixed fee, which entitles the customer to visit our parks, including certain waterparks, throughout the duration of the parks’ operating season. Our pass products are noncancelable and nonrefundable. We earn sponsorship revenue from separately-priced contracts with third parties pursuant to which we sell and advertise the third party’s products within the parks in exchange for consideration. Advertisements may include, but are not limited to, banners, signs, radio ads, association with certain events, sponsorship of rides within our parks and retail promotions. We earn international agreements revenue pursuant to arrangements in which we assist in the development and management of Six Flags-branded parks outside of North America. Within our international agreements, we have identified three distinct performance obligations as brand licensing, project services and management services. We do not consider revenue recognized for the performance obligations related to our international agreements to be significant, neither individually nor in the aggregate, to any period presented.

At January 2, 2022, $58.7 million of unearned revenue associated with outstanding long-term contracts was reported in "Deferred revenue," of which $24.6 million and $49.4 million was recognized as revenue for long-term contracts during the three and nine months ended October 2, 2022, respectively. As of October 2, 2022, the total unearned amount of revenue for remaining long-term contract performance obligations was $21.4 million. At January 1, 2021, $77.6 million of unearned revenue associated with outstanding long-term contracts was reported in "Deferred revenue," of which $37.7 million and $72.6 million was recognized as revenue for long-term contracts during the three and nine months ended October 3, 2021, respectively. As of October 3, 2021, the total unearned amount of revenue for remaining long-term contract performance obligations was $72.8 million.

As of October 2, 2022, we expect to recognize estimated revenue for partially or wholly unsatisfied performance obligations on long-term contracts of approximately $19.7 million in the remainder of 2022, $9.3 million in 2023, $6.9 million in 2024, $0.9 million in 2025, and $1.1 million in 2026 and thereafter.

Short-term Contracts and Other

Our short-term contracts consist primarily of annual passes, season passes that have a duration of less than twelve months, consisting of season passes purchased by customers during the operating season to which they relate and memberships with customers, certain sponsorship contracts and international agreements with third parties. We earn revenue from a customer’s purchase of our annual pass, season pass and membership products, which entitles the customer to visit our parks, including certain waterparks, throughout the duration of the parks’ operating season for a fixed fee. We earn sponsorship and international agreements revenue from contracts with third parties, pursuant to which we sell and advertise the third party’s products within our parks on a short-term basis that generally coincides with our annual operating season, and pursuant to certain activities in connection with our international agreements. The transaction price for our short-term contracts is explicitly stated within the contracts.

We generally recognize revenue from short-term contracts over the passage of time, with the exception of season pass and membership revenues. We recognize season pass and membership revenues in "Park admissions" over the estimated redemption rate, as we believe this appropriately depicts the transfer of service to our customers. We estimate the redemption rate based on historical experience and other factors and assumptions we believe to be customary and reasonable. We review the estimated redemption rate regularly and on an ongoing basis and revise it as necessary throughout the year. Amounts received for multi-use admissions in excess of redemptions are recognized in "Deferred revenue".

Other revenues consist primarily of revenues from single-use tickets for entrance to our parks, in-park services (such as the sale of food and beverages, merchandise, games and attractions, standalone parking sales and other services inside our parks), accommodations revenue, and other miscellaneous products and services. Due to the short-term transactional nature of such purchases, we apply the practical expedient to recognize revenue for single-use ticket sales, in-park services, accommodations, and other miscellaneous services and goods for which we have the right to invoice.