On January 1, 2018, we adopted Topic 606 using the modified retrospective method applied to those contracts which were not completed as of January 1, 2018. Results for reporting periods beginning after January 1, 2018 are presented under Topic 606, while prior period amounts are not adjusted and continue to be reported in accordance with our historic accounting under Topic 605.

The impact of adoption of Topic 606 on our consolidated statements of operations for the year ended December 31, 2019 and 2018 was as follows:

We recorded a net reduction to our opening "Accumulated deficit" of $4.9 million, net of taxes of $1.3 million as of January 1, 2018, to recognize the cumulative impact of adopting Topic 606, with the impact primarily related to our international agreements revenue. During the years ended December 31, 2019 and 2018, we recognized $0.1 million more and $0.9 million less revenue, respectively, as a result of applying Topic 606.

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 years ended December 31, 2019, 2018 and 2017, 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. Sales and usage-based taxes are excluded from revenues.

(a)	Other revenues primarily include sales of single-use 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 with customers, sponsorship contracts and international agreements with third parties. We earn season pass revenue when our customers purchase 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. Current year season passes classified as long-term contracts are sold in the year preceding the operating season to which they relate. 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 long-form agreements to be significant, neither individually nor in the aggregate, to any period presented. Refer to Note 2 for additional information on our accounting for performance obligations in these contracts.

The transaction price for our long-term contracts is explicitly stated within the contracts. Our sponsorship contracts and international agreements may include estimated variable consideration such as penalties for delay in performance of contract terms, and certain volume-based discounts and rebates. There were not significant changes to our estimates of variable consideration. Our brand licensing and management services performance obligations include royalty payments and management fees, respectively, based on gross sales from Six Flags-branded parks. We have elected to apply the sales-based royalty exemption to the brand licensing performance obligation, and accordingly do not estimate revenue attributable to the gross sales-based royalty. We have also elected to apply the direct allocation exemption to the management services performance obligation and accordingly do not estimate revenue attributable to the gross sales based management fee.

We recognize season pass revenue 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 that we believe to be customary and reasonable. We review the estimated redemption rate regularly, 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." We recognize sponsorship and international agreements revenue over the term of the agreements, using the passage of time as a measure of complete satisfaction of the performance obligations in "Sponsorship, international agreements and accommodations." Amounts received for unsatisfied sponsorship and international agreements performance obligations are recognized in "Deferred revenue." As a result of the adoption of Topic 606, we recognized an increase to "Sponsorship, international agreements and accommodations" revenue previously recognized in prior periods of $0.1 million and a decrease of $0.9 million during the years ended December 31, 2019 and 2018, respectively.

At January 1, 2018, $111.6 million of unearned revenue associated with outstanding long-term contracts was reported in “Deferred revenue,” and $109.7 million was recognized as revenue for long-term contracts during the year ended December 31, 2018. As of December 31, 2018, the total unearned amount of revenue for remaining long-term contract performance obligations was $100.8 million. At January 1, 2019, $100.8 million of unearned revenue associated with outstanding long-term contracts was reported in "Deferred revenue," and $161.0 million was recognized as revenue for long-term contracts during the year ended December 31, 2019. As of December 31, 2019, the total unearned amount of revenue for remaining long-term contract performance obligations was $85.1 million. As of December 31, 2019, we expect to recognize estimated revenue for partially or wholly unsatisfied performance obligations on long-term contracts of approximately $107.0 million in 2020, $24.1 million in 2021, $23.2 million in 2022 and $5.0 million in 2023 and thereafter.

Short-term Contracts and Other

Our short-term contracts consist primarily of season passes and memberships with customers, certain sponsorship contracts and international agreements with third parties. We earn revenue from a customer’s purchase of our 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". There was no change in the pattern of recognition for season pass and membership revenue during the year ended December 31, 2019 under Topic 606, as compared to historic accounting under Topic 605.

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.

Arrangements with Multiple Performance Obligations

Our contracts with customers may include multiple performance obligations. For such arrangements, we allocate revenue to each performance obligation based on its relative standalone selling price. We generally determine standalone selling prices based on the observable prices charged to customers.

Practical Expedients and Exemptions

We generally expense (i) sales commissions when incurred, and (ii) certain costs to obtain a contract where the amortization period would have been one year or less. These costs are recorded within Selling, general and administrative expenses.

We do not disclose the value of unsatisfied performance obligations for (i) contracts with an original expected length of one year or less and (ii) contracts for which we recognize revenue at the amount for which we have the right to invoice for services performed.

For certain of our contracts that have an original expected length of one year or less, we use the practical expedient applicable to such contracts and do not consider the time value of money.