Assuming you report your income using the cash method (which most people do) you will have to report income when you receive it. And when they mean receive it, they also mean when you constructively receive it:

http://www.irs.gov/publications/p538/ar02.html#d0e1685

[ QUOTE ]
Under the cash method, you include in your gross income all items of income you actually or constructively receive during the tax year. If you receive property and services, you must include their fair market value in income.

Constructive receipt. Income is constructively received when an amount is credited to your account or made available to you without restriction. You need not have possession of it. If you authorize someone to be your agent and receive income for you, you are considered to have received it when your agent receives it. Income is not constructively received if your control of its receipt is subject to substantial restrictions or limitations.

Example 1.

Interest is credited to your bank account in December 2003, but you do not withdraw it or enter it into your passbook until 2004. You must include the amount in gross income for 2003, not 2004.

Example 2.

You have interest coupons that mature and become payable in 2003, but you do not cash them until 2004. You must include the interest in gross income for 2003, the year of constructive receipt. You must include the interest in your 2003 income, even if you later exchange the coupons for other property, instead of cashing them.

Delaying receipt of income. You cannot hold checks or postpone taking possession of similar property from one tax year to another to postpone paying tax on the income. You must report the income in the year the property is received or made available to you without restriction.

[/ QUOTE ]

This is only a guess, but I would think that each time you "receive" the income during the year is when your session ends. Another thread (in the Internet Magazine forum, with more experienced poker people than I) have debated what constitutes the end of a "session" on-line, and they didn't seem to be 100% sure either. But it might be worth checking out if you haven't already.