"You need to keep records of your losses or the IRS won't accept them under audit."
What would you recommend for these records? If gambling at a casino, is it possible to get a receipt for the chips purchased or would a "record book" be valid?
You may deduct gambling losses only if you itemize deductions. Claim your gambling losses as a miscellaneous deduction on Form 1040, Schedule A (PDF). However, the amount of losses you deduct may not be more than the amount of gambling income you have reported on your return. It is important to keep an accurate diary or similar record of your gambling winnings and losses. To deduct your losses, you must be able to provide receipts, tickets, statements or other records that show the amount of both your winnings and losses. Refer to Publication 529, Miscellaneous Deductions, for more information.
http://www.irs.gov/taxtopics/tc419.html
If you bet enough to worry about this, I would guess you could use markers. Ask the pit boss to rate your play (for comps.) You would then be in their computer system. You might be able to get a copy from the casino.
If you play anonymously, just cash your chips and leave. They never ask for your name.