You are correct that the person may not claim a charitable contribution deduction for purchasing lottery tickets from a charity.  The IRS has ruled that there is no charitable deduction because of the quid pro quo value of the chance to win a prize.  But in this case, because the person must declare the $500 gambling winnings as income, the person may offset the $100 the purchase price of the tickets so that the net taxable income will be only $400.  (The charity has to report the gambling winnings to the IRS on Form W-2G if the winnings are $600 or more)

The general rule for claiming deductions on gifts of personal property to a charity when the property has not been held for more than a year is that the donor may deduct the lesser of the tax cost of the property or its fair market value.  (To get a full fair market value deduction, the property would have to be held for more than a year and used in the charity’s charitable program.)  In this case, if the transaction is properly analogized to a sale or exchange, unlike a $100 purchase of a $500 television where the purchaser would have a basis of $100, the tax rules provide that property received in a transaction generating income to the recipient will be deemed to have a tax basis equal to the gross amount of income received that is applicable to the property.  Since the purchaser of the tickets received gross income of $500 in winning the TV, the tax basis would be $500, equal to the value of the set. The donor could deduct the $500 value as a charitable contribution.

If the ticket purchaser won a 50-50 lottery and received $500 in cash, the deduction for giving the $500 back to the charity would also be $500, but for a much simpler reason.  Cash gifts are deductible based on the amount of the cash contributed, without regard to rules about tax basis.