First, you can take a tax deduction for any donations to a tax exempt organization; mostly 501(c)(3), but some others. It must be listed here.
https://www.irs.gov/Charities-&-Non-Profits/Exempt-Organizations-Select-Check
Second, in most cases, the value of the deduction is limited to what you paid for the cards, or what they are worth now, whichever is less. If you received them as an inheritance, the deduction value is the value on the date of death of the previous owner, or their current value, whichever is less. If you received them as a gift, the value of the deduction you can claim is the prices the original owner paid, or the current value, whichever is less.
However, if you donated them to an organization that will keep them and use them for the purpose of the charity, you can claim the current value even if the current value is more than you paid. For example, donating baseball cards to a baseball museum, or donating game cards to a game museum.
If the total claimed value is more than $5000, you need a qualified appraisal, and a form 8332 signed by the appraiser and by a financial official of the charity.