Gambling winnings are taxed as "ordinary income," which means at your bracket rate(s).  Any federal withholding will count in your favor, but it's not a set "final" amount.  That income will get combined with other "ordinary income" on your tax return, where the final calculation of tax owed takes place.

If you had gambling losses, you're allowed to use those to offset gambling winnings, but only as an itemized deduction on Schedule A (meaning you have to itemize), and only to the extent of gambling winnings.