Taxes on lottery winnings (taxed before or after payout amount)?

I was wondering if someone wins a prize lets say $100,000. If you look at the tax brackets you are at 24% tax rate. However, I noticed lottery tickets explain a payout after the prize such as Powerball, in fine print of 50% payout. So, that will make the $100,000 to $50,000 after the payout which puts you in a different tax bracket of 22% instead. My question is are you taxed on the original prize ($100,000) or at after the payout amount ($50,000) because if you are then you are at a lower tax bracket at 22% keeping more money. This is all hypothetical of course if that is only your income for the year. Thanks