If you win a prize to donate to charity do you get it as a tax write off?

It would be a tax write-off . . . of itself. So net zero effect on taxes.

Though if you ever “itemize” deductions, then it might make a difference in some arcane way.

No. It didn’t come out of your pocket.

Prize is taxable income in the USA; the donation value would only be the tax rate you are in i.e your tax rate is 26% tax rate you can only take 26% the value. Same with lottery winnings.

I am not a CPA.

Depends on the charity (for example if they lobby you can’t) and how much you can deduct depends on how much the percentage is of your adjusted gross income.

In a way, yes. In order to claim the prize you must first pay the tax owed on receiving this prize.
Then you can donate it and only potentially get. tax deduction depending on what it is.