What percentage of money does the government collect from a game contest winner?

When a game contestant wins a large sum of money from a lottery, sweepstakes, game show, etc. what percentage of that contestant's winnings does the government collect? I assume it's approximately 20 to 30 percent depending on what the tax laws of each state mandate. Please advise.

Federal tax on a million dollar win would be about $350,000. Then if you live in a state where state tax is collected, you can count on shelling out anywhere from $25,000 to over $100,000.