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How that is withheld is essentially not important, it is how much is due. If excess is withheld, you will get it back when you file taxes.
But to your question, it does depend on what state you live in for a "specific" rate. Generally winnings from casinos are do not have taxes withheld. Winnings from states lotteries, depending on payout, withhold at a rate between 25-31% for federal tax purposes and the appropriate state rate (most state range between 3-6%). Some states do not tax their own lottery winnings. Bottom line, you can expect somewhere around 28-35% withheld on the $10k.
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