This answer comes from Jean Scott, illustrious author of The Frugal Gambler and More Frugal Gambling.
Good question. I completely understand the need to protect your personal information by not carrying a Social Security card that could be lost or stolen, then used to steal your identity. In fact, when in doubt, the default should be to protect your private information, in my opinion. The worst that can happen is your jackpot will be withheld until you produce proof of your Social Security number.
I have heard of very rare cases where players had their W-2G jackpot amount held up until they presented some documentation. One was a "foreign-looking" person who acted "suspiciously." However, most casinos will routinely take your word when you simply state your number.
But do remember that you can't refuse to give them your number. Well, you could refuse, but you wouldn't get paid. The government requires the casino to submit a W-2G with your Social Security number on it.
