They are supposed to report if you win over a certain amount. I think the amount varies depending on what game you win it on (I don't know why that matters) and, I believe, it is somewhere in the neighborhood of $1500 on slots.
If you do win enough for the ship to report it to the U.S., it is still fairly easy to avoid paying taxes on it because you are allowed to offset your gambling winnings with gambling losses that occur within the same tax year. Go into any U.S. land-based casino and ask a cashier for a "loss slip" for $xxxx amount. Keep the amount of each loss slip small, say under $2500, and the cashier will give you one based solely on your word that you lost that amount playing in their casino. Go back several times, if necessary, to get enough loss slips to offset your entire winnings. Then turn these loss slips in at tax time to prove that you had gambling losses to offset your winnings. To be extra safe in case of an IRS audit, make an ATM withdrawal or cash a check at the casino in the amount of each loss slip on the day that you are claiming the loss.
Of course, unless you're content in hiding money under the mattress, the above only works if you win a relatively small amount so that it's not easily apparent that your winnings are never really being lost.
I'm not saying that I have actually done this or that it is the right thing to do, but I worked for a tax accountant for 15 years, and you would be surprised how many clients avoid paying taxes on gambling winnings with the above technique.