I am going to visit Colombia. If I gamble at the casino, how much US currency can I bring back without a problem? $9,500?
Under US Law
Assuming that the gambling is legal, you can bring back as much currency as you want without a problem, but you must declare the cash and cash equivalents you bring into the country if the total is USD 10,000 or more. To calculate the total, anything that is denominated in another currency must first be converted to USD. US Customs and Border Protection has details on their website:
How much currency / money / monetary instruments can I bring into the U.S.?
There is no limit on the amount of money that can be taken out of or brought into the United States. However, if a person or persons traveling together and filing a joint declaration (CBP Form 6059-B) have more than $10,000 in currency or negotiable monetary instruments, they must fill out a "Report of International Transportation of Currency and Monetary Instruments" FinCEN 105 (former CF 4790).
Please be aware, if persons/family members traveling together have more than $10,000, they cannot divide the currency between each other to avoid declaring the currency.
For example, if one person is carrying $5,000 and the other has $6,000, they have a total of $11, 000 in their possession and must report it on a FinCEN 105. If a person or family fails to declare their monetary instruments in amounts more than $10,000 their monetary instrument(s) may be subject to forfeiture and could result in civil and or criminal penalties.
The FinCEN 105 can be obtained prior to traveling or when going through CBP. If assistance is required, a Customs and Border Protection (CBP) Officer can help with filling out the form.
If the gambling was illegal, I do not think that you would have a problem under US law, but you might of course have trouble under Colombian law. To be certain that illegal gambling in a foreign jurisdiction will not expose you to some liability under US law, you should consult a lawyer.
Under US tax law, you must also report winnings from gambling on your income tax, so you should do that to avoid problems after you return to the US. The IRS has information on their website:
Topic Number 419 - Gambling Income and Losses
The following rules apply to casual gamblers who aren't in the trade or business of gambling. Gambling winnings are fully taxable and you must report the income on your tax return. Gambling income includes but isn't limited to winnings from lotteries, raffles, horse races, and casinos. It includes cash winnings and the fair market value of prizes, such as cars and trips.
A payer is required to issue you a Form W-2G.pdf, Certain Gambling Winnings, if you receive certain gambling winnings or have any gambling winnings subject to federal income tax withholding. You must report all gambling winnings as "Other Income" on Form 1040, Schedule 1.pdf and attach this to Form 1040.pdf, including winnings that aren't reported on a Form W-2G.pdf. When you have gambling winnings, you may be required to pay an estimated tax on that additional income. For information on withholding on gambling winnings, refer to Publication 505, Tax Withholding and Estimated Tax.
You may deduct gambling losses only if you itemize your deductions on Form 1040, Schedule A.pdf and kept a record of your winnings and losses. The amount of losses you deduct can't be more than the amount of gambling income you reported on your return. Claim your gambling losses up to the amount of winnings, as "Other Itemized Deductions."
If you're a nonresident alien of the United States for income tax purposes and you have to file a tax return for U.S. source gambling winnings, you must use Form 1040NR.pdf, U.S. Nonresident Alien Income Tax Return. Refer to Publication 519, U.S. Tax Guide for Aliens, and Publication 901, U.S. Tax Treaties, for more information. Generally, nonresident aliens of the United States who aren't residents of Canada can't deduct gambling losses.
To deduct your losses, you must keep an accurate diary or similar record of your gambling winnings and losses and be able to provide receipts, tickets, statements, or other records that show the amount of both your winnings and losses. Refer to Publication 529, Miscellaneous Deductions, for more information.
For additional information, refer to Publication 525, Taxable and Nontaxable Income, or review How Do I Claim My Gambling Winnings and/or Losses?
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There is also a flyer available in PDF form, called You Won!, which has a similar overview with a somewhat different presentation.
Under Colombian Law
I am indebted to the now deleted answer by Weather Vane, which points out that Colombia also has restrictions on the import and export of cash. The limit is the same: USD 10,000. If you exceed the limit, therefore, you will have to report it to the Columbian authorities; otherwise, you might never get the chance to report it to the US authorities.
You may also be liable for income tax in Colombia, but I do not know anything about that. If the casino is legitimate, you should not be surprised if Colombian tax is withheld, in which case you may be able to get some of it back by filing an income tax return, depending on the withholding and taxation rules. For your US income taxes, you can deduct or claim credit for taxes paid to a foreign jurisdiction.