I want to live in Las Vegas for 6 months.

I am a Canadian citizen. I want to move to Las Vegas and live in an apartment for 6 months. I have an online business doing affiliate marketing. Am I allowed to continue running my online business while staying in Las Vegas? I am guessing it is allowed since all I need to run my online business is a laptop.

Or maybe I don't even need to mention I run an online business? I thought the USA customs just ask to see proof of adequate finances to be able to stay for 6 months. Does anyone have any advice on this?

If you are in the US working, legally you would require US permission to work, even though you are self employed. Their laws are if you're on US soil, you need a US work permit.

Technology however is far ahead of the laws, but they do reserve the right to inspect your laptop and your personal luggage. If they determine that you will be working while in the US, they can deny your entry and not let you back in again until you either prove a) that you will not be working while there (which means don't bring your laptop) or b ) get a work permit.

Option B of course being nearly impossible if you're self employed on the internet.

Am I allowed to continue running my online business while staying in Las Vegas?

No, it's not legal to work as a visitor, it depends where you physically are when the work is performed. I had a serious grilling about this topic at Sweetgrass once so they are wise to it. As soon as they see you have a laptop with you and/or you tell them you work in something to do with the internet or IT then they're likely to ask you (especially if you say you're staying for six months I would have thought).

Under caselaw, "incidental" work is allowed, e.g. someone phones from the office to ask a question.

The other thing to bear in mind is that if you are working in the US, your income is subject to US taxes as well.