James Curtis, this is the facts as they seem to be: The ESTA allows advance checking and there is now a record sharing program between the US and UK and others. I got stopped in 2009, did a bit of digging into this and it's based on what's known as the FCC or Five Country Conference Protocol (information taken from this FOI request, see the final link for the FCC report, p.16ish, the bit where it says 'some of these will contain both immigration and policing info'
https://www.whatdotheyknow.com/request/us_access_to_uk_criminal_record)which agrees to sharing records of interest for the purposes of immigration, asylum, the prevention of criminal activity etc and is based on your fingerprints which they'll take at border entry....So if your dabs are in the system, it's highly likely they will emerge as will your conviction. My conviction doesn't really count under US law, (but i got arrested regardless which is sufficient to exclude you from VWP, the question is have you been arrested OR convicted, not whether it involves moral turpitude) but drugs seems to requires intent of distribution, possession doesn't seem to count and assault which might (a caution assumes an arrest) means you may have crimes of moral turpitude and have been arrested. Arrest makes you ineligible for the Visa waiver. You have more odds of getting caught if you've been in the country before because your prints will be in the system and if the random check draws a match, that's you.... I flew for four years before i got stopped. Failing to admit arrest or conviction at Immigration is also an offence so if you lie if you're asked, it's another strike....I said yes, spent a sweaty two hours in an interview room but got admitted, but was advised that I wouldn't be able to return again without a visa (I now have a ten year so it can be done and have been back). You may be returned on the next flight, right of entry is down to the admitting officials. If you get caught and returned your odds of reentering the US are minimal, it's ten years before you can reapply! More guidance here on what constitutes moral turpitude, but I'd get a visa...
https://help.cbp.gov/app/answers/detail/a_id/736/~/admission-to-the-u.s.-with-either-a-misdemeanor-or-criminal-record.