https://www.tax.ohio.gov/faq/tabid/6315/Default.aspx?QuestionID=627&AFMID=11354
Pursuant to R.C. 5747.063, if a person’s winnings at a casino facility are such that the IRS requires reporting on form W-2G or 1042-S ($1,200 or more not reduced by the wager for slot winnings; more than $5,000 reduced by the wager or buy-in for table win; or $600 or more if the winnings are more than 300 times the amount wagered or are subject to federal income tax withholding), the casino operator shall deduct and withhold Ohio income tax from the person’s winnings at a rate of four percent (4%) of the amount won. (Please note that, prior to June 12, 2012, each casino operator was required to withhold Ohio income tax at a rate of six percent (6%) for those people meeting the thresholds mentioned above.)
The casino operator shall issue a form W-2G (or form 1042-S for a foreign individual) reflecting the amount deducted and withheld, and also shall obtain any additional information deemed necessary. Please click here for a link to the statutory language relating to casino withholding.
Casinos are not required to withhold school district income tax from prize winnings. Nonetheless, a taxpayer remains liable for the taxes imposed by section 5747.02 or Chapter 5748. of the Revised Code. An individual residing in a school district with a traditional income tax base who incurred prize winnings may need to make estimated tax payments as required by section 5747.09 of the Revised Code using form SD-100ES.
Key points for Ohio are $1,200 or more NOT reduced by wager for slot winnings. And regards to your question regarding betting 1000 and winning 201, I assume he interpreted that to mean you bet $1,000 and only received back $201 in that roll, which to him would be a net loss of $799. Most of us understand you meant you got back $1,201 with NET winnings of $201 but that would be my guess of his interpretation and answering the way he did. Apparently Ohio winnings aren't profit and loss winnings, they are actually returns (revenues). You would have to file a return reporting your revenues and then offset your costs (original bets) to achieve a net income number.
Also you might want to look into that school district tax item because if they did issue you a W2-G, there will be a traceable record of your win and I would imagine they are vigilant in chasing down that money.
This is dated but Jean Scott had an Ohio entry in her blog a few years ago.
https://jscott.lvablog.com/2013/06/09/gambling-taxes-in-ohio/