Sports books do notice take out taxes on winning tickets, regardless of the amount.
On race tickets that pay 300-1 or better they do.
I think what you're asking about is when does paperwork kick in and the answer is the same as for any other cash transaction anywhere. At anything over 10K a Treasury form is filled out documenting that an amount in excess of 10K changed hands. This is not a tax form and you don't necessarily owe taxes because the form was filed. A way to avoid the form is to "bet down" the ticket payout if possible. That means make enough new bets that when exchanged for the winning ticket results in 10K or less being received in cash. If the book has sports chips you could also take payment in that form. Many books have done away with sports chips in the past two years including CGTech and Westgate.
Try searching Lee's Discount Liquor for wine. They have multiple locations in the valley including one on both East and West Flamingo. They have the largest wine selection in the state.