My wife and I attended an Elderhostel in Erlanger, KY (one of the Cincinnati suburbs) a few years ago, and one of our field trips was to Rabbit Hash, KY, just across the river from Rising Sun, IN, where one of the casino boats is moored. Apparently, the fact of the KY border being on the north side of the river isn't universal, because the Indiana casino boat is able to travel on the river. However, we were told that the state of Kentucky had laser beams trained along the parts of the river that were Kentucky waters and, if the casino boat broke the beams of those lights, all gambling had to cease until they were once again in Indiana waters.

And, yes, at least for the Ohio/Kentucky border, the KY state line is on the northern bank of where the river was at some time in the past, so there are parts of Cincinnati that are technically in Kentucky.

But just this last week when we stayed overnight in Kentucky on our way home, we heard a news report that casino gambling is being considered for KY. Apparently it will require a change in the state constitution, though, so it may be hard to accomplish.