How about this idea...

A new issue comes up in your part of the country, say a new casino opens in Indiana for example.

You find ten people who need this chip, send out the original round robin with ten of this chip with the specification that they can take only ONE of that particular chip (they could take any others, of course), but the replacements they leave can NOT be a duplicate of any other chip in the RR.

When the RR got back to you, you would have ten "fresh" chips... hopefully you would even need one or two

Could work.