I'm not a dice collector and won't pretend to know much about them but I think it would be highly unusual if the 1944 on the dice, was the date issued.

There was a large illegal club in East Cape Girardeau, IL called the Thunderbird. I have a number of chips from there.
The chips were actually delivered to John Wilson, Villa Hotel, McClure, IL in the early 1950's.
Maybe you can use this info to research a little further.