Here is what I know-- though I'm sure some here might have more accurate info...
Topps never marketed the cards of the dice game. It was more of a test product, an internal thing. What seems to support this is that almost every other Topps issue of the era used color and the surviving Dice cards were black and white. Again, not saying that as FACT. My knowledge here is limited.
I remember reading that someone at Topps named Woody Gelman was like their creative director and would issue samples and letters to established hobbyists and sometimes the card was stapled or otherwise affixed to the letter.
Rumor was there were a few sheets with 20 cards. I think Fritsch owned one of them. The one Dice Game Mick I recall for sale was raw hand-cut.
So that one had to come from a sheet, but I remember seeing another one that PSA slabbed that looked factory cut to me.
There was also a send away official Topps product called the plaque/mask and was from 63? That's also rare. I believe the Dice card is considered tougher and more valuable though. Maybe some of our big Mantle collectors can shed some more light for you.
Link to a past sale:
Dice Game Card Sold