A very good point, indeed. You know, the more I think about it, cards or a spinner might have replaced dice as the randomizer. Cards were in no short supply since a lot of people played rummy, canasta, bridge and the like. Dice might have been thought of as 'too much like gambling', and they're not as easily portable as cards are. But you had Monopoly (A quick search on this shows the history of Monopoly goes back a lot further than I thought, to 1904) and other board games with Dice, I assume. So maybe not.