Playing cards for randomization (keeping Ace-6) maybe 2 or 4 packs shuffled together. Each card is just as random as a d6 (without knowing the other). All together keep the average guaranteed. Maybe shuffle them all back when few of them (say <10) remain in the deck to prevent “knowing” the remainder is better/worse if the history so far has been worse/better.
It’s a lot easier to cheat with cards than dice.
Not that a pristine fellow like myself would know of course. I, um, heard it from, um, TV, yeah, that’s it.