Randomizing a deck of cards
Shuffling a deck of cards is a relatively poor way to randomize. It can take surprisingly many passes to completely randomize the deck, more than people use in a game. It’s possible to intentionally or unintentionally fail. The best way to randomize cards might be to spread them all out, mix them around, reassemble the deck, and repeat several times. People don’t typically do this.
It might be interesting to randomize a deck by throwing dice to order the cards. I wonder if bridge players would notice, or if it would change their play. You could say (and I would agree) that making up the deck is part of the game; that there are rules for making up the deck; and that rolling dice and looking up the corresponding cards isn’t part of the game. Anyway, a thoroughly randomized deck would be detectable through statistical analysis, and I suspect it would affect the game. The players would notice that things seemed to be going oddly.
On a big table, lay out the cards, with jokers, in rows of nine. The first die determines which of the six rows to choose. The second die could determine from what position in the row to start counting, and the third die the number to count off to choose the card. Or you could make a look-up table for three dice, following Diceware’s example.
You could set up a deck like this, and carry it in your pocket. Just in case.