How Good is Your Shuffle
Here is a fun tidbit for all the degenerates out there like us that spend every day just sitting there shuffling cards, and occasionally hanging out with other people who shuffle cards.
How good do you think your shuffles are? How much do they really mix the deck? I know we have all heard some version of Persi Diaconis’ admonition that we have to shuffle seven to twelve times to achieve real randomness, but what does that actually mean for us in the day-to-day?
Well, thanks to a handy chart in Professional Blackjack by Stanford Wong, now I can give you a rough idea. Here is a challenge: take an ordinary deck of cards and look at any two adjacent cards. Now do a casino style riffle-riffle-strip cut (6 - 10 packet running cut)-riffle sequence. Spread the deck again and find those two cards. About half of you are now finding that after all that shuffling and cutting, those two cards have no more than 5 cards between them. About a third of you are finding that there are in fact only three or fewer cards separating them!
While I’m still not sure this has a magical application, it does open up an interesting bet possibility. Betting someone that if they pick two adjacent cards, give the deck a fair shuffle, and the cards will still be near (if not next to) each other seems good. So as long as you have the payouts at least 2-1 in your favor (think “If you win I’ll give you a dollar, if I win, you know what, why don’t you buy my next drink since this is so impossible?”) you have a pretty reliable bar bet. You won’t win every time, but on the whole you’ll come out ahead.
(For those interested the exact odds are 46% of the time those cards will end up with 5 or fewer cards between them and 32% for three or fewer cards. I can’t find the book right now to give you a page number in Professional Blackjack but I’ll try and update this when I find it.)