Card Shuffling Question

Factual Questions
1

I have a friend who claims that if you take a brand new deck of standard playing cards out of a package and shuffle it three times then it is thoroughly shuffled meaning that additional shuffling won’t mix it up any better. That doesn’t sound right to me. Especially with a brand new deck! I don’t have time to do the experiment so…

… how many shuffles are necessary (the minimum) to make sure the cards are as mixed up as they will ever be?

2

Twenty years ago I read in Discover magazine that it takes seven average shuffles to thoroughly mix the deck. Sorry no cite.

3

I citelessly corroborate this.

4

I seem to recall it too. If this is true, does it have anything to do with the fact that the square root of 52 is approximately 7?

5

CITE!

6

My Intro to Prob Theory book had a blurb on that as well I believe. Actually, it might have been my Rationality class, but it really doesn’t make a difference since I have no cite either way.

7

Here are some interesting cites about shuffling.

8

You can’t shuffle too well though. Eight perfect shuffles will put the deck back in its original order.

9

I’m entered in the 50-meter shuffle in the next geezer olympics.

10

Here’s a good essay on “perfect shuffling”;

http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Simmons/Essay4/Essay4.html

Much of your question is dependent upon;

How much mixing is sufficient? (if the cards are still somewhat in order, the dealing should further randomize them - the only case where I can think this would make a difference is in Blackjack).

How proficient is the shuffler, and what shuffling method are they using? I’ve seen 3 kinds of shuffling used; riffling, hand tossing, and the spread out on the table and mix “'cause I can’t shuffle” shuffle.

How much do you want to play cards vs. shuffle?

I used to play euchre for hours on end. If you’re not familiar, it uses 24 cards from a standard deck. Typically, we’d shuffle 3 times, offer a cut, and deal.

The thought was, it’s much easier to manipulate a smaller deck to get the cards you want when you’re the dealer/shuffler - so if everybody shuffled the same amount of times - and offered a cut - the theory was no-one could be cheating.

I believe it is customary for the dealer to offer a cut to the person sitting behind the dealer in order of play for any card game.

11

[QUOTE=Rocket]

and the spread out on the table and mix “'cause I can’t shuffle” shuffle.

/

[QUOTE]

Actually, I’ve been watching a lot of the world poker tour recently, and the dealer shuffles that way. I doubt they would hire dealers that can’t shuffle… perhaps the way they do it randomizes more sufficiently?

12

Yeah – I’ve played plenty of poker in casinos and they always shuffle this “I can’t shuffle” way.

Don’t know if blackjack dealers do it.

13

[QUOTE=chaoticdonkey]

[QUOTE=Rocket]

and the spread out on the table and mix “'cause I can’t shuffle” shuffle.

/

In Vegas, I’ve seen many different methods of shuffling (at poker tables). Some have automatic shufflers (each hand swaps a newly shuffled deck). Others use the “I can’t shuffle” method. And some use thie “I can’t shuffle method” followed by several standard shuffles.

I sat at one table (manual shuffle) and asked why anyone at anytime can call for a “new deck”. One helpful player pointed out that during the “I can’t shuffle” method, many of the cards do not, in fact, change position. The dealer simply moves many of the cards around in circles without changing their order. This leads to one side of the table winning the majority of the hands. Call for a new deck and the winning might swing to your side.

14

I can think of two reasons for “I can’t shuffle” shuffles (is it just me or is shuffle starting to sound wierd?) in casinos and tournaments.

  1. Speed. You can mix up a single deck a heck of a lot faster by spreading the cards around. If it takes even a skilled dealer 5-7 seconds to split, shuffle, and reorganize the deck. Figure it takes at least 35-49 second (per 7 shuffle set) to mix up the cards. But if you just spread the cards you can probably have the deck reorganized in about half that time. It may not seem like much, but in a casino time is money.

2.Cheating. It’s almost impossible for a dealer to cheat using the “I can’t shuffle” shuffle. At best he might be able to drop an extra card into the deck, but he wouldn’t be able to withdraw one easily. The extra card would be easily picked up by either a player at the table, or the security cameras. Whereas an expert shuffler can manipulate a deck almost anyway he/she wants.

15

At every poker table I’ve played at (that didn’t have an automatic shuffler), the dealer did the “I can’t shuffle” shuffle followed by two or three riffle shuffles. Never the “I can’t shuffle” shuffle alone.