How random is a shuffled deck?

[Morbo]

I do not know every part of a professional dealer's shuffling methods but how do you really confirm that when he/she shuffles that the cards are randomly distributed? Ponder for a moment, if you take for example the top card of the deck before the dealer starts shuffling, can this card really land in ANY spot in the deck? And lets say that it is bound to land in the top 1/4 of the deck, does this matter for randomness in any way? And what about cutting the deck?

[1800GAMBLER]

Good luck cracking all the possible outcomes of his deal in less than 10 seconds. That's why it's 'varied'. It's not random though, but a coin flip isn't random either.

[LetsRock]

Depending on how thorough of job the shuffler does and how the deck is halved when shuffling, the cards can get shuffled to a releatively random state. Yes, a lazy shuffler can get the top card or the bottom card to remain in their places, but cutting the deck will change this and those cards would end up somewhere in the middle of the deck.

If you're trying to predict that a card will or will not be in play based on "knowing" it's starting position before the shuffle, don't waste your time.

[JPNet]

Actually, according to a book by John Haigh, in a "perfect" riffle shuffle where the cards are interleaved 1 from the left, one from the right, after 8 perfect shuufles the deck would be exactly like it was before the shuffling began.

He then quotes the work of Persi Diaconis who was able to demonstrate that whatever the shuffling method, the deck will remain very similar to it's original state for a period, and then over a relatively brief time becomes effectively random. For a simple shuffle where the top card is placed at random amongst the other 51, you need 240 movements. In the case of an "imperfect" riffle shuffle you need 8 or 9 to achieve randomness.

Because of the cyclic nature of a "perfect" riffle shuffle noted at the beginning, an expert shuffler may not randomize the cards as well as a clumsy amateur.

[ACW]

There's been a lot of debate about this by bridge players in recent years. Bridge is essentially a game of random distributions of cards. When tournaments started using computer dealt hands around 10-15 years ago, players complained that the hands were too wild - lots of long suits and short suits, rather than the more balanced hands given by conventional shuffling and dealing.
Of course, the reason for this is that most human shuffles don't randomise the deck. This is particularly bad in bridge, since cards tend to collect in groups of four of the same suit, due to the rules of play. Also, high cards tend to be played after lower cards. The net effect is a significant (and noticeable) difference in the hands dealt by computer than those dealt humanly.
I'm sure the same effect occurs in poker, but it doesn't matter nearly so much as the cards mucked follow an essentially random pattern to start with.

[John Feeney]

Don't forget the "scramble" that is standard procedure in a lot of cardrooms. I think it does a lot to eliminate any problems of non-randomness associated with shuffling only, say, three times.

[Yardbird]

[ QUOTE ]
Good luck cracking all the possible outcomes of his deal in less than 10 seconds. That's why it's 'varied'. It's not random though, but a coin flip isn't random either.

[/ QUOTE ]

EXACTLY!

Computers cannot generate random numbers; only psuedo-random numbers... That's why there have been a number of documented cases of math-whizzes defeating digital lotteries: they essentially 'cracked' the code (determined the seed and algorithm) by deduction, and proceeded to extrapolate future results with virtual certainty. Courts have upheld such exploits as feats of skill and not cheating, in much the same way as counting cards while playing blackjack cannot be considered cheating.

In 2+2's "The Professional Poker Dealer's Handbook" [Harris, Paymar & Malmuth] the standard shuffle is summarized as a wash followed by two riffles (alternating final top cards between right and left), stripping the deck, another riffle, and finally a cut. That is a very effective method which IMHO is an optimization between brevity and efficiency. Nonetheless, it still isn't "random" in the strictest sense of the word. It's a manual process effected my countless circumstances, and it is only the degree of imprecision in identifying those stimuli that renders the shuffle effectively random.

There is nothing in nature this is truely random---we live in a closed system (as nearly as can be determined)---not even Brownian motion can match the strictest mathematical definition of randomness AFAIK. Although, from a philoophical perspective, that may actually be an indication of the limitation of mathematics as a modelling system for reality rather than a proof for the existance of random events in the universe; but, that would be better argued by big number and chaos theoreticians more accredited than I.

So, the answer to the question "How random is a shuffled deck?" is "enough."

I postulate that the Expaected Value of a play in poker would best be determined by its mean effectiveness over every possible distribution of the cards; therefore, the randomness of the deck is irrelevant, and, making only positive plays over the course of infinite time still won't guarantee you'll be a winner because there are no random events. Besides, even if you assume that the law of averages is sound, your lifespan is too small a sample relative to that eventuality to make a reasonable prognostication of your net success.

So now you have "the egg-head's" answer to the question. [img]/images/graemlins/cool.gif[/img] [img]/images/graemlins/tongue.gif[/img] [img]/images/graemlins/grin.gif[/img]

[Louie Landale]

"Random" may mean a card can reasonably be anywhere in the deck. A more useful definition is whether cards that started next to each other can be randomly distributed.

I strongly suspect that a card that started on the top of the deck can be reasonably distributed. But I also reasonably suspect that cards that start adjacent to each other have a significantly higher chance of remaining adjacent after the suffle and a cut: that is, a purely random pair has about a 26:1 chance of being adjacent; but if they started adjacent the actual chance for real-life dealers may be around 18:1.

I'm guessing of course. I also don't know how to put this information to practical use. Well, except for one way: if the last and featured trip 7s and these cards went into the muck together, and you are on the button with a hand featuring a 7 I suspect there is a higher chance than normal that a 7 will flop. Notice that if you are in EARLY position then I'd suppose there is a LESS than average chance a 7 will flop, since the other 7s are in adjacent hands.

I also suspect that the above paragraph will be a good enough excuse for folks to play all sort of trash; and is therefore probably detrimentaly even if its slightly true.

- Louie

[Lou Krieger]

[ QUOTE ]
I do not know every part of a professional dealer's shuffling methods but how do you really confirm that when he/she shuffles that the cards are randomly distributed?

[/ QUOTE ]

This is interesting from a theoretical perspective but from a practical viewpoint, if a dealer's mechanics are sound then scrambling the deck, and going through the four-step procedure of shuffle, shuffle, riffle, shuffle will provide a deck that is random enough .

After all, poker's been played this way for years, without any major issues attendent to the relative randomness of the deck. I don't see any advantage gained by shuffle tracking at the poker table, except under circumstances where the dealer is sloppy about his work.
_______
Lou Krieger

[schwza]

[ QUOTE ]

There is nothing in nature this is truely random---we live in a closed system (as nearly as can be determined)---not even Brownian motion can match the strictest mathematical definition of randomness AFAIK.

So now you have "the egg-head's" answer to the question. [img]/images/graemlins/cool.gif[/img] [img]/images/graemlins/tongue.gif[/img] [img]/images/graemlins/grin.gif[/img]

[/ QUOTE ]

An egg-head response... According to our current understand of quantum mechanics, there is an incredibly high amount of true randomness in nature. Measure the location of a particle and then measure its location again in one second, and it is impossible to know with certainty where the particle will be. We can only calculate a probability distribution corresponding to many different places it could be measured to be.

This lack of knowledge is not a product of a lack of technology or methodology - quantum mechanics states that it is impossible to know where the particle will be. Its measured position is truly random.

Now in 100 years quantum mechanics may be laughed at like the flat-Earth belief, but the real egg-heads seem to dig it for now.

Incidentally, Ultimatebet's card-shuffling algorithm uses physical data that operates on the same principal.