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Topic: Knuth shuffle

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	Donald Knuth - Wikipedia, the free encyclopedia
		Knuth (pronounced "Ka-NOOTH" [1]) is best known as the author of the multi-volume The Art of Computer Programming, one of the most highly respected references in the computer science field.
		In addition to his writings on computer science, Knuth is also the author of 3:16 Bible Texts Illuminated (1991), ISBN 0895792524, in which he attempts to examine the Bible by a process of stratified random sampling, namely an analysis of chapter 3, verse 16 of each book.
		Knuth published his first "scientific" article in a school magazine in 1957 under the title "Potrzebie System of Weights and Measures." In it, he defined the fundamental unit of length as the thickness of MAD magazine #26, and named the fundamental unit of force "whatmeworry".
	en.wikipedia.org /wiki/Donald_Knuth (871 words)

	Shuffle - Wikipedia, the free encyclopedia
		Shuffling is often followed by a cut, to ensure that the shuffler has not manipulated the outcome.
		Because standard shuffling techniques are seen as weak, and in order to avoid "inside jobs" where employees collaborate with gamblers by performing inadequate shuffles, many casinos employ automatic shuffling machines which perform continuous shuffles on a pack of cards, and can produce any number of cards on demand.
		The mathematician and magician Persi Diaconis is an expert on the theory and practice of card shuffling, and an author of a famous paper on the number of shuffles needed to randomize a deck, concluding that it did not start to become random until five good riffle shuffles, and was truly random after seven.
	en.wikipedia.org /wiki/Shuffle (1165 words)

	Donald Knuth - the free encyclopedia (Site not responding. Last check: 2007-09-18)
		Knuth (pronounced "Ka-NOOTH" [1]) is best known as the author of themulti-volume The Art of ComputerProgramming, one of the most highly respected references in the computer science field.
		In recognition of Knuth's contributions to the field of computerscience, in 1990 he was awarded the singular academic title of Professor of the Artof Computer Programming, which has since been revised to Professor Emeritus of the Art of Computer Programming.
		Knuth published his first "scientific" article in a school magazine in 1957 under thetitle "Potrzebie System of Weights and Measures." In it, he defined the fundamental unit of length as thethickness of MAD magazine #26, and named the fundamental unit offorce "whatmeworry".
	www.free-web-encyclopedia.com /?t=Donald_Knuth (654 words)

	donald knuth - Article and Reference from OnPedia.com
		Knuth (pronounced "Ka-NOOTH" http://www-cs-faculty.stanford.edu/~knuth/faq.html) is best known as the author of the multi-volume The Art of Computer Programming, one of the most highly respected references in the computer science field.
		He is married to Jill Knuth, who published a book on liturgy titled 'Banner without Words', published by Resource Publications in 1986.
		Knuth, Donald E. Knuth, Donald Knuth, Donald Knuth, Donald Knuth, Donald Knuth, Donald Knuth, Donald Knuth, Donald Knuth, Donald Knuth, Donald Knuth, Donald
	www.onpedia.com /encyclopedia/donald-knuth (737 words)

	Computer Generated Random Numbers (Site not responding. Last check: 2007-09-18)
		Shuffling also takes care of the problem of points lying "mainly in the planes" as was discussed earlier.
		By shuffling the output, we have converted the first-order Markov process to something like an Mth-order Markov process where M is the size of the shuffling deck we use.
		Shuffling the output of any random number generator using the technique given is therefore highly recommended.
	www.std.com /~franl/crypto/random-numbers.html (10155 words)

	Crazy Harry Online Poker Shuffling
		To guarantee the fairest in play, a shuffling algorithm is applied to ensure that a truly random deck is used.
		Our sort shuffle is based on using a random number generator that generates 2^32 different values pulled from a 4096 bit entropy pool.
		This is different than the Knuth shuffle used by some other systems, and it has some advantages.
	www.crazyharrypoker.com /shuffling.asp (337 words)

	PHP: shuffle - Manual
		This may enable random shuffling of arrays with less guarantee of true randomness, but more guarantee that the output looks different from the input, which is probably what you want.
		One effect is that an element in the middle of the array is heavily biased toward being "shuffled" to the middle.
		Also, the mt_rand() should be (0, $i) not ($i+1), with $i+1 there's a 1 in N chance on the first pass it shuffles in 1 past the end of the array, putting a blank at the last element.
	www.php.net /manual/en/function.shuffle.php (1019 words)

	Casino Elite the Internet Online Gambling Website
		Most sites currently use either a single-pass full Knuth shuffle, or an incremental Knuth shuffle (which is essentially the same, but does the work as cards get dealt).
		The problem with the regular single-pass Knuth shuffle algorithm is that it relies on a random_range() function which is supposed to produce a uniformly distributed random number, however this isn't usually the case.
		When it comes to shuffling, the random number generator used is at least as important as a good shuffling algorithm.
	www.casino-elite.net /shuffling.html (1416 words)

	Algorithms::Numerical::Shuffle - Shuffle a list. (Site not responding. Last check: 2007-09-18)
		For an in situ shuffle, the memory overhead is constant; otherwise, linear extra memory is used.
		If the outcome of a random generator is solely based on the value of the previous outcome, like a linear congruential method, then the outcome of a shuffling depends on exactly three things: the shuffling algorithm, the input and the seed of the random generator.
		Hence, for a given list and a given algorithm, the outcome of the shuffle is purely based on the seed.
	www.mathematik.uni-ulm.de /help/perl5/doc-5.005_03/Algorithms/Numerical/Shuffle.html (272 words)

	: Class RKUPermutation (Site not responding. Last check: 2007-09-18)
		Permute an integer array according to variant 1 of Knuth's algorithm.
		Permute an array according to variant 1 of Knuth's algorithm.
		The time used to permute is proportional to the number of shuffles.
	www.daimi.au.dk /~ursem/EAdocs/RKUjava/math/RKUPermutation.html (321 words)

	Re: new coreutil? shuffle - randomize file contents
		There is >scope in sort that is far beyond shuffle.
		They are orthogonal challenges, and while extending sort with a "head" operator would be contrary to the unix-y way of small, separate do-one-thing-well filters, the efficiency gains are an overwhelming plus (and not only in the context of shuffling).
		I don't think is necessarily the case, even if "secure" shuffling is required.
	www.mail-archive.com /bug-coreutils@gnu.org/msg04166.html (310 words)

	random_shuffle
		Knuth credits Moses and Oakford (1963) and Durstenfeld (1964).
		Note that there are N! ways of arranging a sequence of N elements.
		The reason this comment is important is that there are a number of algorithms that seem at first sight to implement random shuffling of a sequence, but that do not in fact produce a uniform distribution over the N! possible orderings.
	www.sgi.com /tech/stl/random_shuffle.html (251 words)

	Randomize an array? - GameDev.Net Discussion Forums
		From how I read that, Trap's algorithm is one of Knuth's shuffling algorithms, although I'm not sure if its the same one used in random_shuffle.
		Posted - 2/26/2005 5:14:37 PM In Knuth's shuffling algorithm you can't swap with an element that has already been swapped, otherwise the result will be biased.
		In Knuth's shuffling algorithm you can't swap with an element that has already been swapped, otherwise the result will be biased.
	www.gamedev.net /community/forums/ViewReply.asp?id=1930028 (843 words)

	Golden Riviera Poker
		Additionally, we make use of a shuffling algorithm that guarantees a truly random deck is always used.
		This method eradicates the issue of single pass that the Knuth shuffle has, involving the modulo bias.
		It is possible to reduce this effect by using a multi-pass Knuth shuffle, but we have decided to select a superior shuffle algorithm instead.
	www.goldenrivierapoker.com /EN-US/fair.asp (588 words)

	Poker by the Gaming Club Online Poker Room
		The shuffling algorithm used to ensure a truly random deck is of extreme importance.
		This method of shuffling eliminates the problem that a single-pass Knuth shuffle has involving the modulo bias.
		It is possible to mitigate these effects by using a multi-pass Knuth shuffle, but this becomes obsolete with the introduction of the superior algorithm.
	www.set2gopokerroom.com /poker-help/game-fairness.asp?VT=&EventID=24610 (642 words)

	Poker Shuffle
		The most common shuffling technique is called a riffle, in which half of the poker deck is held in each hand with the thumbs inward, then poker cards are released by the thumbs so that they fall to the table intertwined.
		The pile shuffle is not a randomization technique, but a method to dissolve clumps of sticky poker cards.
		Because standard shuffling techniques are seen as weak, and in order to avoid "inside jobs" where employees collaborate with gamblers by performing inadequate shuffles, many casinos employ automatic shuffling machines which perform continuous shuffles on a pack of poker cards, and can produce any number of poker cards on demand.
	www.imperialpoker.com /poker/poker-shuffle/index.php (1200 words)

	Integrity at Bugsys Club
		The three goals of a shuffling algorithm are: correctness, lack of bias, and lack of predictability.
		The problem some other sites have noted with the Knuth shuffle (introduction of a bias towards lower numbers) is actually a problem with their random_range function used to generate a number between 0 and 51 from the number their PRNG gave them, which is why they needed to shuffle several times.
		Because BugsysClub Poker uses the Mersenne Twister PRNG and the incremental Knuth shuffle (with a range function that is free of bias) you are guaranteed that you will receive a 'true' shuffle for any given hand.
	www.bugsysclub.com /club/about/integrity.htm (1046 words)

	Merlyn - Javascript Random - J R Stockton (Site not responding. Last check: 2007-09-18)
		A perfect full shuffle or deal introduces complete randomness; no trace of the original order is left.
		Therefore a partial shuffle will generate a random subset of entries, followed by the result of a Draw.
		If the order of the result matters, repeatedly pick an element at random from those as yet unchosen and swap it with the end unchosen one,...; after enough selections, the required result will be at the end.
	www.merlyn.demon.co.uk /js-randm.htm (2023 words)

	The Old Joel on Software Forum - Card shuffling routine
		Las Vegas has determined that after 7 shuffles by the dealer, the cards are sufficiently random that a normal person would never be able to see a pattern.
		Blackjack card-counters who also shuffle-track have done a lot of study and shuffle simulation to help predict clumps of face-cards in multi-deck shoes, especially right after new decks are introduced when the cards do not end up shuffled fully.
		Their critical flaw wasn't with their shuffling algorithm (don't remember if they had a good one or not, wasn't really relevant), their flaw was how they generated their random numbers.
	discuss.fogcreek.com /joelonsoftware?cmd=show&ixPost=178050 (2288 words)

	[No title]
		Because of this, the interface to the shuffle generator, * but not the additive 55 generator, is advertised when this file is * loaded.
		The remaining bits of seed * are used to perform an initial shuffle on the shuffle state table.
		We however, restore the additive 55 and shuffle * generators back to its seeded state in order to be sure that it * will be left in the same state.
	www.utdallas.edu /~cantrell/ee6345/4_4BSD-Lite/usr/src/contrib/calc-2_9.3t6/lib/cryrand.cal (5516 words)

	Wild Jack Poker - Security (Site not responding. Last check: 2007-09-18)
		A multi-pass Knuth shuffle could also alleviate the problem, but it is unnecessary as the new algorithm is superior.
		Therefore, the number of shuffled deck combinations is 52x51x50x49x3x2x1, which results in 8x1067 permutations.
		Using the shuffle method, the initial permutation available is (232)52.
	www.wildjackpoker.com /security.php (786 words)

	[No title] (Site not responding. Last check: 2007-09-18)
		Donald Knuth, _The Art of Computer Programming, v.
		is according to Knuth's revised recommendations in the 9th !
		does everything short of shuffling the output numbers.
	george.ph.utexas.edu /~dsteck/code/random_pl.2.0.3/random_pl.f90 (4403 words)

	[No title]
		A very similar // discussion can be found in the "Seminumerical Algorithms" volume of Knuth's // "Art of Programming." // // This code has been rendered in C++ largely for pedagogical purposes.
		This simply takes // the "default" multiplicative congruental random number generator, // which returns a result in the range from 1 to max_long, throws // away the first few elements (because the default seed has very low // Kolmogorov complexity...), shuffles, and then scales the resulting // sequence to the range (0.0,1.0).
		Likewise, the "shift" has been // folded in to the shuffle class.
	people.cs.uchicago.edu /~johnross/cs106/prandom.cpp.txt (884 words)

	shuffle the lines of a large file (Site not responding. Last check: 2007-09-18)
		Previous message: shuffle the lines of a large file
		I vaguely remember having read something along these lines (not shuffling as you mean it, but still, reorganising a lengthy file) in Knuth's "Art of Computer Programming", in one of the exercises within the chapter on Sorting methods (volume 3).
		That's long ago, but if I remember well, Knuth did not consider this as an easy exercise.
	mail.python.org /pipermail/python-list/2005-March/269867.html (183 words)

	A Lower Bound for Sorting Networks Based on the Shuffle Permutation - Plaxton, Suel (ResearchIndex) (Site not responding. Last check: 2007-09-18)
		This settles an open question posed by Knuth, up to a \Theta(lg lg n) factor.
		The proof technique employed in the lower bound argument may be of separate interest.
		Plaxton, C. G., and Suel, T. A lower bound for sorting networks based on the shuffle permutation.
	citeseer.ist.psu.edu /plaxton94lower.html (615 words)

	Random number generation and shuffling at Paradise Poker. (Site not responding. Last check: 2007-09-18)
		This paper covers some of the commonly used algorithms and their flaws, and it discusses how Paradise Poker shuffles decks of cards.
		We found that shuffling twice removes 99% of the bias, and shuffling 3 times makes it pretty much immeasurable, then we decided to triple it for good measure and bump it up to 10 times to keep the marketing people happy.
		We believe you'll agree that this is by far the most comprehensive shuffling solution available at any internet poker site.
	www.paradisepoker.com /shuffling.html (1496 words)

	Integrity
		Any players that attempt to collude will be banned from Poker Europe and their names will be placed on an industry-wide list to alert other casinos of their inappropriate behavior.
		This is different to the Knuth shuffle used by some other systems, and it has some advantages.
		For comparison, it is 10^382 times more likely that one could randomly choose the same molecule of water from the ocean twice in a row than it is that we would ever generate the same set of values to create a shuffled deck from.
	www.pokereurope.com /support_integrity.html (736 words)

	PS Wiki Encyclopedia (Site not responding. Last check: 2007-09-18)
		Such fields include coding theory, cryptography, and simulation.
		A good example of a random permutation is the shuffling of a deck of cards: this is ideally a random permutation of the 52 cards.
		One method of generating a random permutation of a set of length n uniformly at random (i.e.
	70.84.119.226 /~puresear/PSWiki/index.php?title=Random_permutation (238 words)

	Re: i need help with this card game!
		>> > >> > I don't know what Knuth says but something like this: >> > >> > int i; >> > for(i=0; i<51; i++) >> > /* swap cards[i] with cards[random number in range 0..51] */ >> > >> > is fine.
		However I'm not sure that is what osmium is talking about since he never mentioned the method of generating random numbers, his comments appear to relate to the shuffling algorithm itself.
		> Specifically since Knuth states that the MSB should be used lest the LSB > may suffer from (unwanted) regularities.
	www.talkaboutprogramming.com /group/comp.lang.c/messages/724113.html (435 words)

	World Poker Exchange - Shuffling (Site not responding. Last check: 2007-09-18)
		The shuffling algorithm used to ensure a truly random deck is very important.
		We use a sort shuffle using a random number generator that generates 2^32 different values pulled from a 4096 bit entropy pool.
		Here is an example of exactly how the shuffling algorithm works:
	www.wsexpoker.com /game_info/game_integ.asp?game=2 (319 words)

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