Blackjack Shuffle-Tracking and the Non-Random Shuffle
Ruffled by the Non-Random Shuffleby Arnold Snyder
(Blackjack Forum Vol. X #1, March 1990)
© Blackjack Forum 1990
[Arnold Snyder is the author of The Blackjack Shuffle Tracker's Cookbook: How Players Win (and Why They Lose) With Shuffle-Tracking.]
On January 9, 1990, The New York Times published an article about two mathematicians, Persi Diaconis (Harvard University) and Dave Bayer (Columbia University) who have recently completed a computer study of casino-style card shuffling. Their paper proves that it takes seven riffles to "randomize" a single deck of cards. "Random" is defined as the probability that a card in the deck prior to the shuffle will have the same likelihood of occupying any position in the deck after the shuffle.
First of all, I'd like to thank all 173 of my readers who sent me clippings of this article, or any of the edited variations of this article which appeared in newspapers across the country after the story was picked up by the wire services.
Some of these condensed wire service stories have really riled a lot of blackjack players. One Associated Press variation was titled: "Computer Says Blackjack Shuffle Hurts Gamblers." I've been virtually swamped by letters and calls from blackjack players asking, "What can we do?"
Players who read the original New York Times article, to the contrary, were led to believe that the non-random shuffle was not detrimental to the players, but exploitable by them. Diaconis is quoted as saying: "There are people who go to casinos and make money on this. I know people who are out there doing that now." This has prompted queries from some of my readers asking if this means that alleged non-random shuffle systems like "TARGET'' and "BIAS Barometer" might actually work.
At the 1987 Gambling Conference, Dr. John Gwynn and I presented a paper entitled: "Does Casino Blackjack Differ From Computer-Simulated Blackjack?" On page I of our paper, it says: "Indeed, casino shuffles are not random. The most recent work on shuffling indicates that seven riffles are required to randomly arrange a deck of cards." The reader is referred in our bibliography (p. 15) to a 1986 American Math. Monthly article by Persi Diaconis and D. Aldous, entitled: "Shuffling Cards and Stopping Times."
After the N.Y. Times article came out, I contacted Diaconis to obtain a copy of the latest study. I would like to thank Persi Diaconis for providing me with the paper so promptly, and for permitting Blackjack Forum to quote from it.
Despite what the newspapers may have led you to believe, the latest Diaconis-Bayer paper, entitled "Trailing the Dovetail Shuffle to Its Lair," does not make any statement whatsoever regarding casino shuffles "hurting" blackjack players, nor did Diaconis and Bayer produce any data whatsoever on casino blackjack via computer simulation or mathematical analysis. Their study also was confined only to the "riffle" shuffle. The various types of thin strips, quick (thick) strips, partial strips, washes, etc., which casino dealers employ along with riffles, would throw a monkey wrench into Diaconis' and Bayer's data.
Limiting their analysis to the riffle shuffle makes their findings more applicable to games like bridge and poker, where players continuously and deliberately put cards into order by suit, rank, sequence, etc., and where stripping is less common. The simple overhand shuffle has the same effect as stripping, but many players consider this shuffle amateurish. By limiting their shuffles to a few riffles, players do preserve sequences of cards, the knowledge of which can be exploited by sophisticated players.
Shuffle-Tracking: How Professional Players Exploit Non-Random Shuffles
I do know blackjack players who exploit non-random shuffles in casinos (in fact, I am one of them). They use various methods of shuffle tracking and card location strategies (based on pre-shuffle sequences). The difficulty of shuffling 6 or 8 decks quickly has always been the Achilles heel of casinos that offer shoe games. Attempting to track these shuffles, however, has been the downfall of many good players.
Tracking is difficult and usually requires either a hidden computer (now illegal in Nevada) or a very skillful player, who has spent a lot of hours studying the theory of tracking and practicing to develop his or her skill. Diaconis' published comment about "people who go to casinos and make money on this" is not a reference to players using blackjack betting schemes like TARGET.
The Diaconis-Bayer study is concerned primarily with the riffle (dovetail) shuffle's preservation of pre-shuffle "sequences" of cards. As they put it on p.4 of their paper: "Rising sequences, the basic invariant of riffle shuffling...do not intersect, so each arrangement of a deck of cards in uniquely the union of its rising sequences. Rising sequences record the pack history of a sequence of riffle shuffles, until this information overwhelms the number of cards available to carry it."
Simply stated, an observer who knew the sequence of the cards prior to the riffle(s) can be assured that these sequences will be retained (though finely chapped up) following a series of riffles. In a casino, very sophisticated shuffle-trackers can make use of such sequential information at the blackjack tables. If only two riffles, for example, have been employed — as is often the case with multiple-deck shoe games — an observant team of players who knew the pre-shuffle sequences could know an ace is likely to land as the first card on one of the next two or three hands.
This is what the most sophisticated blackjack tracking teams have been doing for years to beat the shoe games. This is why the casinos have been continually trying to change their multiple-deck shuffle routines. This, in fact, is why fewer decks protect the casino from expert shuffle-trackers. Fewer decks are much to easier to mix up.
As a matter of fact, since 1983, a sizeable amount of computer research has been done on the non-random shuffle as it I relates specifically to casino blackjack. For the sake of Blackjack Forum readers who are confused about the current attention being focused on the non-random shuffle, and especially how it may affect your potential win rate, I would like to review what we know from past studies, as well as describe a few non-random computer simulations I have recently completed myself.
The History of Research on Non-Random Shuffles
The first important non-random shuffle studies were conducted by Stanford Wong. In his June 1983 Blackjack World newsletter, Wong published the results of a study he had done to search far "streakiness" in blackjack, i.e., wins and losses clumping together in a way that could be exploited by the player.
Wong was testing the validity of one of the theories of the then new TARGET system. This system, touted by Eddie Olsen and Jerry Patterson, claimed that in casino blackjack the player could make money in shoe games by betting on hot (winning) tables and avoiding cold tables. Winning streaks allegedly would tend to continue, as would losing streaks.
Patterson and Olsen were not the first to make such a claim. Charles Einstein, the inventor of the card counting strategy which was later computer optimized by Julian Braun as the Hi-Opt I system, claimed in his second book, Basic Blackjack Betting (GBC, 1980), that blackjack players could use his "rhythm" betting system to make money. In a nutshell, rhythm consisted of raising your bet after a win, and lowering it after a loss. Einstein claimed the system would work because wins in blackjack clumped together in a non-random fashion, as did losses.
Wong's statistical search for streakiness proved fruitless. In his June 1983 Blackjack World, he reported that his 20-million-hand simulation of the 8-deck Atlantic City game showed that "... there is no support whatsoever for the notion that good hands beget good hands and bad hands beget bad hands." He also published an extensive chart of his computer derived data.
In his August '83 Blackjack World, Wong published a letter from one of his readers who had written to complain that Wong's simulation was not valid for the casino game since "... streak betting works because of faulty shuffling." So, Wong tried another test, this one without any shuffling whatsoever.
One of the TARGET theories held that when a shoe became favorable for the player, it would tend to remain so through the shuffle, as would an unfavorable shoe. Wong programmed his computer to run through one million 6-deck shoes (44 million hands), in which played cards were reordered exactIy as they would be in a dealer's discard rack. After dealing out 4.5 decks, however, he did not shuffle at all, but simply placed the unplayed cards on top of the discards, performed one random cut, and began dealing again.
Needless to say, good shoes did not beget good shoes, nor bad, bad. Wong published a chart showing the player win/loss for each shoe compared with the previous shoe's result. Even after one million shoes, Wong discovered: "Differences between win rates ... are so small that they could well be random."
What was most surprising about Wong's study, however, was that his flat-betting basic strategy player in this 6-deck Atlantic City game did not lose at the rate of -.5%, as expected, but won at the rate of +.25%! Wong had discovered that the playing and pick-up procedures in casino blackjack did, in fact, re-order the cards in a non-random fashion that favored the player by +.75%!
Wong also published a challenge to his readers in that issue of Blackjack World: "If you still believe in TARGET after reading this article, I invite you to make a card-by-card list of a shuffle that you think generates the 4% edge that Patterson claims (in TARGET promotions), send it to me, and I will redo the study using your shuffle each time."
None of Wong's readers took up this challenge, but Peter Griffin was intrigued enough by Wong's discovery that the reordering of the cards favored the player to ask Wong what would happen if Wong shuffled at regular intervals. So, in his October '83 Blackjack World, Wong reported the results of another million shoes, shuffling every 50 shoes, in which he came up with a player win rate of +.23 % — not significantly different f rom the +.25% win rate with no shuffling. This result showed that the player-biased order which the play of the hands put the cards into did not require thousands of rounds of play, but in fact, asserted itself rather quickly.
Wong also ran no-shuffle simulations with various numbers of players at the table from I to 5. This did have a significant effect on the players' win rates. His results showed:
So, in alI cases, the basic strategy players showed a result with no shuffling that was more advantageous than the random shuffle expectation — though with 5 players, the difference is not significant.
Wong ran one other test, reported in his October '83 Blackjack World, to determine what was causing the player bias with no shuffling. Comparing the card patterns with random shuffling to those with no shuffling showed significant differences. As Wong reported: "... The difference between well-shuffled cards and unshuffled cards is that if the cards are not shuffled, high cards tend to follow high cards, and low cards tend to follow low cards."
So, although Wong could find no validity for the theories of TARGET, he did make a few important discoveries. One, the playing procedures in casino blackjack order the cards in a way that favors the players. Two, this player bias appears to be caused by the clumping of high cards with high cards and low cards with low cards. And three, as the number of players at the table increases, the effect diminishes. Unfortunately, Wong did not find any way for the player to exploit this bias in the casinos. The fact remains: All casinos shuffle.
Some questions remained unanswered, however. Although it appeared unlikely that the player could obtain the huge advantages from poor shuffling claimed by the TARGET system, some players still wondered if "poor" shuffling might retain some small amount of the natural player bias caused by the clumping of high cards with high cards, and low with low. If the player observed such clumping in a game in which the dealer seemed particularly sloppy about mixing the cards, could the player expect even a few tenths of a percent advantage over his random basic strategy expectation?
Also, Wong did not test the effects of "runs" of cards which appear when new decks are brought into the game. Dealing and pick-up procedures destroy these runs within one or two shuffles, but can a player exploit clumped cards by seeking out tables in which new decks have just been placed into the shoe?
In 1986, in a series of articles first published by Mason Malmuth in the Experts Blackjack Newsletter, Mason sought to answer some of these questions with his own computer simulation studies. Mason's articles are currently available in an expanded format as a chapter in his book, Blackjack Essays (1988, Malmuth).
Mason was specifically looking for house and/or player biases caused by runs of cards in new deck order. Mason's "nonrandom" shuffle consisted of four sloppy riffles and a random cut, with no boxing, stripping, washing, etc.
Mason's riffles, to be sure, were truly sloppy. His dealer interleaved cards in equally likely runs of 1, 2, 3 or 4 cards. If the cards from one half of the deck finished riffling prior to the cards from the other half, the remainder were dropped on top in a clump, as a human dealer would do. Tests of professional dealers have shown that clumps of 4 cards rarely occur in a riffle, with 65% to 80% of the interleaved cards being single cards.
Furthermore, unlike Wong, who never started with cards in new deck order (ace to king, ace to king, king to ace, king to ace), Mason brought in new decks after every round of play. To Mason's surprise, 500,000 hands of simulated play with these conditions showed the flat betting, basic strategy player losing at the rate of -1.21%, instead of breaking even, as expected, in this single-deck, Vegas Strip game. Therefore, Mason theorized that if the "runs" of cards were causing the house bias, then by looking at results in which these runs were shorter, he should be able to "create" a player bias.
Unfortunately, his attempts to do this were not highly successful. Although he did manage to find a player advantage of +.39% on one 500,000 hand run, all other attempts failed, producing no result significantly different from the random basic strategy expectation.
Mason concluded that "... these are some of the most confusing results I have ever looked at..." and, "... I was sure, at one time, that I had found a player bias, but now I wonder if I just looked at a statistical fluke.... The idea that a player can walk into a casino and look for certain characteristics that are highly correlated with a player bias in progress is just not an event that I believe can occur with more than a very small probability."
Commenting on the dealer bias he had managed to create with his "non-random" sloppy riffles, he acknowledged that "... with a skilled professional dealer, this is probably most unlikely... The fact that brand new cards are being used is probably not enough of a reason to leave the game."
Mason's study indicated that new deck sequences may tend to affect the player's expectation, but, alas, his data was inconclusive and was also confined to a single player in a single-deck game. Most of the streak-betting systems being sold for the purpose of exploiting the non-random shuffles tout their effectiveness for multiple-deck games with multiple players at the table.
Mason's shuffle technique, sloppy as it was, also fairly effectively eliminated most of the new-deck sequences. His analysis showed that all of the decks he "created" contained between 32 and 35 sequences. This means that the deck with the shortest sequences had an average sequence length of 1.49 cards, while those with the longest sequences had an average sequence length of 1.63 cards. Not much difference.
In 1987, at the Seventh International Conference or Gambling and Risk Taking, Dr. John Gwynn, Jr., and I presented a 26-page paper titled: "Does Casino Blackjack Differ From Computer Simulated Black jack?" [Link at the left of this page.] This was the most comprehensive study of the effects of non-random shuffles on casino blackjack done to date.
Our initial plan was to simulate as closely as possible actual casino shuffle routines in both single and multiple-deck games. In order to accomplish this, we enlisted the aid of two other experts on the casino-dealt game. The common casino shuffle routines were provided by author Steve Forte. As stated in our paper: "Mr. Forte at one time owned and operated a professional casino dealing school in Las Vegas after having spent some years as a blackjack dealer, pit boss, and casino manager. In 1986, he personalIy surveyed all of the major casinos in Nevada; at this time he recorded each casino's standard series of cuts, breaks, riffles, strips, discard procedures, etc., in an effort to devise various 'shuffle tracking' and 'card location' strategies."
As a matter of fact, Steve knew more about exploiting non-random shuffles than any player I knew. He had spoken at length with me on various occasions describing some of his discoveries and and techniques. Note, however, that Steve had no faith in the "streak betting" systems which were being sold commercially. Shuffle tracking strategies are more related to card counting than betting systems, insofar as the shuffle-tracker is exploiting specific knowledge of the cards remaining to be dealt. Winning and losing "streaks" play no part in valid shuffle-tracking strategies — which, incidentally, are typically far more difficult to apply than card counting strategies. Tracking strategies often must be applied not only to specific casino shuffle routines but to specific dealers whose actions are sufficiently consistent from shuffle to shuffle.
Anthony Curtis also obtained empirical data from four professional Las Vegas dealers to determine how they broke a deck for a riffle and how well their riffling mixed the cards. His data showed that a professional dealer interleaves a single card 66% of the time, 2 cards 26% of the time, 3 cards 5% of the time, 4 cards 2% of the time, and 5 or more cards less than 1% of the time.
A previous empirical study of professional dealers published by Richard Epstein in his The Theory of Gambling and Statistical Logic, Second Edition (Academic Press, 1977) showed a more thorough mixture, with single cards interleaving 80% of the time, 2 cards 18% of the time, and 3 or more cards only 2% of the time.
Due to the enormity of the task of programming his computer to simulate all that we had initially hoped to simulate, Dr. Gwynn decided to start with 7 different shuffles in a single-deck game, in order to search for basic significant differences.
One was a random shuffle. One was no shuffle (just a random cut). One simulation used one "perfect riffle," i.e., the deck was cut precisely into two equal halves, with 100% single-card interleavings. One used two perfect riffles. One used three imperfect riffles (mimicking casino riffles, a la Epstein). One used a riffle-strip-riffle-riffle routine (using the more common "thick" strip used in most Las Vegas casinos). And the last shuffle tested used a riffle-riffle-strip-riffle routine. The deck was dealt out 75%, playing Vegas Strip rules, the players flat betting and using basic strategy.
After 20+ million hands each, these were the player's expectations per hand:
The most significant result shows a player expectation with no shuffling that is .72% greater than the player's expectation with a random shuffle. This result indicates that, as with Wong's 1983 no-shufle simulation study of the 6-deck Atlantic City game, the pick-up procedures in casino blackjack order the cards in a way that favors the player by about 3/4%.
The only other mathematically significant difference occurred with 2 perfect riffles. In this simulation, the player did .08% worse than with a random shuffle. This is fairly useless information since you'll never find a casino dealer who employs this bizarre shuffle. All of the "casino style" shuffles showed no significant difference for the basic strategy player from what a totally random shuffle produced.
Thus, although it may be of significance to mathematicians that it takes seven riffles to randomize a single deck, Dr. Gwynn found no significant difference for the basic strategy blackjack player with only 3 imperfect riffles, in a 20+ million hand simulation.
Dr. Gwynn then tested many other theories of the non-random system proponents. Some "significant" differences between shuffles were discovered, for the most part in the non-casino style shuffles — i.e., no shuffle, one perfect riffle, and two perfect riffles. However, with all of the casino style shuffles, no player exploitable differences were found.
There were no significant differences in the frequency of wins, losses, and pushes. The per hand and per unit expectations for hands dealt with positive, negative and zero counts (using the High-Low Count) exhibited no significant differences. No correlations were discovered between the win/loss outcomes of consecutive decks.
In summary, Dr. Gwynn's extensive computer simulations uncovered virtually nothing exploitable, nor of any significance whatsoever between the completely random shuffle and the imperfect, non-random, casino-style shuffles he mimicked. To be honest, some players were still not satisfied that there might not be something exploitable due to poor shuffling in the casino game.
As one Blackjack Forum reader put it: "Why did you limit your study to single-deck games? TARGET is being sold for multiple-deck games. Why did you limit your study to a single player at the table? Multiple players do have an effect on the clumping of the cards in the discard tray. Dealers in Atlantic City usually use only two riffles, surely imperfect, with no stripping, in order to shuffle 8 decks in a reasonable amount of time.
"Furthermore, you and Gwynn never introduced cards in new deck order. In real casinos, cards always start in new deck order. I would estimate that many shoes are only shuffled about 50 times between new decks. You do see small clumps of cards coming out in sequence right after new decks are brought into the game. What effect does this have? We still don't known."
In order to answer some of these questions, I recently ran a series of computer simulations using John Imming's Real World Casino System Generator.
New Research on Non-Random Shuffles
I started with an 8-deck shoe, 6 decks dealt out. I put 7 players at the table, all flat-betting and playing basic strategy. After 100+ million hands (14.3 million hands per player), and a random shuffle, the players' expectation was -.4 9%.
To test the effects of no shuffling, I set up the same game, but this time I mimicked Stanford Wong's simulation of reshuffling once every 50 shoes. I input a thorough shuffle with fine riffling and stripping in order to "randomize" the deck every 50 shoes as Wong had done. My intent was not to mimmick an Atlantic City style shuffle, but to test the effects of not shuffling in a manner similar to Wong's 1983 6-deck study. I then simulated 10 million hands each with I player, 3 players, 5 players, and 7 players at the table. These were my results, compared to the completely random 100 million hand simulation:
1 player (no shuf): +30%
This data is consistent with Wong's. It shows that the single player's expectation was .79% greater when no shuffle was used between shoes, but that this advantage diminishes as more players are added to the table. Multiple players at the table appear to have a randomizing effect on the basic strategy player's expectation.
Still, we would like to know the effect of a "poor" casino style shuffle, with cards in new deck order added at regular intervals. For this test, I introduced new decks every 50 shuffles. The decks were given one "gross wash." Imming's gross wash consists of picking up cards in new deck sequences of from I to 15 cards. The "average" run is 8 cards, and the dealer is just as likely to pick up a 15 card run as he is a 6 card run, as he is a 2 card run, etc. This orders the decks in a series of new-deck runs of varying length, but does not otherwise mix the cards.
After the gross wash, which was only performed every 50 shoes when new decks were entered into the game, the only shuffle routine I used between deals was one "gross riffle" and a random cut. A "gross riffle"consists of 50% 2-card drops, 37.5% 3-card drops, 6.25% 4-card drops, and 6.25% 5-card drops. No single card interleavings were performed. When the dealer finished dropping cards from one pack, the remaining cards from the other pack were dropped in a clump, as a human dealer would do, occasionally causing clumps greater than 5 cards.
Each of the eight decks was shuffled separately, then they were stacked on top of each other, with no attempt being made to intermix the various decks into various portions of the shoe. My intent here, again, was not to mimic an actual Atlantic City shuffle, but to search for the effects of a grossly inadequate shuffle, combined with multiple players at the table, with cards in new deck order, poorly washed, being introduced at frequent intervals.
Because I used only one gross riffle and a random cut as the entire shuffle routine between decks, the cards remained in long series of new-deck runs after the gross wash, and consistently retained sequences set up in the discard rack by the previous shoe's play and pick-up procedures.
After 100 million hands, the flat-betting players' advantage was -.45%, or .04% better than with a completely random shuffle. This result, though a "visible" difference of .04%, is not mathematically significant due to the fact that there are 7 players at the table. The insignificant difference indicates that even an incredibly poor wash and shuffle, for all practical purposes, randomizes a shoe game.
Some of the player advantage that we know accrues from the clumping of like valued cards may or may not still be present, but we would have to run a simulation of more than 100 million hands to find out. The potential gain, if there is any, would be measurable in hundredths of a percent at most. It's useless information. Even if you could find a shuffle this poor in a casino game, it would not significantly alter your strategy or your long run expectation.
If you do observe cards coming out of a shoe in short runs and clumps following the introduction of new decks, the effect on your expectation is so minute as to be ignored. Contrary to current "myth," however, this effect is more likely to be slightly advantageous rather than disadvantageous.
The next simulations I ran were to compare the effects of "streak betting" in the randomly shuffled game with the "gross wash/gross riffle" game. To do this, I set up the program to use a l-to-50 betting spread, doubling the bet after each win, halving the bet after each loss, and ignoring pushes.
A series of six wins caused the bets to raise from 1-2-4-8-16-32-50 units, and vice versa downward for a series of six losses. This betting progression is a very sensitive indicator of the possibilities of streak betting because the player will quickly go from a 1 to a 50 unit bet when any series of bets shows 6 more wins than losses. As long as his wins continue to equal or exceed his losses, he'll remain near his top bet size. But just as quickly, he'll go back down to a single unit bet when a similar series of losses exceeds wins.
Running this simulation for 100 million hands in the randomly shuffled game showed a player expectation of -.46%. This difference of +.03%, over the flat bet expectation, is not significant.
I then ran 100 million hands using the same streak betting system in the grossly shuffled game. The result was a player expectation of -.49%, again, no significant difference from the flat bettor's basic strategy expectation. In both of the streak-betting simulations, the players' average bets were 8.26 units.
Any Blackjack Forum readers who are concerned about whether or not the "non-random" casino shuffle alters your expectation, or if you are worried that it may take 7 shuffles to "randomize" the cards, note that in these 8-deck A.C. simulations, no significant difference to your expectation can be found, in 100-million-hand tests, between the random shuffle and a shuffle consisting of one gross riffle, even when poorly washed new decks are introduced every 50 shuffles.
It is worth noting here that a good shuffle-tracker could absolutely murder the grossly shuffled games. The Diaconis-Bayer riffle study would accurately identify the cards employed in this game as far from random. Our major concern, however, is that no "weird" order is imposed upon these poorly shuffled cards that alters the non-tracking players' expectations, or that validates any otherwise futile "streak betting" system.
I will continue to advise my readers to put no faith whatsoever in streak-based systems. There is still no evidence to support such strategies.
PLAYER BY PLAYER SIMULATION RESULTS
I am currenty working with John Imming to set up a simulation program which can be used to test other non-random and casino-style shuffle effects. To be honest, we do not expect to find anything of value to the player, based on all of the work that has been done thus far searching for player exploitable effects from the non-random shuffle.
If any Blackjack Forum readers have suggestions for tests, shuffles, etc., we would certainly be open to considering any angles we may have overlooked. For now, my advice is to ignore the alleged effects of the non-random shuffle.
Note to players who want to use John Imming's Real World Casino System Generator to perform their own "nonrandom" simulation tests: You should have no trouble reproducing my results if you input the same variables. Do note that the shuffle routines have limitations which may cause "bizarre" results.
We were baffled for some time by the fact that the basic strategy players' expectations differ according to seating position, number of players at the table, and deck penetration, when the shuffle consists of only one wash on decks in new deck order. There are numerous reasons for this, however. Consider for instance, that with a single gross wash, both of the third base player's cards will often be in "sequence" with the dealer’s cards.
Also, some of John Imming's Real World Casino shuffle routines are theoretically "flawed." His "washes" (fine and gross) are both more "gross" than you would ever find in a casino. Also, they more closely resemble very thick "strips" than washes.
John Imming has currently been hard at work at a new program which he calls the "Ultimate Blackjack Engine." I have been testing various functions of this program which vastly expands the "real world" shuffle routines from totally random cuts to more random washes, to High Low stacking routines, more rule variations (including the over/under), etc.
"The Ultimate Blackjack Engine" is still in the testing and development phase, and at this time, John cannot estimate the date of availability, price, or even all of the features. Don't bother asking! ♠
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||Shuffle Tracking Non-Random Shuffles
Shuffle tracking is a legitimate and highly profitable professional gambling technique at blackjack. Now, however, phony blackjack systems based on non-random shuffles are cropping up. This article discusses the TARGET blackjack system that claims to exploit non-random shuffles.