Probing the Non-Random Shuffle
Shoehenge: Probing the Mysteries of the Non-Random Shuffleby Arnold Snyder
(Blackjack Forum Vol. X #4, December 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.]
Many times over the years I have had to eat my own words. So many times, in fact, that my words have become an essential part of my diet.
How often have I insisted in print and otherwise that any non-random shuffle that you are likely to find at a casino blackjack table makes no difference whatsoever to your expectation as a player?
You see, this computer freak named Imming comes out of nowhere with this program that mimics human shuffles. And you start playing with it and testing it and gaining confidence in its results, because all of the results seem to support what you already know and already believe.
The thing is, there are hundreds of serious players out there who now own this software, and they're all running tests that just a year ago would have been impossible for any average player to run because software like this wasn't available at any price. So, it's inevitable that letters start coming in from players who are using this software asking why they're getting such and such weird results when they set up certain weird conditions. Most of these results can be explained pretty easily. And then one day, hmmm... What have we here?
Recap of Earlier Research on Non-Random Shuffles
If you haven't read the feature article in the March '90 issue of Blackjack Forum (Vol. X #1), "Ruffled by the Shuffle," I would suggest you read that article as background material for this one. In that article, I not only reviewed numerous previous computer studies on non-random shuffles — by Stanford Wong, Dr John Gwynn, Mason Malmuth, and Percy Diaconis, I published a lot of data I had personally obtained using John Imming's Real World Casino software.
A brief recap of the results indicate:
My readers, however, cynical, mistrustful bunch that you are, still were not satisfied.
One reader wrote: "It is interesting to see that it doesn't take much of a shuffle to return the players' expectation to normal. But what happens immediately after new decks are brought into play? We often see short runs of cards m sequence by suit, indicating that the initial shuffle was poor. Although your simulations show that the players' expectations average out to about normal when new decks are brought in every 50 shuffles, is a player's expectation normal on the first round after fresh decks are put into play?"
The Effect of New-Deck Order on Blackjack Basic Strategy Players
This was an interesting question which had not previously been answered. The first simulation I set up to discover the effect of cards in new deck order on basic strategy players. I set up an 8-deck shoe in new deck order, put seven players at the table, all using basic strategy, and played through six of the eight decks with Atlantic City rules. No shuffle was done, not even a cut. I just played through that one shoe in new deck order.
The house lost at the rate of 28%, 6 of the 7 players won. First base won at the rate of 67%. There's nothing all that exciting about this weird result. Obviously, we'll never find a casino that will offer this game.
Next, I tried the same game with one difference — a random cut was performed prior to the deal. Now the house lost at the rate of only 15%. But 5 of the 7 players won, first base taking top gain again with a 38% win rate. Interesting, but of no practical value.
Next, I performed a "wash" on the decks which consisted of cards being picked up in clumps of up to 8 cards in sequence. This is the "gross wash" in version 3.0 of Imming's RWC Universal Blackjack Engine. Then, with no other shuffling, the cards were dealt. With this wash, 35 out of every 36 cards dealt are in new-deck sequences, running up or down; the length of the sequences varies from 2 to 8 cards. At the end of every shoe, I started again with fresh decks. I ran 10 million hands for each player.
With a single player at the table, the effect of the sequences again worked to the basic strategy player's advantage. Instead of losing at the rate of 0.5%, the player won at the rate of 1%.
Seating Position and Non-Random Shuffles
With three players at the table, however, it became obvious that seating position is everything when the cards are in sequential order. The first base player's expectation was still 1.5% above his normal basic strategy expectation. The third base player's expectation, however, was 1.2% below his random basic strategy expectation. The player in the middle seat, was about a quarter percent below normal.
Running simulations for various numbers of players at the table, the trend was obvious: the first base side of the table wins; the third base side loses. With a full table, seven players, the first three players at the table all do notably better than they would expect from basic strategy. The player sitting dead center, seat 4, is only about 0.1% over his basic expectation. The players in seats 5, 6, and 7 do not do so well. Seat 5 does about 0.4% worse than he'd expect with a random shuffle. Seat 6 does 1.9% worse. And seat 7, third base, loses at a rate 4.5% worse than his random shuffle expectation.
Although we'll never find a casino that will deal unshuffled cards, these tests provide us with some insight into the ways sequences affect players. Even when changing penetration levels and the number of decks in play, as well as the number of players at the table, cards in new-deck sequences are advantageous for the first base players and disadvantageous for third base.
Card Counting and Non-Random Shuffles
I then tested a theory of the non-random shuffle system proponents—that card counting wouldn't work if the cards were in sequences. With seven players at the table, and no shuffling—just that one gross wash—card counting was actually much stronger than when the cards are in random order.
With a random shuffle, betting one unit on advantageous hands only, the player's average gain over his basic strategy expectation is about 1.3%. With just a gross wash, however, this same betting strategy raised the counter's expectation by 2.2%! Again, the lion's share of the profits went to the first base side of the table. Third base still loses, though at a slower rate.
Is it possible for players to make money by seeking out poorly shuffled new decks and sitting at first base?
Remember, these results are all for playing new-deck sequences with decks that haven't been shuffled at all, but simply "rearranged" in sequential clumps of varying length. All casino dealers, in fact, shuffle.
However, these results do indicate that sequential cards have a notable effect that varies by seating position. We've all seen short sequences of unshuffled cards come out immediately after new decks have been brought into play. Certainly, not 35 out of 36 cards, as in this simulation test, but the fact remains that sequences have measurable effects. The question is: How much of the sequential effect will be retained through a sloppy shuffle, and how many shuffles does it take until the game returns to normal?
As soon as I put in two very gross riffles, even on the first round after the shuffle, the first base player's advantage completely disappeared. The third base player, who had been losing at a rate 4.5% worse with a gross wash than his expectation with a random shuffle, was still losing after two gross riffles, but only at a rate of 1.4% worse. But 1.4% is a significant amount!
Does this mean that the third base side of the table should be avoided immediately after new decks are introduced?
Possibly. The gross wash and two gross riffles I used in this simulation were, to be sure, still far more gross than anything you'd expect to find in a real casino. A "wash" that retains 35 out of 36 cards in new-deck sequences would be highly unusual.
And Imming's "gross riffle" interleaves cards equally in one, two, three and four card clumps. Empirical studies of professional dealers show that pros almost never riffle a four-card clump, and rarely a three-card clump. The new-deck sequences we see after fresh decks have been brought into play are more likely caused by "lopsided" picks which leave a relatively small proportion of the cards unriffled.
When I tested a more thorough shuffle, however, which was poor but not impossible, all seven players at the table lost more on the first hand after the shuffle than they would expect to lose with a completely random shuffle. With a finer wash, and two "fine riffles," first base did best again, but lost at a rate of about 0.2% below his random basic strategy expectation. Third base did worst, losing at a rate of 0.6% below his random expectation.
One interesting discovery was that when a card counting strategy was used, the discrepancies between the first-base and third-base win rates disappeared. Although basic strategy players who play through all hands do notably worse on the third base side of the table, card counters (who leave the table when their advantage disappears) all win at approximately the same rate regardless of seating position. This indicates that the third base disadvantage occurs at negative counts. For some reason, the negative counts do not affect the first base side of the table in the same negative way.
It must also be noted that on the first round after a poor shuffle on fresh decks, as described above, even the card courters' win rates were all about 0.3% below what their expectation would be with a completely random shuffle. Counting still beats the game, but at a slower rate.
Eddie Olsen's Phase II System for Non-Random Shuffles with "Card Clumping"
This raises the question: is it possible that a different basic strategy might be advisable if the player knows that a significant portion of the cards are in new-deck sequences? I know of one such strategy that has been published. In July of 1987, Eddie Olsen (inventor of the TARGET system), in his Blackjack Confidential newsletter, published a new basic strategy he called "Phase II," specifically designed for games with like-card clumping, and especially for poor washes and insufficient shuffles on new decks.
Then in July of 1988, he published a revised version of the Phase II strategy based on more extensive empirical data. Olsen suggests in his revised Phase II article that the player can test the Phase II strategy by dealing and playing through an unshuffled 4-deck shoe and comparing the results to the standard basic strategy results. (Olsen did not, incidentally, mention that seating position might affect the player or the strategy.)
I tried a somewhat different test. I played through six decks in new deck order with no shuffle, first with basic strategy, then with Phase II. With basic, the player won at a rate of 44.7%. With Phase II, the player's win rate went up to 52.6% - a gain of almost 8% just by altering the basic strategy!
But, had Olsen discovered a real strategy that could milk the new deck sequences caused by an inadequate shuffle? No casino, in fact, would deal a game off the top of new decks with no shuffling whatsoever. I wanted to see what would happen in the 8-deck game, 75% dealt, A C. rules, with 7 players at the table, when the cards were in sequences, but grossly washed.
I used Imming's gross wash again which leaves 35 out of 36 cards in new-deck sequences, with no other shuffling. Unfortunately, even this minimal reordering of the cards invalidated Olson's Phase II strategy. These are the results, after 140 million hands for each simulation (20 million for each individual player), showing the overall house advantage, and each player's advantage by seating position:
Phase II, unfortunately, killed the advantage on the first base side of the table. Varying the number of players at the table, and using various sloppy shuffles, all of the Phase II results I obtained indicate that this strategy would be ill-advised when cards are clumped in new deck sequences (unless no shuffling at all is done).
Olsen states that his strategy was devised by analyzing the results of some 468,000 hands played in the A C casinos over a six-year period. I would guess this is why his strategy fails. Although 468,000 hands may seem like a lot to any one player, it is statistically insignificant for purposes of devising a playing strategy.
Olsen, for instance, in his Phase II strategy, changed 26 of the basic strategy pair split decisions. According to Julian Braun's simulation studies (How to Play Winning Blackjack, p.82), some of these pair split decisions will occur only 38 times per 100,000 hands. So, in an observation of 468,000 hands, we'd expect to see these hands only about 178 times each.
Many of the individual hit/stand decisions would not be observed more than a couple thousand times each. In devising a strategy via simulation, it is often necessary to play out more than a million hands for each individual decision. Basing your decisions on the results of a few hundred or a few thousand hands is futile. The standard deviation for such a statistically small sample is too great to yield a valid strategy.
Change Blackjack Basic Strategy for the Shuffle?
This, however, does not mean that some changes to basic strategy might not be in order if extreme new deck sequences were observed.
The problem is that the more out of sequence the cards are, the less applicable your new "sequential" basic strategy will be. Also, and most importantly, your basic strategy would assuredly vary by seating position. To be honest, if I saw a large proportion of cards coming out in new deck sequences, my strategy would be simple: sit at first base!
It is also probably impossible to come up with a universal strategy for use against all poor shuffles in a casino environment. If I program the computer to use two "fine" riffles, following a finer wash of the fresh cards, then stack each deck one on top of the other with no attempt to intermix the cards, the house advantage on the first round after the shuffle goes up by about 0.4%.
If I use two washes, one "gross" the other "fine," followed by one "fine riffle," the house advantage right after the shuffle is the same as with a completely random shuffle, though the advantage for specific players at the table varies. First base, again, does best, with an expectation of about 0.3% better than with basic strategy. (There's something about that first base seat that sequential order favors.)
Small differences in the poor shuffles can cause significant differences to the various players. Any casino that purposely shuffled fresh decks poorly, possibly believing that sequential cards hurt the players, could risk being taken to the cleaners by high rollers on the first base side of the table.
Based on the data I've obtained thus far using the Real World Casino software, I would personally avoid sitting on the third base side of the table immediately after fresh decks were introduced if I felt the shuffle were inadequate. For me, this is a big change in my opinion, but the fact is it takes a fairly thorough shuffle to completely eliminate the third base disadvantage.
I don't know whether or not any of the non-random theorists have ever pointed out the first-base/third-base effects of sequential cards. If not, then they have missed the most striking effects of a poor shuffle on fresh decks. This first-base/third-base dichotomy is present with virtually every poor shuffle on fresh decks I've tested.
I've also learned that if a very poor shuffle is continued through a shoe, it can take a number of shuffles to completely eliminate the non-random effects. Players should realize, however, that these effects are, at most, measured in tenths of a percent. In his Phase II article, Eddie Olsen estimates that the Atlantic City "zone" and "stutter" shuffles put the basic strategy player at about a 15% disadvantage to the house. Highly unlikely, in my opinion.
Version 3.0 of Imming's Universal Blackjack Engine, which I used in these tests, allows only one type of standard multi-deck shuffle, the old "center cut, riffle and stack." The new version 4.0, which will be available by the time this issue of Blackjack Forum goes to press, will allow user-programmable shuffles, including "zone" and "stutter" variations.
From the tests I've run thus far, however, my initial conclusions are:
It seems unlikely to me that any type of shuffle, "stutter" or otherwise, could create a strong house advantage (15%?), though I will assuredly test the A C. style stutter shuffle when I get the new version 4.0 of this software (as I'm sure hundreds of other players will!)
Contrary to what the non-random shuffle theorists have also reported, card counting does work, even when the sequential effects of a poor shuffle on fresh decks are present. Card counters who play only when the count is in their favor need not worry about entering games at any betting position after fresh decks have been introduced, though the advantage from counting may be lowered a few tenths of a percent.
Thanks to John Imming's efforts, and his phenomenal Real World Casino software, for the first time average players can test systems that they previously had to accept on faith. And so-called experts like me sometimes have to eat our own words. ♠
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