Category: Blackjack

The Non-Random Shuffle and Streaks

by Dr. John M. Gwynn, Jr. and Arnold Snyder
(Blackjack Forum Vol. VIII #1, March 1988)
© Blackjack Forum 1988

(This is a synopsis of a paper on non-random shuffles and computer simulation of blackjack presented at the 7th International Conference on Gambling and Risk Takng.)

[Arnold Snyder is the author of The Blackjack Shuffle Tracker’s Cookbook: How Players Win (and Why They Lose) With Shuffle-Tracking.]

It has been public knowledge for more than 25 years now that the game of blackjack can be profitably exploited by players who diligently apply strategies based on card counting. First popularized by Dr. Edward Thorp’s 1962 best-seller, Beat the Dealer, card-counting strategies have been expounded upon, refined, and extolled by dozens of authors since. The validity of card counting has been proven many times via computer simulation of the game.

In the past five years, however, some of the standard computer blackjack simulation techniques have been seriously questioned by a number of authors, players, and system sellers. Most authorities on the game believe that the blackjack simulation methods generally employed to test systems are applicable to the game as dealt in the casino, even though all casino procedures are not simulated. The prime complaint of those who question the simulation data concerns the methodology of computer “shuffling.” In a computer simulation, the most time-efficient method of shuffling is to place cards in order via a “random number generator” that assigns each card in the deck or decks a new randomly chosen position with each shuffle.

Detractors of this methodology complain that in the casino shuffle — as applied by less than perfect human dealers — “clumps” of cards often remain together from shuffle to shuffle due to “lopsided” cuts and sloppy riffles; other procedures, such as the order in which dealers pick up played hands, tend to clump high cards with high cards in the discard rack; etc. Indeed, casino shuffles are not random. The most recent work on shuffling indicates that seven riffles are required to randomly rearrange a deck of cards.

In the past five years, numerous new blackjack systems based on these non-random shuffles have appeared. Players are being advised by some system sellers to avoid certain types of shuffles while seeking out others. Non-card-counting systems for beating the game are also being extolled as valid by some system sellers due to these non-random shuffles. Strategies based on “streaks” of wins and losses, allegedly caused directly or indirectly by the non-random shuffles, are also being sold.

Unfortunately, none of these new systems and methods has been accompanied by any published computer simulation data that would support the system sellers’ claims. Nor is any logical mathematical theory presented that would support the validity of these new systems. Some of these systems inventors have claimed they have personally produced non-random blackjack computer simulations that have proven their systems to be valid, but none have published any hard data to support this claim.

Most of the non-random shuffle systems are primarily touted to be used in multiple-deck blackjack games. In this paper, we will limit our computer simulations and analyses to single-deck blackjack games. This is due solely to the time factor involved. It is our intention to continue testing many more of these non-random theories, claims, and systems in both single-deck and multiple-deck games; the results will be published as obtained.

Analyzing Live Casino Non-Random Shuffles

In order to write a computer simulation program that would mimic the shuffle of a human blackjack dealer, it was first necessary to analyze the types of shuffles that dealers in casinos employ.

The common casino shuffling procedures were all provided by Las Vegas author Steve Forte. 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 personally 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.

“Shuffle tracking” and “card location” are advanced strategies, based on card-counting theory, and are most often employed in conjunction with card counting. These tracking and location strategies do take advantage of “non-random” human shuffles. A player applying one of these techniques might do so by first breaking down and analyzing a casino’s shuffling routine so as to learn how to follow the positions of specified cards in the discard rack when they are reshuffled. Although little has been written on card tracking of this type, this will not be a topic of study for this paper. In fact, the data from the simulations sheds no light on this type of strategy.

The purpose of this study is to simulate non-random shuffles and attempt to answer the following questions. Does a “poor” shuffle have a notable effect on the basic strategy player’s win/loss rate? Does it cause lengthier and/or more frequent “streaks” of wins/losses? Does it lower the effectiveness of card counting in determining favorable hands? Are there “biases,” independent of any conventional card counting information, induced by certain non-random shuffles, i.e., positive counts no longer indicate a player advantage because the deck is “dealer biased?” Are certain shuffles disadvantageous to players? Et cetera.

In short, how does nonrandom shuffling affect the game of blackjack? In this paper, we initially chose to simulate two of the most common single-deck shuffles, Riffle-Riffle-Strip-Riffle and Riffle-Strip-Riffle-Riffle. Mr. Forte indicated that most casinos require one of these as a minimum single-deck shuffling procedure. It was then decided to add Riffle-Riffle-Riffle, a procedure that would be used if the dealer omitted the intervening strip; this would mix the cards a little less.

In 1987, Anthony Curtis obtained data from four Las Vegas dealers to determine how they broke the deck for a riffle and how well their riffling mixed the cards. He asked each dealer to perform one riffle on a new deck; then he recorded data about the riffled deck. After each riffle, the deck was reordered and the dealer riffled again. Each dealer performed ten such riffles. Curtis reported the fol lowing data about these 40 riffles.

There were 906 singly interlaced cards, 358 2-card clumps, 72 3-card clumps (less than 2 per riffle), 28 4-card clumps (less than I per riffle), 10 5-card clumps (I per 4 riffles), and only two clumps larger than five cards (I per 20 riffles). On 33 out of the 40 trials, the break was within 2 cards of the center. Three breaks were 3 cards from the center, one break was 4 cards off center, two breaks were 5 cards off center, and one break was 7 cards off center (this break resulted in a 7-card clump after the riffle). Since dealers always break and riffle more than once during a shuffle, it is unlikely that any large clump would be preserved throughout a complete single-deck shuffle.

Richard Epstein, author of The Theory of Gambling and Statistical Logic, stated that when professional dealers riffle the cards, they drop one card 80% of the time, two cards 18% of the time, and three or more cards only 2% of the time. Applying Epstein’s distribution to the same 40 breaks that Curtis reported on, a little approximation yields around 1100 singly interlaced cards, about 250 2-card clumps, and nearly 30 clumps of 3 or more cards. The Curtis data, small sample that it may be, indicates less precise riffling that Epstein reported.

This research deals entirely with single-deck blackjack under the further assumptions that a single player goes head up against the dealer and plays a single hand. The authors are aware of the non-random shuffle theory that multiple players at the table have a sianificant effect on the subsequent non-random ordering of the cards. Again, it is our intention to test the effect of multiple players, and to publish these results as obtained. This initial study is a starting point, not a definitive evaluation of all non-random theories. All simulatians used Las Vegas Strip rules: dealer stood on soft 17; doubling was permitted on any first two cards (not offer splits); only one card could be drawn to each split ace; aces could not be resplit.

Basic strategy governed the play of all hands, and insurance was never taken. The High-Low count was kept for certain measurements, but it was not used to vary strategy. The number of split hands was limited to four because a single deck was used and tens were never split. In this description, the player is identified as male and the dealer as female and right-handed.

Every attempt was made to come up with a realistic model of actual casino play, where the order of cards in the deck is possibly nonrandom. Variables that might influence this order included: was the dealer’s up card dealt before or after her down card; in what order did she pick up the player’s cards when he did not split a pair; did she pick up the player’s split hands clockwise or counter-clockwise; were the player’s cards or her cards placed in the discard rack first; in what order did she pick up her own cards; what rules governed reshuffling; did she place the unplayed cards on top of or below the cards from the discard rack when preparing to reshuffle; how did the player cut the shuffled pack before she dealt from it. A myriad of combinations was possible if one ran the gamut of reasonable choices; hence, a single realistic choice was made for each of the above variables.

When the dealer picked up the cards used in any round, she placed all of the player’s cards in the discard rack before her own. In case a pair was split, she dealt the split hands left-to-right (clockwise) but picked up the unbusted split hands right-to-left (counter-clockwise). If any split hand busted, she placed its cards in the discard rack before play continued.

With these fixed, only the shuffling technique differed from simulation to simulation; for any one simulation, the same technique was used throughout. Seven different shuffles were selected for use in the simulations:

• Random shuffIling denoted RAN.
• One perfect riffle, denoted IPR.
• Two perfect riffles, denoted 2PR
• Riffle-Riffle-Riffle, denoted RRR.
• Riffle-Strip-Riffle-Riffle, denoted RSRR.
• Riffle-Riffle-Strip-Riffle, denoted RRSR.

Three of these shuffling techniques (RRR, RSRR, RRSR) attempted to simulate casino dealer behavior; three others were obviously inadequate (NOSHUF, I PR, 2PR).

The reshuffling rules reflected dealing through 3/4 of every deck. Immediately after each shuffle, the player always cut the cards close to the center of the deck; then the dealer burned the top card by placing it in the discard rack without the player seeing it.

To begin each simulation, the deck was randomly ordered before an initial shuffle; this guaranteed no dependency on the original deck order. Hence, the simulations would only measure the differences between random and other shuffles after the cards were thoroughly mixed. Many non-random shuffle system proponents claim that the continual introduction of cards in “new deck order” is a major cause of the subsequent non-random ordering of the cards via imperfect shuffles. The authors intend to test this effect, and to publish these results as obtained.

Eight simulations were run, one using each type of shuffle and an additional one using the random shuffle. To avoid confusion, the two random simulations were denoted RANI and RAN2. Each simulation dealt 2,650,000 freshly shuffled decks, resulting in over 20,000,000 hands played (a pair split into two or more hands only counted as a single hand played). During each simulation, numerous data were gathered for later analysis; hopefully, this data would provide enough information to determine if random and simulated dealer shuffling produced significant differences in the game of blackjack.

The reason for running two simulations with a random shuffle was as follows. If the gathered data seemed to indicate any significant “difference” between two shuffling methods, the data from RAN1 and RAN2 could be compared to see if the same “differences” appeared. If so, this observed “difference” could be deemed spurious and simply the result of random fluctuations.

Results of the Non-Random Shuffle Simulations

Table I shows the results of the simulations for a flat bet of one unit, giving the total number of hands played, expectation per hand played, and expectation per unit bet. All expectations are given in percent; in addition, all expectations are per hand played unless specifically stated to be per unit bet.

The results for no shuffling agree approximately with those of Stanford Wong, who found that no shuffling gave an increase of about 0.75% over basic strategy for the 6-deck Atlantic City game. The results for 2PR are a mystery. Two standard errors for the difference in expectations between two runs is about 0 07% and 2PR’s differs from others (excluding NOSHUF) by a little more than this. Extensive analysis of the voluminous gathered data led to the following conclusion: within the limitations of this study, point count basic strategy players cannot telI the difference between simulated dealer shuffling and random shuffling.

Point count systems presume that the unseen portion of the deck contains an essentially random mix of cards. The question here is whether non-random shuffles induce sufficiently many patterns in the unseen cards to perturb a count system’s ability to determine which hands are favorable, and, more precisely, how favorable.

Based on the three runs using simulated dealer shuffles (RRR, RSRR, RRSR) and the two runs employing random shuffles (RAN1, RAN2), the High-Low count was an equally effective indicator of player advantage.

HypotheticalIy, assume that the player can sit at the table and not play some hands, i.e., bet 0. If the player bets 0 on the unfavorable hands and 1 on the favorable ones, he will obviously win. The player uses a point count to help decide which hands are favorable; there is a number K such that a true count K indicates favorability and a true count

Table 1. Flat Bet Results for the Eight Simulation Runs

Simulation	Hands Played	Exp per Hand	Exp per Unit
RAN1	20094500	-0.1124	-0.0996
RAN2	20094022	-0.1169	-0.1036
NOSHUF	20114382	0.6054	0.5375
1PR	20146678	-0.1001	-0.0889
2PR	20095750	-0.1911	-0.1694
RRR	20110333	-0.1141	-0.1012
RSRR	20098374	-0.1078	-0.0956
RRSR	20095345	-0.1016	-0.0900

Table 2. Per Hand 0-1 Betting Expectation as a Function of K Simulation Run

K	RAN 1	RAN2	RSRR	RRSR	RRR	NOSHUF	1 PR	2PR
-1	0.90	0.86	0.88	0.87	0.88	1.40	0.87	0.83
0	0.92	0.90	0.91	0.90	0.80	1.38	0.90	0.85
1	0.85	0.85	0.85	0.85	0.83	1.09	0.84	0.82
2	0.81	0.81	0.81	0.81	0.80	1.00	0.79	0.77
3	0.73	0.74	0.74	0.73	0.72	0.89	0.71	0.70
4	0.63	0.63	0.64	0.64	0.62	0.73	0.60	0.60
5	0.56	0.55	0.55	0.56	0.55	0.63	0.53	0.52
6	0.47	0.46	0.46	0.48	0.46	0.53	0.45	0.45
7	0.41	0.40	0.40	0.41	0.40	0.45	0.39	0.39
8	0.32	0.32	0.32	0.33	0.32	0.35	0.32	0.30

For each integer K from -I to 8, the difference in per hand 0-1 betting expectations was examined for all ten pairs of the simulations RAN1, RAN2, RSRR, RRSR, and RRR. None of these 100 expectation differences was significant at the 95% level. These results strongly imply that a point count system is just as effective for casino shuffling as it is in theory, i.e., when random shuffling is employed. For all eight of the simulations, Table 2 shows the observed 0- I betting expectation. For NOSHUF, the 0-1 betting expectations showed the greatest differences when compared to the other runs.

In the simulations, the player always rounded the true count to the nearest integer before using it to make a bet. In determining the player’s expectation per hand, the number of hands played included those on which 0 was bet.

If one plots the expectation per hand at integer values of K, the function increases to a maximum and then decreases. It is conceivable that the maximum might not occur at the same integer value of K for all of the simulations runs, especialIy since non-random shuffling (which includes no shuffling) was used in six of them. However, the function’s maximum occurred at the same value, K = 0, for every simulation except NOSHUF, for which it occurred at K = -1.

The hands were then partitioned into three classes: hands won, hands lost, and hands pushed. A Chi Square test with two degrees of freedom was used to compare the frequencies of hands in these three classes between pairs of simulations. At the 95% level of confidence, there was no significant difference between any two of RAN1, RAN2, RSRR, RRSR, and RRR. Hence, the frequencies of wins, losses, and pushes did not vary significantly between random shuffling and any of the three simulated casino shuffles.

Whereas the frequencies of wins, losses, and pushes seemed to be useful in measuring the differences between two shuffling procedures, the frequencies of hands dealt with positive counts, with negative counts, and with zero counts did not. Most important to the player are his expectations on hands in each of the three categories. If one considers only the hands dealt with positive counts, the per hand expectations did not differ significantly (at the 95% level) between any two of the simulations RAN1, RAN2, RRR, RSRR, RRSR; this was also the case for the difference in per unit expectations for these hands. Expectations for hands dealt with negative counts and for hands dealt with zero counts exhibited identical behavior.

Suppose the hands are partitioned into nine categories: wins with a positive count, wins with a negative count, wins with a zero count, losses with a positive count, losses with a negative count, losses with a zero count, pushes with a positive count, pushes with a negative count, and pushes with a zero count.

A Chi Square test with eight degrees of freedom was used to compare the frequencies of hands in the nine categories between each pair of simulations. For RAN1 versus RAN2, RAN1 versus RSRR, and RAN 2 versus RSRR, the difference was not significant at the 95% level; for the other 25 pairs of simulations, each difference was significant at the 99.5% level. It seems that considerable fluctuations are to be expected in the frequencies of hands in these categories.

As for expectations, however, there was little variation in each of the nine categories if one confined the discussion to RAN I, RAN2, RSRR, RRSR, and RRR. Clearly, hands in each of the three push categories always had expectation 0. For each of the other six categories, the differences in per hand and per unit expectations were examined for all ten pairs of these five simulations. Based on expectation per unit, none of these 60 differences was significant at the 95% level. If RRR was excluded from the list, the per hand expectations for hands in any category also did not significantly differ (at the 95% level) between any pair of the remaining four simulations.

Table 3. Percentages and Expectations of Hands Won and Lost with Positive, Negative and Zero Counts

	Win +	Lose +	Win –	Lose –	Win 0	Lose 0
RAN1 % Hands	15.33	16.30	16.95	19.43	11.23	12.31
RAN1 Per Hand	119.64	-107.26	121.98	-112.26	120.67	-109.55
RAN1 Per Unit	105.66	-99.69	103.31	-99.63	104.42	-99.66
RAN2 % Hands	15.31	16.29	16.96	19.33	11.23	12.33
RAN2 Per Hand	119.63	-107.26	122.00	-112.26	120.66	-109.57
RAN2 Per Unit	105.68	-99.69	103.32	-99.63	104.42	-99.66
RSRR % Hands	15.33	16.31	16.94	19.32	11.23	12.32
RSRR Per Hand	119.64	-107.22	122.00	-112.24	120.66	-109.55
RSRR Per Unit	105.69	-99.68	103.33	-99.63	104.42	-99.66
RRSR % Hands	15.38	16.36	16.89	19.26	11.23	12.32
RRSR Per Hand	119.60	-107.24	121.99	-112.24	120.69	-109.57
RRSR Per Unit	105.67	-99.68	103.30	-99.62	104.42	-99.66
RRR % Hands	15.20	16.18	17.07	19.47	11.22	12.30
RRR Per Hand	119.59	-107.19	121.94	-112.17	120.68	-109 51
RRR Per Unit	105.67	-99.68	103.32	-99.63	104.43	-99.66

For the five simulations using random and simulated casino shuffles, Table 3 shows the percentages (of all 20+ million hands) in each of the six non-push categories as well as the per hand and per unit expectations for these hands.

Some players contend that their casino observations indicate a higher percentage of player losses on positive counts than theory predicts. After examining Table 3, such players might feel vindicated by pointing out that RRSR showed a higher percentage of losses on positive counts than RAN1. If they ignored the fact that the expectations (both per hand and per unit) on these hands did not differ significantly at the 95% level, they would be disappointed that RRSR’s losses on these hands were less than RAN1’s in spite of RRSR’s higher percentage of such hands.

This example has additional implications concerning casino observations. Between RRSR and RAN1, the difference in percentages of hands lost on negative counts is only 0.06% For such a small difference to be significant at the 95% level, the player would have to observe over 2 million total hands, assuming RAN1’s percentage of losses on positive counts is the theoretical one. It seems doubtful that any player has made such extensive casino observations; even if some player has done so, it is even more unlikely that he kept accurate enough records to note this small difference.

The results for hands in the nine categories strongly imply that the simulated dealer shuffles RSRR, RRSR, and RRR do not perturb the per unit expectations of hands won or lost on positive, negative, or zero counts. They further strengthen an earlier statement that the count provides the same indication of the player’s expectation for these simulated casino shuffles as it does for random shuffling. Also, since the per unit expectations of the hands in each category do not differ significantly in spite of the variations in the frequencies, any perturbations in the frequencies of the nine categories probably cannot be exploited.

Non-Random Shuffles and Winning/Losing Streaks

Analysis of the data on winning and losing streaks indicates no significant differences between simulated dealer shuffling and random shuffling. The analysis will be confined to streaks of 1, 2, …, 9 consecutive losses and I, 2, …, 9 consecutive wins. For the purposes of this study, a streak of consecutive wins encompasses all hands from the first win and continues to (but does not include) the next loss. This means that embedded or following pushes are included as hands in the streak. Hence, Win-Push-Win-Win-Push is defined as a streak of three consecutive wins during which five hands were played. Analogously, a streak of consecutive losses begins with the first loss, continues to but does not include the next win, and includes embedded and trailing pushes.

The first test involved the frequencies of I, 2, …, 9 consecutive losses and of 1, 2, …, 9 wins. Each frequency was first divided by the total number of streaks to obtain a probability. Then a Z test was used to compare corresponding probabilities (one for each of the 18 different types of streaks) for all 28 pairs of simulations.

Comparing each of RAN1, RAN2, RRR, RSRR, and RRSR with all of the other four runs required ten sets of 18 tests each. Of these 180 tests, one streak differed significantly at the 99% level, another at the 98% level, and two more at the 95% level; these four differences occurred in testing four different pairs of simulations. The remaining 176 tests did not differ significantly at the 95% level. Hence, apart from expected statistical variation, the streak probabilities did not differ at the 95% level between any two runs.

These results strongly indicate that streaks occur with the same probability whether casino shuffling or random shuffling is employed. However, one fact seems obvious: the less random the shuffle, the more the differences in streak probabilities.

Table 4, shows some of the win-loss streak data from RAN1. This will give an approximate indication of what the player might expect to see during actual play. Negative streak lengths indicate losing streaks and positive streak lengths indicate winning streaks. The percent of streaks is the number of streaks of this length divided by the total number of streaks, which was 9,170,446 in this simulation.

Hands is the total number of hands played, including pushes, during streaks of this length. Hands per streak is column 4 divided by column 2. Expectation per hand is the net win/loss divided by the total number of hands played during streaks of this length (column 4). Expectation per unit bet is the net win/loss divided by the total money bet on all streaks of this length.

Table 4. Streak Data for RAN1

Length	Streaks	Percent of Streaks	Hands	Hands per Streak	Exp. per Hand	Exp. per Unit Bet
-10	6451	0.0703	70614	10.95	-100.26	-90.84
-9	12440	0.1357	122434	9.84	-100.28	-90.95
-8	23702	0.2585	207443	8.75	-100.23	-90.94
-7	45266	0.4936	346625	7.66	-100.22	-90.91
-6	86152	0.9395	565501	6.56	-100.29	-90.90
-5	163906	1.7873	896124	5.47	-100.33	-90.95
-4	315032	3.4353	1378864	4.38	-100.41	-90.91
-3	599285	6.5350	1966487	3.28	-100.42	-90.94
-2	1144036	12.4752	2502201	2.19	-100.52	-90.96
-1	2181809	23.7917	2384899	1.09	-100.62	-91.00
1	2404684	26.2221	2630072	1.09	100.40	95.71
2	1143846	12.4732	2501308	2.19	100.47	95.70
3	543899	5.9310	1784734	3.28	100.49	95.65
4	258802	2.8221	1131224	4.37	100.59	95.72
5	122860	1.3397	6714597	5.47	100.61	95.64
6	58107	0.6336	381254	6.56	100.52	95.61
7	27681	0.3019	212073	7.66	100.53	95.59
8	13284	0.1449	116154	8.74	100.81	95.64
9	6257	0.0682	61541	9.84	100.82	95.62
10	3074	0.0335	33521	10.90	100.48	95.82

Excepting streaks of length 1, there were always more losing streaks than winning streaks of any length; as the length increased, the ratio of losing streaks to winning streaks increased. In short, the player should expect considerably more losing than winning streaks. Since the table is truncated, the following data may be of interest.

There were 7144 streaks of 11 or more consecutive losses and 2729 of 11 or more consecutive wins. The longest number of consecutive losses was 23 and the longest number of consecutive wins was 21.

Similar to streaks of consecutive wins and losses, a streak of consecutive positive counts encompasses all hands from the first positive count and continues to (but does not include) the next negative count; embedded or following zero counts are included as hands in the streak. An analogous definition of streaks of consecutive negative counts also makes embedded and following zero counts part of the streak.

With minor exception, the authors could not find the same patterns in streaks of positive and negative counts that appeared in streaks of wins and losses. Even between two random runs there were significant differences (at the 95% level) between streak probabilities. These probabilities seem to show considerable fluctuation and are probably not a good measure of a shuffle’s adequacy. This is not surprising since the frequencies of hands with positive, negative, and zero counts also do not seem to provide a reliable measure.

Table 5. Numbers of Streaks with 30 or More Like Counts

	RAN1	RAN2	RRR	RSRR	RRSR	NOSHUF	1PR	2PR
NEG	1984	1975	2118	2000	2083	28596	5110	4262
POS	597	583	578	611	707	16679	1774	1283

The minor exceptions had to do with the numbers of streaks of length 30 or more. The numbers of such streaks were enormous for no shuffling and decreased rapidly to reasonable values as the amount of shuffling increased. This implies that grossly imperfect shuffling increases the probability of long streaks of like counts.

However, it is not clear that the long streak probabilities provide a sufficiently fine measure of the shuffle’s adequacy. There were significant differences (at the 95% level) in the frequencies of long negative streaks between RAN1 and RRR and between RAN2 and RRR.

In addition, there were significant differences in the frequencies of long positive streaks between RRSR and RSRR at the 98% level, between RRSR and RAN2 at the 99% level, and between RRSR and RRR at the 99% level. Table 5 shows the numbers of such streaks for each of the simulations. NEG indicates streaks of 30 or more hands with negative counts; POS indicates streaks of 30 or more hands with positive counts.

Data was gathered to allow computation of the correlation between outcomes of consecutive decks. After the play of each deck was completed, three accumulations took place. First, the mean expectation of this deck’s hands was computed and added to the sum of the deck means. Second, the square of this deck’s mean was added to the sum of squares of deck means. Finally, this deck’s mean was multiplied by the mean of the previous deck and added to the sum of consecutive deck products.

Intuitively, one would expect a statistically insignificant correlation for random shuffling and a statistically significant one for no shuffling; this was indeed the case. Table 6 shows the correlation coefficients for all seven shuffling methods; the note below each coefficient tells whether or not it was significantly different from zero (SIG or NOT, respectively) and at what level. The table values were computed using expectation per hand played; those obtained using expectation per unit bet were similar.

The major conclusion is that for each of the simulated dealer shuffles, there was no significant correlation between the outcome of one deck and the outcome of the next. The lack of any significant correlation between consecutive decks adds to the evidence that each of RSRR, RRSR, and RRR is an adequate shuffle.

Table 6. Correlations for Outcomes of Consecutive Decks

RAN1	NOSHUF	1PR	2PR	RRR	RSRR	RRSR
0.00032	0.00407	0.00208	-0.00098	-0.00013	-0.00053	-0.00015
SIG 99%	SIG 99%	NOT 95%	NOT 95%	NOT 95%	NOT 95%	NOT 95%

The correlation for NOSHUF and 1PR are perfect examples of values that differ significantly from zero in the statistical sense but are otherwise insignificant. Even for NOSHUF, whose coefficient is larger, the correlation between consecutive deck outcomes seems too small to be exploitable.

For single-deck play, two projects immediately came to mind as natural extensions of this research. The first would be to rerun the three simulated casino shuffles with a new deck being introduced every 100-200 hands. Of course, each new deck would be introduced in its usual order, and a simulated new-deck shuffle would precede dealing the first hand. It is conceivable that hands dealt after the initial and next two or three shuffles might have different characteristics than those dealt after more shuffIing has taken place.

A second interesting project would be to use a less precise riffle in RSRR, RRSR, and RRR. Such a riffle would be governed by a distribution with a decreased frequency of dropping single cards and elevated frequencies of dropping two or more cards; Anthony Curtis’ observations could be used to construct such a distribution. Simulations using this distribution for riffles would be run both with and without introducing a new deck every 100-200 rounds.

Acknowledgements: We owe much to Peter Griffin, who provided invaluable guidance toward proper statistical analysis of the gathered data and made several suggestions that significantly improved the paper.

We are also deeply indebted to Steve Forte, who isolated and explained each of the common shuffle techniques and procedures as employed in Nevada and Atlantic City casinos (even though we have not yet used the Atlantic City data).

In addition, we thank Anthony Curtis, who got four professional dealers to shuffle for him and provide new first hand data about how dealer riffling mixes the cards. ♠

Moving Up from Low Stakes Blackjack

by Barfarkel
(From Blackjack Forum, Vol. XXIII #4, Winter 2003/04)
© 2004 Blackjack Forum

[Barfarkel is the author of You’ve Got Heat: The Vegas Card Counting Adventures of LV Pro ]

The first time I stacked up four greens on a maximum bet, my heart was pounding. My initial reluctance to make a max bet had only just been overcome, after almost two whole days of shying away from pushing out those four greenies on a single hand.

As the bored dealer routinely called out, “Checks play,” I sank lower in the chair, and scanned the pit for signs of activity. Nothing happening. Were they deliberately ignoring me, hoping I’d hang myself with too much rope? Is that why they were over on the other side of the pit, far away from my table? Had they put the Eye in the Sky on me, hoping I’d get too bold so that I’d be an easy target to identify as a card counter?

As the questions and paranoia whirled through my mind, the lack of pit activity seemed to yawn at my mental histrionics. At first I couldn’t quite believe that they were going to let this pass—after all, I had just made a max bet right under their noses.

But soon I came to my senses and calmed down, realizing that they couldn’t care less that a player they didn’t even know had bet $100 on a hand. That’s chicken feed by Vegas standards. But not to me. Even though it was only $20 more than my usual $80 top bet, there seemed to be an emotional barrier to the magic sum of $100. Somehow, that figure became big money to me.

The risk of losing it was making my palms sweat. In fact, the $100 bet represented the fact that I was now embarking on a new era of my card counting avocation—green chip play.

OK, strictly speaking it’s actually a red-to-low-green spread. As I’m now discovering, betting greens tend to create more paranoia in ones’ mind. The tough part is knowing if and when this newfound fear is justified.

I’ve made higher bets than this in the past, but then it was part of a team’s bankroll. Now it was my own hard-won money on the line. A few years ago, when I was just starting out counting cards in casinos, I bought into a shared-bankroll blackjack team. I threw in half of my personal blackjack funds, $1,000, and owned 10% of our five-man $10k team bankroll.

Fortunately, I had an experienced mentor to prepare me for the higher betting levels. Among other things, he told me that I must consider the chips I’m betting only as colored pieces of clay that are used solely to keep score, just like in any other game. Don’t think of them as real money that you could use to buy a new laptop or DVD player. Think of them as marbles or Monopoly scrip.

I’m amazed now when I look back and recall that I had no problems betting green chips as part of a team, even at the very start of that venture. It’s always easier betting other people’s money. When I lost a $150 bet, I simply reminded myself that I had just lost $15 of my own money. No big deal. I’d get it back soon enough.

Plus, it was huge fun to be betting stacks of green every hand, while winning and losing hands at about the same ratio as when I was betting reds with my own bankroll. So why was I now so afraid of pushing out four greens on a hand of blackjack?

Casino Heat as You Move Up from Low Stakes Blackjack

In the first place, Las Vegas had changed for the worse. Pits were now quite intolerant of card counters—much more than they were even two years ago. The bean-counter mentality that had infected casino upper management now held that even lower-stakes advantage players were a direct threat, and must be dealt with.

In years past, red chip counters—and even low green spreaders—could fly under the radar and be somewhat tolerated, as long as they didn’t camp out or get too outrageous with the bet spread. Now that had changed.

Later in my trip, I would get booted out of one of the Coast properties after making just one $100 bet. I had been playing for a half hour on swing shift and losing. I switched to another $109 double-deck table in a different pit. I had been betting $15 and $20 in negative and neutral counts. After ten minutes or so, the count started rising. I bet $40, then $75. The count stayed high. I pushed out a $100 bet and won. As I’m stacking my winnings, I get the tap on the shoulder.

“No more blackjack,” the floorman said. “Your game’s a little too strong for us.” I just couldn’t believe that they would back off someone playing at my relatively low stakes. But boot me they did. And this is a large casino with three or four blackjack pits and thirty-four tables—twenty-four of them double-deckers. Who would ever believe that the day had come in Las Vegas when one $100 bet would get you booted?

The Psychology of Moving Up from Low Stakes Blackjack

Another reason that I felt such trepidation purshing out max bets was that, despite the low risk-of-ruin numbers that BJRM 2000 had generated for me, I was quite protective of my bankroll. After some disastrous team losses, I went solo with the $2,000 I had left, late in 2001. Playing a red spread for two years, I had put a ton of time and effort into winning the $8,000 that I had netted over seven or eight trips since then. I wanted to continue to play conservatively.

When you play a green spread, variance can be vicious. I had not yet steeled myself to be able to accept huge losses. It’s not unusual to lose 80 or 100 green units in just one session. Do that three consecutive times, and I’m right back in red-chip land where I started.

I had come too far over too long a time to piss away my hard-won $10k bankroll cavalierly. The emotional impact of radical bankroll swings and the increased possibility of getting botted were the two main reasons for my initial reluctance to stack up those four greens.

There was only one silver lining in this storm cloud. By the time this barring occurred, I had overcome my max bet gun-shyness. I was now having very little problem making a $100 wager. Thankfully, it didn’t take very long. It still made my heart thump harder, but I got over it quickly and had gotten somewhat used to it by this point in the trip.

Come to think of it, making a $30 or $40 bet used to give me the same fearful reaction when I first started counting cards. I guess you can get used to anything, given enough time.

Still, I missed the relative freedom to spread and lack of heat of my former red chip approach. Then I could camp out and play long sessions with little or no scrutiny. Now that I’m spreading green, I have to limit my session times. In order to get in the same number of hours, I have to move from casino to casino more frequently. I have to play shorter sessions.

You don’t want to give the pit and the Eye too long a look at your betting and playing strategies. This results in more down time during which I’m traveling rather than playing. As a result, I’ve had to put in more hours out of my day in order to get the same amount of playing hours in.

The added time is spent moving from store to store, and there are more sessions played, albeit each one of shorter duration. And I guess I could factor into my trip expenses the added wear and tear on my car and the additional gasoline expenditure, but I haven’t yet figured out how to adjust my accounting procedures to integrate those new factors.

Offsetting the additional travel time is the fact that I’m now getting more hands per hour. Since the $25 minimum tables are rarely as crowded as the $5 and $10 tables, I’m playing faster. Not only that, but there are fewer ploppies at the green tables, so I get more out of my high counts. The tens and aces don’t get as dispersed among the other players as they used to, so I now get more hands at high counts, and the plus situations last longer.

Each time I calculate my spread and risk of ruin on BJRM 2000, I now have to remember to set it to a greater number of hands per hour. This is a better situation, but comes at the price of higher, swifter variance. Because it’s a better game, with more high count situations, I tend to win or lose more quickly. The old saying that “You lose the most at the best games,” now seems truer than ever. That’s the underlying irony of this double-edged sword. Be careful what you wish for.

And again, naturally they watch those $25 double-deck tables more closely. While betting a green spread, I now have to keep track of how many minimum-to-maximum bet cycles I’ve gone through. I know I should flee once I’ve gone through two cycles, but sometimes I try to push the envelope and stay for a third one. That’s how I mark the session time these days—not the minutes and hours played, but the number of min-to-max cycles I’ve generated.

Betting green is a whole different culture. I had been used to playing pitch games in downtown Las Vegas with relative freedom and ease. With my former red spread, I was one of the lowest bettors in the casino. As such, I would be totally ignored. I would have to keep pitching the floor people for a coffee shop comp throughout the session. It was part of my act to try to get noticed. Hopefully, they would regard me as a harmless comp-hustling nuisance. That’s what I wanted them to think.

Now the dealers call out “Checks play” almost as soon as I sit down at the table. You get noticed right away. I’ve found that I have to use a lot more betting cover, especially early in the session. My plan of attack has changed so that now I’m considering how to fool the pit and Eye in the Sky. This has become one of my primary concerns, especially at places where they don’t know me. Now I’m trying not to get noticed.

Like most of you, I hate to lose. We all feel the unjustness of a loss when we know we have the advantage and are supposed to come out ahead over time. In my red chip days, I’d camp out if losing and play marathon sessions in order to get even. Can’t do that anymore. Win, lose or draw, I have to end the session after those two or three bet cycles.

I’ve had to become more philosophical about booking a loss. In fact, I’ve taken a page from Ian Andersen (author of Burning the Tables in Las Vegas) in this regard. I now advertise my loss to anyone who will listen. While not allowing myself to whine, I try to present a nonchalant front, aided by a sense of humor about the losses. Of course, I’m doing this so that they’ll remember me as a loser and welcome me back when I return. Longevity has now become one of my primary concerns.

Longevity as You Move Up from Low Stakes Blackjack

In concert with this is the need to rat-hole chips. In my red chip days, I would always forget to use this technique, but now it becomes increasingly important. As many of you know, you don’t hide the highest chip denomination, but only the lower or mid colors. If you are playing at a $25 table, it’s smarter to hide the green chips, and not the blacks. Otherwise it’s too easy for them to figure it out later when they count the chip tray, after you’ve left the table.

If you get busted hiding chips, this puts real suspicion on you the next time you appear. They keep a much closer watch on the higher denominations. Of course you can only employ this tactic if there are other players at your table. Rat-holing chips while playing heads-up is suicidal. They’ll be able to tell rather easily.

One of the things I’ve learned from reading Cellini’s book The Card Counters’ Guide to Casino Surveillance is that you should avoid using your shirt pocket to hide chips. Try to use your pants pockets instead. The reason is that once several chips are stored in your breast pocket, they distend the shape of the pocket. In most cases, the Eye will be able to see the impression they make on the outside of your pocket, in the exact shape and size of the chips.

If they suspected you at all before they notice this, it confirms their suspicions. That’s not good. Now they’ll really be watching you. The only exception to this guideline is if you have a business card in your shirt pocket. Then you can drop the chips behind the card so that the hidden chips don’t push against the fabric and make a chip-shaped impression.

Of course, the comps are better at the green-chip level. I’m now getting restaurant comps for the mid-level eateries, like the Mexican and Italian cafes, instead of the former buffet and coffee shop comps I used to score. With negative and neutral count bets of $15, $20 and $25, I’m not yet getting the gourmet restaurants, but that’s only a matter of time. Part of the reason is that since I’m playing shorter sessions, I’m not giving the casinos the number of hours they require to qualify for those better gourmet comps. I have to put together several short sessions, on different shifts, rather than one long session like in the past.

Oh, by the way, I never did tell you how that first max bet hand at the beginning of this article turned out. I had played a half-hour already, bleeding away my buy-in (mostly with negative decks). When the count finally rose to a true of +5, this was my first opportunity to make a $100 bet. After several prior sessions of shying away from it, I finally pushed out those four greenies with trembling hands, and triumphantly turned over my first blackjack of the session!

This turned my hitherto losing session into a winning one. I hesitate to think how I would have reacted if I had lost that one. I guess I would have found out quickly how much heart I really had. ♠

Power Numbers Blackjack System Confronted

by Arnold Snyder and John Leib
(From Blackjack Forum XV #3, September 1995)
© 1995 Blackjack Forum

Have you see this Power Numbers Blackjack advertisement, or one similar to it, in a newspaper or magazine in your area?

Variations on this ad have been sent to us by readers in California, Nevada, New York and New Jersey. When John Leib saw a version of this ad in a San Diego newspaper, he called the 800 number and received the complete promo pack from the “Leonard Benson Company.” This includes some 14 pages of materials, with testimonials from satisfied users, and a question/answer brochure by the inventor of the system, Dr. Morton Jacobs.

One ad flyer claims that users of the “Power Numbers Blackjack” system can “gain a mathematical advantage over the casinos without counting and win $1,000 or more per day.” The blackjack system, according to the ad, “is reasonably priced and can be learned by anyone in a few hours.” And, “for a minimal investment of money and time, you will have a sound way of being able to make serious money the rest of your life.”

Some of the ad claims are astonishing, such as: “POWER NUMBERS BLACKJACK™ players have an advantage ranging from 5% to an incredible 20% and more! … You’ll be winning 10 units for every 50 to 150 units in action.”

The Power Numbers Blackjack course costs $495, but the ad John Leib received stated that if he ordered within ten days, he could get it for only $379. Leib didn’t send in his money, but instead, sent the following letter:

Dear Leonard,

Today I received your information pack regarding POWER NUMBERS BLACKJACK™. I am quite impressed by both the effectiveness and simplicity of this system. It should be promoted to the blackjack-playing public in more impressive fashion than now is the case.

I can help you do this. I am a frequent contributor to Blackjack Forum, arguably the most prestigious publication for getting the word out. A positive review in BJF would assure wide acceptance of POWER NUMBERS BLACKJACK™, as you are attempting to do in the generic press. And such review in BJF could be quoted in other media.

Here’s my proposal:

1. I will learn POWER NUMBERS BLACKJACK™ to your satisfaction, right in your office in Las Vegas.
2. I will follow precisely the recommendations/directions of POWER NUMBERS BLACKJACK™ in actual casino play, using for each session the minimum $160 initial bankroll supplied by you. You or one of your students can play at the same table to be sure I am doing it right.
3. We will do this ten times, each for sufficient time to win ten units or until you or your student signals me to terminate the session.
4. All money in the bankroll at the end of each session will be returned to you, so this trial will cost you nothing and will, in fact, give you a net gain.
5. I will write an account of this demonstration, including the results, which will be published in Blackjack Forum. You will be given an advance copy and the opportunity to comment on my experience.
6. I will reveal nothing about the workings of POWER NUMBERS BLACKJACK™ to anyone, and will report only my impressions about the ease with which I was able to master POWER NUMBERS BLACKJACK™ and the success it has provided at the casino tables.
7. If POWER NUMBERS BLACKJACK™ performs for me as you have found it to perform for others, I will buy it at the full $499 price, and will use it in casinos with my own money. I will also recommend it to those I think might benefit from it.

This is a wonderful opportunity for you to get very influential ink free. And it is an opportunity for me to learn something in the process. It’s a win-win situation for the two of us. I’m positive Blackjack Forum will agree to publish my results. We can get their agreement before we proceed. Please let me know when you would like to start. I’m very excited about this project.

Sincerely,
John E. Leib

Will Leonard Benson accept John Leib’s proposal to “test” his system for Blackjack Forum? We’ll let you know next issue!

John Leib’s full report, “22 Hours of Power Numbers Blackjack” is in the Spring ’96 Issue of Blackjack Forum. ♠

A Report on the Claims, Training, and Results in Play

by John Leib
(From Blackjack Forum XVI #1, Spring 1996)
© 1996 Blackjack Forum

[Ed. note: In the September ’95 issue of Blackjack Forum, we published a letter that mathematician John Leib wrote to Leonard Benson, in which Leib offered to test the POWER NUMBERS BLACKJACK™ system, which Benson was heavily promoting through newspaper advertisements all over the country. (Benson, by the way, continues to promote and sell the system.)

Leib told Benson he wanted to use Benson’s money to test the non-card-counting system, and stated that he would publish his analysis and results in Blackjack Forum. This is Leib ‘s follow-up report on his experience learning and playing the POWER NUMBERS BLACKJACK™ system. — Arnold Snyder]

Leonard Benson Responds to the Challenge

Monday, September 11th, I returned from that ritual which humbles most of us: my 50th high school class reunion. When I got to the house, my wife had a telephone pink slip which I had not expected; I had gotten a call from Leonard Benson, purveyor of the Jacobs POWER NUMBERS BLACKJACK™ way to relieve the casinos of their money.

I had not expected the call because the claims made for POWER NUMBERS BLACKJACK™ did not seem possible to satisfy in actual casino play. I, as perhaps most of you, figured this was just another scam, designed to take money from the gambling public by use of the motivating feature shared by gamblers: greed. I was sure Leonard Benson knew it was a scam which could not withstand critical testing in actual casino play.

I had attempted to chide Leonard Benson into some response by my original letter (which was reprinted in the September issue of Blackjack Forum).

After that issue was distributed, I sent another letter, calling attention to my ability to deliver on getting ink in Blackjack Forum describing the results which I would experience by actually using POWER NUMBERS BLACKJACK™ with real money. If Leonard Benson knows the system does not work, he surely would not initiate further contact, and instead would hope that, by ignoring my challenge, it would pass.

But he had called! What could he possibly want to talk about? The next day I called him and found him receptive to my proposal! We talked about how ten trials might not be enough, what with one fluctuation or another, and agreed to go for 25 trials instead. Except for the time involved, I knew the more the merrier. Leonard said he wanted to talk it over with Dr. Jacobs, the inventor of POWER NUMBERS BLACKJACK™.

Later that same day, Leonard called to confirm agreement with my proposal. Dr. Jacobs thought it was a great idea, too. Leonard promised to send me the complete set of materials so that I could become proficient at utilizing POWER NUMBERS BLACKJACK™ before I got to Vegas and was certified as competent to put it to the test with their money.

I must say that this agreement to test POWER NUMBERS BLACKJACK™ in this unbiased way, agreeing to publication of the results, good or ill, told me that they were serious about the validity of POWER NUMBERS BLACKJACK™. This was not a scam! I was very skeptical about its value, even if they weren’t, but I was determined to give them a fair shake.

Leonard Benson Provides the Power Numbers Blackjack Training Materials

True to Leonard’s promise, the material was shipped September 13th and arrived three days later on the 16th. I decided to chronicle the pertinent events from that point forward in diary form.

As advertised, the package contained:

A 2 hour video tape that explains, illustrates and plays the POWER NUMBERS SYSTEM™. There is no guesswork.

An 83-page Home Study Manual and Workbook explaining the POWER NUMBERS BLACKJACK™ system in step-by-step detail.

A felt blackjack layout, chips and 6 decks of casino cards for practicing at home.

Free phone consultation on the Blackjack Hotline whenever you have questions.

Well, the free phone consultation wasn’t in the package, but everything else was.

I immediately dived into the Home Study Manual (HSM) and noticed rather soon that the claim of “no guesswork” did not quite apply to it. There were several inconsistencies, ambiguities and optional playing choices which would necessarily call for “guesswork” when one of these situations arose at the table.

Later, on viewing the 2 hour video (for which the claim was made), I found further areas requiring interpretation by the student (and, therefore, “guesswork”), as well as inconsistencies with the HSM.

On Sunday the 17th, and again on Monday the 18th, Dr. Morton Jacobs (the creator of POWER NUMBERS BLACKJACK™) called me to see how I was faring in my pursuit of truth. I told him that my plan was to catalog my questions and concerns, and review them with him in Las Vegas the following Monday (the 25th). I wanted to play like a computer in the fashion he though would show off POWER NUMBERS BLACKJACK™ in its best light.

In particular, I explained that I would be reviewing POWER NUMBERS BLACKJACK™ in casino play against the claims made for it in the pre-sale literature, as I thought this was the appropriate standard since this was the promise made to the potential customer to encourage him to buy. Dr. Jacobs agreed with this thinking.

My plan was to layout the claims I felt were substantive, and then gain agreement on the machine-like casino play which should produce results which would validate these claims. Dr. Jacobs was in agreement with this approach, so all seemed to be “go” and I began to catalog claims and casino play questions where there still seemed to be “guesswork.”

Over the next week I did a lot of reading, watching and dealing, so that I would be well versed in the areas which required no “guesswork,” and had uncovered and recorded the areas where there was “guesswork.”

Note: I cannot reveal any of the concepts or details of POWER NUMBERS BLACKJACK™, as that is part of my agreement with the Leonard Benson Company. Only the actual results of casino play and my evaluation of how well it supports the pre-sale claims may be reported.

Sunday, September 24th. Full of my newly acquired knowledge (and newly acquired questions), I headed for Las Vegas. Five hours of determined driving got me there. I called Dr. Jacobs, but we couldn’t get together that evening. It was imperative that I be in full agreement with him on how to play and how to bet before I engaged in any actual casino play. So we planned to do this the next day.

My Power Numbers Blackjack Competency Test

Monday, September 25th. I was invited to Leonard’s apartment to meet with him and Dr. Jacobs. The discussion was frank on both sides. I told them that the ideal situation would be for Dr. Jacobs to play and for me to observe, and this was seen as a good thing all around. All my preparation to actually use POWER NUMBERS BLACKJACK™ was not to be used in casino play, but this preparation did give me the ability to critically monitor Dr. Jacobs in action. We soon developed a good rapport and became at ease.

Dr. Jacobs was to play for a high roller that night at the MGM, and I was invited to come along.

Casino Play with Power Numbers Blackjack

Monday, September 25th. At the MGM I met the high roller, a Midwesterner named Al. Apparently Dr. Jacobs had played for him twice the day before, also at the MGM, and had won both times. Al was, of course, evaluating Dr. Jacobs, and was impressed. The first session had been using $100 units, the second was $200. (These earlier sessions are not included in my review because I did not witness them.)

So now it was time to move up to $300, and that was the level for the play on this night. The results were spectacular. In one hour Dr. Jacobs had won $2050. (After winning $1950 at the $300 level, he had dropped back to $50 units, and won another $100, two units. We stopped for the night and were comped to a fine dinner before we left the hotel. I had been accepted.


Tuesday, September 26th. Now it was time to move up again, to the next level: $400 units. This meant a bank of $8000, which didn’t seem to bother Al. We were still working out on the MGM, and they didn’t seem to mind. One thing that impressed me about POWER NUMBERS BLACKJACK™ was the level of camouflage, the difficulty of detection that it provides. There was never any heat regardless of the betting spread and the amount we were ahead. I say “we” because, emotionally and acceptance-wise, I had become a member of the team trying to make the system work.

For a few hours we hovered around even, up a few units, down a few units, but mostly up. There was a time on a two-unit bet that the dealer had a two-card 19 and we had a two-card 18. If we had won that bet, we probably would have ended the session and quit for the night, up seven units ($2800). But we didn’t win and we didn’t quit. Things went downhill from there.

About a quarter to five the next morning, after seven hours in pursuit of our goal, we broke for breakfast. We were down fifteen units ($6000) and needed a time away from the emotional roller coaster to evaluate the situation. Over bacon and eggs, we considered what to do now.

It’s the same old story we have all been through at least once in a casino: we come to win some set amount with a betting and playing system and a pre-selected bankroll. We are sure of the soundness of our approach and know, rationally, that even if it isn’t winning at the moment, there is no basis to change. And we are prepared to lose the entire bankroll if the specific cards we must confront just don’t like us up to now, whatever “now” is. And we know we may lose all of this session’s bankroll occasionally. Not to worry. The system is sound and will overcome transient negative behavior in the long run.

Then this significant downsizing actually happens and all of our cool pre-session analysis and thought escape us. The plan no longer is inviolate and we look for changes to implement which will, by themselves, turn the trend around.

And on this early morning, hunkered down over coffee and eggs, the process began. I was mostly listening. After all, I was just an observer, and I didn’t want to taint my reporting by influencing the outcome. So the money man (Al) and the expert (Dr. Jacobs) made all the decisions. I only answered direct questions, and never said, “If I were doing it, then I would…”

Then we did something Kellyesque [Editor’s note: the author is referring to the Kelly principle for bankroll management, which professional gamblers use. To Kelly bet is essentially to bet a fraction of your total, non-renewable bankroll proportionate to your edge.] Since we had only one quarter of the original bankroll left, we dropped the unit size from $400 to $100, a move I though was only valid if this was not a renewable bankroll (which was not the case, since this was only a “session” bankroll). I did not voice this concern.

Another concern was that Dr. Jacobs was asking advice from us on how to modify his system. This hardly showed a strong conviction (at that moment) in the long-run correctness of the system. The emotions were overcoming clear thought.

So now we were back to a 20-unit bankroll, and in my mind this terminated the original session and began a new session. I mentally made a note to score it this way. Perhaps Leonard will not agree with this determination of scoring practices, but it made sense to me. This change in the system [ed. Note: reducing the unit due to loss] was not in accordance with what was advocated in the POWER NUMBERS BLACKJACK™ manual or video, which was the system I was attempting to evaluate. So I decided to separate the data and deal with “units,” not dollars.

Dr. Jacobs played with the new bet sizing. His play didn’t always seem to agree with my understanding of POWER NUMBERS BLACKJACK™, but no mention was made that we were no longer getting data that was useful to my review. (If Dr. Jacobs had said that, I would have gone home and gotten some sleep.) Two hours later, we had lost the remaining $2000. Not a good night for showing off POWER NUMBERS BLACKJACK™. At 8:15 in the morning it was all over.

Later, both Leonard and Dr. Jacobs said I shouldn’t count that last portion of play since it wasn’t POWER NUMBERS BLACKJACK™. It isn’t clear how they would have wanted it viewed if we had made a remarkable recovery with this new approach. I am including it in my data as Session #3. You can adjust my conclusions as you like, removing this session if you feel so disposed.


Wednesday, September 27th. Much of this day’s activities were a continuation of the play started the night before, and are chronicled above. Then we all went home to rest.

Later that evening I was called home to San Diego for personal reasons. I called Dr. Jacobs and told him I was leaving, but would be back in November and would like to continue the data taking at that time. I told him that the best of all possible worlds for me (and, I presumed, for an objective review of POWER NUMBERS BLACKJACK™) would be to have him play at low stakes just to provide data for my review. This way we could treat it as a laboratory experiment, and not get emotionally involved with the size (in dollars) of the wins and losses.

Dr. Jacobs thought this was a great idea, and offered to put me up in his guest bedroom when I was in town. Through the trials of the previous two nights, we had become good friends.

Another Trial of Leonard Benson’s Power Numbers Blackjack

COMDEX in November(the world’s largest computer trade show) presented the next opportunity to take data on the effectiveness of POWER NUMBERS BLACKJACK™. Dr. Jacobs was not feeling well and could not commit to playing at any specific time, so I called Leonard and he got one of his students, Mike, to play while I watched.

Mike’s approach to stopping a session was different from that advocated in the POWER NUMBERS BLACKJACK™ manual and video, so a “session” meant something different. But he was playing with his own money, so I could not object. Anyway, the most important thing was whether the basic play according to POWER NUMBERS BLACKJACK™ will win significant money, measured in units per hour, so this data could be incorporated that way. And I needed data.

We played at the MGM again. Mike’s “unit” was $25, so the pressure from the amount of money was not great. Mike played for about an hour and a half, lost 6 ½ units, and declared the session over. We set the next session for the next day, and went home for the night. [An aside: later that night I played at a single-deck game at Circus-Circus, flat betting $3 and playing basic strategy. In about 100 hands, I won 27 ½ units ($82.50). Had I been playing $25 units, this would have been $687.50. And I didn’t even have a system!]

Wednesday, November 15th. Mike and I met at the Mirage for a short session (because his son was in town), and he played there for 25 minutes. He was ahead one unit ($25) when we quit.

Thursday, November 16th. Back at the Mirage with Mike. After 35 minutes, Mike declared the session over, 5.5 units ($137.50) ahead. This brought Mike back to even in my score book. We decided on another session that day.

Later we returned to the Mirage and had phenomenal cards, winning 10 units ($250) in just 15 minutes. Now Mike was helping the recovery from the disaster I had witnessed with Dr. Jacobs and Al.

Friday, November 17th. Mike and I met under the balloon at the MGM in the morning and things went as badly as they had gone well in the previous session. In 20 minutes he lost 6 units and called it a session, but not a day.

As it turned out, it was a day for Mike, at least where I was concerned. My pages to him, which had been promptly returned before, went unanswered that afternoon. Since my time was running out, I called Leonard, and then I called Dr. Jacobs, who was to coach another player that evening and thought that acceptable data could be gathered at the same time, and invited me to come along.

The player, it turned out, was an entrepreneur from Minneapolis named Steve Renner. Steve’s interest in POWER NUMBERS BLACKJACK™ was in marketing it via multi-level marketing (MLM) though WIN (Winners; International Network, 612-349-5221), a company he owned. He wanted to master POWER NUMBERS BLACKJACK™ so he could teach it to his MLM recruits.

The plan was for Dr. Jacobs to watch as Steve played, advising and correcting him in both betting and playing. This was their second such session. They said they lost 10 units the first time, but those results are not included in this evaluation because I have limited myself to what I have actually seen.

Dr. Jacobs chose Bally’s for our session. Play was to be with units of $10. After about 45 minutes and with Steve down 7 units, Dr. Jacobs had to take his daughter to some kind of lessons. He (Jacobs) knew I knew how to play POWER NUMBERS BLACKJACK™, and he suggested I take over coaching Steve while he was gone. (NOTE: He was correct that I knew both how to bet and how to play POWER NUMBERS BLACKJACK™, but nonetheless, I was surprised he let me direct the action while taking data.)

Steve continued playing, with me keeping him strictly on course in both betting and play. The cards continued to show POWER NUMBERS BLACKJACK™ no mercy, and in another 30 minutes Steve had lost an additional 9 units. At this point he thought he should turn the task of digging out over to Dr. Jacobs when he returned.

It was about 9:00 pm when it became clear that Dr. Jacobs would not be back until after he had brought his daughter home (the plan had been for him to return during the four hours she was to be gone), and it would be about midnight when he would get there. Since I had to drive back to San Diego before morning, I called it a session and left. Down 16 units.

Third Trial of Power Numbers Blackjack

I drove all morning New Year’s Day to get back to Vegas and continue the data taking. Leonard knew this would be my last chance before submitting my results for the March issue of Blackjack Forum, and he accepted the task of finding someone to play the POWER NUMBERS BLACKJACK™ system for my observation.

This time it was Chuck, a local student of POWER NUMBERS BLACKJACK™ who said he had seldom lost in more than 100 hours of play up to that point. His unit size was $10. First we played at Bourbon Street and quickly won six units. Then we took on the Maxim, dropping 2 units and calling it a session. Finally we played at the Poker Palace in North Vegas, losing 3.5 units and stopping for the night. Up 0.5 units for the day.

Tuesday, January 2nd. The first stop was back to Bourbon Street and two more quick units, then to the MGM and a 5-unit win, and then to the Tropicana for six more. Ahead 11 units, we declared this a session.

The next session started at the Maxim with a 1-unit win, continued to Bourbon Street for another 2 units, then finished at Bally’s with another 5.5 units. Session over +8.5 units.

The final session for the day combined play at Bally’s and the MGM. +4.5 units at Bally’s, -9 units at the MGM. Net for the session: -4.5 units.

Wednesday, January 3rd. The first session included playing at the Maxim (broke even), Bally’s (-1 unit), and the MGM (+5.5 units). Net for session: +4.5 units.

The second session was conducted at the Tropicana. Results: -5 units.

The third session was downtown at the Golden Nugget. Results: -3 units. Net for the day: -3.5 units.

Thursday, January 4th. Our last day of testing started off with a -4 unit session at the Maxim, followed by a +9 session, split between the Maxim and Barbary Coast. Two other short sessions at Barbary Coast netted +2.5 units and +2 units. Chuck’s contribution to the study of POWER NUMBERS BLACKJACK was a healthy +21.5 units.

This ended my data taking, as I needed to get back to San Diego. We hadn’t quite gotten 25 sessions, but 22 would have to do.

Evaluation of Leonard Benson’s Power Numbers Blackjack

My evaluation of the effectiveness of POWER NUMBERS BLACKJACK™, based only on mathematical considerations, is that the player risks money at a disadvantage of between 2.0% and 2.5%. [Editor’s note: John Leib was an aerospace engineer for Lockheed with a Ph.D in math. I met him after the great gambling analyst, Allan Wilson, recommended him as a brilliant math mind.]

Since I am prohibited from divulging the specifics of POWER NUMBERS BLACKJACK™, I am not free to explain where this range comes from, but suffice it to say that I can back up this estimate by analysis, regardless of the actual data collected.

I analyzed the data, if sloppily, well enough to draw a conclusion of how well it supports the 2.0%-2.5% estimate of player disadvantage. It should be noted that, sloppiness and all, we don’t need to tie this down to the nearest 0.1% to be confident of the validity of the conclusions.

Since there was a loss of 18 units during Session #3 (which is disputed as being the result of improper application of POWER NUMBERS BLACKJACK™, I decided to analyze the data in two ways (you may choose the analysis that appeals to you):

1. Using all the data collected, and

2. Using all data except Session #3.

The argument for (1.) is that:

1. No announcement was made before hand that this data was inappropriate for my analysis. It was not my job to validate the betting/play as being in conformance with POWER NUMBERS BLACKJACK™. And besides, we had Dr. Jacobs, the inventor of POWER NUMBERS BLACKJACK™, betting the money and playing the hands.
2. If POWER NUMBERS BLACKJACK™ works, there would be no rationale for departing from it when things aren’t going well.
3. I was asked to play a hand (at low stakes and with basic strategy) most of the time during Session #3 so we would have a better number of hands from which to know how to bet. This was in line with the precepts of POWER NUMBERS BLACKJACK™, so it looked like we were trying to follow, at least to some extent, POWER NUMBERS BLACKJACK™.
4. It worried me that, perhaps, this session would not have been protested if it had been highly successful.

Analysis of the Power Numbers Blackjack Data

Win Rate:	-0.67 Units/Hr.
Action:	580 Units
Return on Investment (ROI):	-2.6%
ROI Sigma:	4.2%

The return on investment (ROI) of -2.6% is comfortably close to the -2.0% to -2.5% range predicted by rough analytical methods for POWER NUMBERS BLACKJACK™.

It should be noted that a change in the data of only 15 units (0.6 sigma) would have resulted in no loss at all.

Obviously, this limited data cannot adequately pin these numbers down from an experimental viewpoint. The only way to adequately approximate the true ROI figure with great precision is to perform an extensive simulation.

Data Analysis Excluding #3

Win Rate:	+0.15 Units/Hr.
Action:	497 Units
Action Rate:	24.5 Units/Hr
ROI:	+0.6%
ROI Sigma:	4.5%

The data excluding Session #3 showed a net win of 3 units. If one is inclined to throw out this session, then it is impressive that POWER NUMBERS BLACKJACK™ showed a profit; an impression which is limited by the fact that if 13 units (also 0.6 sigma) less were won, the data would match the -2.0% of the predicted range of -2.0% to -2.5%.

The primary conclusion to be made is whether or not POWER NUMBERS BLACKJACK™ is a winning system. From a mathematical analysis point of view, disregarding the actual collected data, the answer is “No.” This conclusion was tested by taking data, and including Session #3 shows the shows the experience was a losing one. Ignoring Session #3 results in a very modest win, a win with little statistical support because of the limited amount of data.

It is my opinion that POWER NUMBERS BLACKJACK™ is less desirable by 1.5% to 2.0% than is basic strategy, even though the situations it finds are better than average. The departures from basic strategy are quite costly. But, even with correct (basic) strategy, the player will be investing money at about -0.5%. In either case, POWER NUMBERS BLACKJACK™ is doomed to long term failure. As I say, this is my opinion.

Power Numbers Blackjack: Results Versus Promises

The time has come to review the promises made for POWER NUMBERS BLACKJACK™, and to compare them to actual casino experience and analytical predictions.

“$1,000 and more Profit Per Day Playing POWER NUMBERS BLACKJACK.”

This was the grabber in the ad, the thing that makes you read the rest of the ad and, perhaps, call the 800 number. But what does it mean? Does this mean that, given enough days, you can average $1,000 per day, or will you, on some good day, net the promised $1,000? The use of the expression, “Profit Per Day”, implies an average; otherwise it should have read, “Profit A Day,” and be qualified with “sometimes.”

Using the (perhaps optimistic) results excluding Session #3 of 0.6% ROI, $1,000 would require “investment” of about $160,000 in the “1 to 3” hours required for a session, or about $50,000 an hour. With an action rate of 25 units per hour, this would require the unit to be $2,000.

“Amazing new discovery gives you a mathematical advantage Without Counting!”

Also from the ad, and the real grabber for one who has some analytical skills at the game of blackjack, particularly when coupled with the expanded claim, “Consistently win 10 units in 1 to 3 hours. Even win against so called ‘bad playing conditions, including bad players, 6 to 8 decks, crowded tables and clumps’.”

The “Without Counting!” claim did not turn out to be as anticipated. While the counting system used is not one recognized by the blackjack press, it is, nonetheless, a form of card counting.

Now, I have always believed that the ultimate test of a gambling hypothesis is experiment (simulation or actual casino play) to compare results to prediction. A mathematical advantage will then show up as a net win if sufficient play is involved. Unfortunately, enough data was not collected to be sure, but averaging a 10 unit win in 1 to 3 hours seems out of reach, at least by rational reasoning.

“It can be learned in 5 to 10 hours.”

Again, from the ad. This seems to be an overly optimistic estimate. The 2 hour video recommends that you watch it at least twice (4 hours plus rewind time).

The HSM takes longer than that, perhaps 4 hours per reading if you follow through the examples, and you should expect to do this at least twice (8 hours).

And then there is the recommendation that you have enough home practice to master the system before you go to actual casino play. My estimate for me is at least another 8 hours. My absolute minimum estimate is, then 20 hours. Probably much more for most players.

My estimate seems to be in line with this quote from the forward in the HSM, signed by Leonard Benson:

“…With a couple of weeks of diligent study and practice you’ll be able to be a consistent winner at blackjack, enabling you to make money the rest of your life.”

“Everyone is winning!”

From promotional material signed by Leonard Benson. This was brought into question by Leonard, himself, in our first telephone conversation when he said, “… We’ve had a couple people that the first time they started they got discouraged ‘cause they lost three times in a row.”

If the probability of winning any given session is .9 (“9 out of 10”, see the next claim), the chance of starting off with three losses is .001, one in a thousand. “A couple of people” experiencing this would suggest a population in the neighborhood of 2,000. In any event, the “Everybody is winning!” claim seems to be factually flawed.

“You’ll win 9 out of 10 sessions.”

From promotional material signed by Leonard Benson. It should be noted here that, given the amount you are prepared to lose and the amount you wish to win in a session of POWER NUMBERS BLACKJACK™, and if you were betting on tosses of a “fair” coin, then you would expect to win 2/3 of the time. This (2/3), then, would seem to be an optimistic number to use.

The argument might be made that many times you will “lock up” a small win and are prepared to risk your entire bankroll to do it. In a fair game, you would need to be prepared to lose nine times your “small” win to enjoy “9 out of 10” success.

“I have restructured the game of blackjack from the laws of probability to those of certainty. Structuring my betting on percentages, instead of luck or random chance betting, bringing it into the realm of reversing the edge of the House to the player.”

From “Comments from Dr. Jacobs.” This claim does not seem to be supported by the facts of POWER NUMBERS BLACKJACK™. While POWER NUMBERS BLACKJACK™ does find situations with better-than-average potential, it does not improve enough above the off-the-top expectation to overcome the disadvantage of shoe games. Making it worse, POWER NUMBERS BLACKJACK™ calls for disastrous departures from basic strategy, compensating (negatively) much more than this improvement gives.

“You will not lose your bankroll if you play POWER NUMBERS BLACKJACK.”

From “Typical questions and answers about Dr. Morton Jacobs and POWER NUMBERS BLACKJACK™.” This is not the sure thing suggested by this statement.

“Q: Will everyone who uses the POWER NUMBERS BLACKJACK system make money?

“A: Yes. You just have to follow the rules.”

From “Typical questions and answers about Dr. Morton Jacobs and POWER NUMBERS BLACKJACK™. This does not seem to be correct.

“Q: Will I have a mathematical edge over the casinos?

“A: Yes. POWER NUMBERS BLACKJACK players have an advantage ranging from 5% to an incredible 20% and more! It’s absolutely amazing. You’ll be winning 10 units for every 50 to 150 units in action.”

From “Typical questions and answers about Dr. Morton Jacobs and POWER NUMBERS BLACKJACK™.” Surely, this is the most “amazing” claim of all. No one can take seriously a claim of an advantage of 20% “and more!” (It is, after all, “incredible.”) 5% might be credible, except that expert card counters would not seriously claim near that level of success.

My rough analysis suggests a negative player’s edge of at least 2.0%.

Observations of Leonard Benson and Dr. Morton Jacobs

There is no doubt in my mind that Leonard Benson and Dr. Morton Jacobs believe POWER NUMBERS BLACKJACK™ is everything they claim. There was no defensiveness. There was no attempt to keep me from seeing everything that was going on at the table, and keeping score for myself (which I did, and my score agreed with Dr. Jacobs’ and the other players’ scores). This was not the behavior pattern of people who are running a scam…

Since the last four days of data showed a strong positive surge for POWER NUMBERS BLACKJACK™, it might be argued that only then was its true potential being revealed. But one must remember that, in cases like this, the data could have come in any order. (This is also true for the individual hands.) So “trends” must include all the data. The last four days could have as easily been the first four days. Would different conclusions then be appropriate? ♠

How Not to Launder Money and Get Caught Doing It

by L.J. Winsome
(From Blackjack Forum XVII #3, Fall 1997)
© Blackjack Forum 1997

In the case of federal forfeitures and money laundering, America may be becoming one of the many countries where — if one fits into one of the myriad “profiles” that indicate drug trafficking or affiliation with drug traffickers — one is guilty until proven innocent.

America is one of the few countries that taxes its citizens on gambling winnings. Apparently, the honor method of income reporting does not seem to be working. Laws have been put in place to ensure that the government knows who is making how much and where. Judging from the illegal seizures of money from innocent people as well as gamblers that have been depicted on television and in the press, they’re going overboard in what they deem “suspicious activity.”

Recently, I stopped over at the Reno airport on a one-way ticket from an international destination. The day before I had purchased a one-way ticket to San Francisco from Reno for the final leg of my journey. Because of this one-way ticket, I was required to go back to security and have my bags checked, even though I had already put them through the x-ray and walked through the metal detector. I had approximately $30K on me, but luckily I was wearing it.

The guard performed a “dump search.” Shampoo bottles were opened, books were rifled through, and every item was taken out of my bag. It was invasive to say the least, and a mere harbinger of what is to come. I’m convinced that if I hadn’t been wearing that money, they would have taken it. They could only have been looking for money or drugs, as I had passed the terrorist test when I went through the first time. Under the guise of the “War on Drugs,” the American government is turning anyone who can take a look into your private life into a sheriff.

Earlier this year, a player from a large team stuck his carry-on through the x-ray at the Philadelphia airport. The airline x-ray detected approximately 100,000 dollars in cash and casino chips. According to the team leader, the player was later apprehended at O’Hare International Airport in Chicago and taken into a back-room.

Two Drug Enforcement Agents confiscated the money. The player said that he tried to explain to them that he was a card counter — pointing out the chips — but they just laughed. The team will now have to spend thousands of dollars in attorney’s fees to prove that this player is innocent. Getting the money back will come later, and some of it could be withheld.

This team is large enough and flush enough to handle lawyers and endless bureaucracies in the form of casinos. An example of a team defending themselves against the powers that be is the well-documented Windsor case (Blackjack Forum December ’95), where Tommy Hyland took on the province of Ontario.

But it may not be worth it to an average low to middle-stakes player, who has less than $10K to $20K confiscated, to go up against a government agency that has all the time and money in the world. In the long run, it may cost more to get the money back than what was lost in the first place. So, besides always carrying your bankroll on your body, you might consider adopting a new hobby of petitioning your congressman or senator to get to work on returning some of your civil rights.

Title 211 U.S.C § 881(a)(6) authorizes the forfeiture of:

All moneys, negotiable instruments, securities, or other things of value furnished or intended to be furnished by any person in exchange for a controlled substance or listed chemical in violation of this subchapter, all proceeds traceable to such an exchange, and all moneys, negotiable instruments, and securities used or intended to be used to facilitate any violation of this subchapter, except that no property shall be forfeited under this paragraph, to the extent of the interest of an owner, by reason of any act or omission established by that owner to have been committed or omitted without the knowledge or consent of that owner.

An article in the San Diego Union says:

“So much illicit cash travels down Interstate 5 to Mexico that law enforcement officers have dubbed the state’s main north-south freeway ‘the cash corridor.’ Millions of dollars are confiscated on this route each year during routine traffic stops in places such as Kern and San Bernardino counties, places that are bisected by freeways from other parts of the country. . . .

Typical seizures net between $30,000 and $100,000. . . . Officers are not allowed to pull cars over unless a traffic violation has been committed. . . . It is not illegal to carry large amounts of cash, but currency can legally be seized if prosecutors prove that the money could not have a legitimate source. Federal law allows money from the sale of illegal drugs to be seized and split among the agencies involved in its capture.”

The Civil Asset Forfeiture Reform Act (HR 1965), introduced by Congressman Henry Hyde, Chairman of the House Judiciary Committee, is pending in the House of Representatives. It’s stated goal is, “To provide a more just and uniform procedure for Federal civil forfeitures and for other purposes.” Those ‘other purposes’ are what the non-profit group Forfeiture Endangers Americans Rights (FEAR) are concerned about.

FEAR, formed in New Jersey in 1992 by a group of concerned citizens, seeks an end to the practices of letting the seizing agencies benefit from the proceeds of property seized, and of letting federal agencies adopt state seizures. According to a spokesperson from FEAR, “Things are getting worse on the forfeiture front. The Hyde/ Conyers bill that we supported — HR 1835 — was gutted by the House Judiciary Committee, with help from the Justice Department, and was renamed HR 1965. Not only does it make the procedures worse than under present law, but it adds a lot of new forfeitable “offenses,” and creates procedures allowing foreign governments to forfeit U.S. property! These provisions are alarming.”

At a late afternoon session, entitled “Money Laundering,” at the 10th International Conference on Gambling and Risk-Taking that took place in early June in Montreal, a representative from the Treasury Department explained how the U.S. government had turned the funny little Saturday morning cartoon characters called smurfs into the crime that the Treasury Department is attacking with the zealotry of the X-Men.

“Smurfing” or “structuring” is what the treasury department is afraid of from gamblers, said Ed Djinis from the US Department of the Treasury, Financial Crimes Enforcement Network, or at least people masquerading as gamblers. According to Chicago attorney Bob Loeb presently working on an illegal forfeiture case, often when suspected drug traffickers are caught with large unexplained sums of money, they claim that it’s gambling winnings, so Treasury Department or DEA officials become inured to this as a viable explanation for the money.

It’s almost an urban legend by now, but every gambler knows that 90% of all $100 bills have traces of cocaine on them. Unfortunately, casino chips don’t leave a tell-tale residue.

Djinis spoke at this conference looking every inch the government bureaucrat: his suit was gray, his tie was blue, and he repeated every concept he made, no matter how uninteresting. His one salient point, however, was a definition of what constitutes “smurfing.”

“If someone engages in currency transactions just below the currency threshold for reporting, it is called structuring or smurfing,” said Djinis. “In one instance it may not warrant much attention, but if the customer does this in a repeated fashion, either in conducting numerous transactions at the cage, or various buy-ins at numerous tables, that would constitute structuring.”

Djinis pointed out that casinos provide many of the services that banks and brokerage houses do, and were necessary in providing stopping points along the audit trail. Therefore they were uniquely positioned to watch for and report on currency transactions that looked suspicious.

Casinos have complied with the Bank Secrecy Act since 1986. It basically requires each casino to secure information on the patron such as the name and social security number. It’s then the casinos obligation to report that information to the government when the patron performs a transaction of over $10K.

An MGM Grand Casino representative, John Donnelly from the firm Levine, Staller, Sklar, Chan, Brodsky & Donnelly, disagreed with the feds’ explanation of the law the moment he took the podium. “Money laundering is not what is at issue. What is at issue is revenue enhancement for the Internal Revenue and Treasury.” He added that the Treasury Department didn’t believe the feds’ position either.

Donnelly explained that casinos are not the appropriate vehicles for money laundering because of the constant surveillance and the knowledge of what is going on at the tables. He pointed out that there has only been one criminal prosecution that has used currency transaction reporting out of a casino, despite that millions of reports that end up being filed in the Treasury Departments depository in Detroit, Michigan.

Djinis concurred, “Looking for suspicious activity and reporting it to the government puts the casino in the position of becoming a government agency, but the train has left the station and the government cannot do this in a vacuum.” Moderator of the panel, Frederic Gushin, Spectrum Gaming Group, New Jersey, disagreed that casinos are not good places to wash cash.

“We saw in Atlantic City, prior to 1986, many instances where criminals were attempting to launder money,” said Gushin.

Gushin related an incident of an LA bank-robber who brought a million dollars into a casino, documented in the book, Running Scared: The Life and Treacherous Times of Las Vegas Casino King Steve Wynn. When the robber brought the money to the cage all other activity stopped, except counting out the money. According to Djinis the more a customer uses a casino as a surrogate financial institution and less a source of entertainment, the more regulations will be imposed on it.

It’s clear that the casinos are loathe to make themselves a beacon on the audit trail, but that’s countered by the fees and commissions that a casino can charge for banking services, as well as the undisguised grin on your casino host’s face when you put more than 10K on deposit. Casinos want to perform these services, and they have to report them when they do. It seems that the train is careening down the track. The casinos have been deputized.

It also appears that regulations are going to become stricter. Here are two summaries of regulations that are pending addendums to the Bank Secrecy Act. They are excerpted from the Federal Register Vol. 62, Num. 98, May 21, 1997:

The Financial Crimes Enforcement Network (“FinCEN”) is proposing to amend the Bank Secrecy Act regulations to require money transmitter and issuers, sellers and redeemers, of money orders and traveler’s checks to report suspicious transactions involving at least $500 in funds or other assets. The proposal is a further step-up in the creation of a comprehensive system (to which banks are already subject) for the reporting of suspicious transactions by financial institutions. Such a system is a core component of the counter money laundering strategy of the Department of Treasury.

The Financial Crimes Enforcement Network (“FinCEN”) is proposing to amend the regulations implementing the Bank Secrecy Act to require money transmitters and their agents to report and retain records of transactions in currency or monetary instruments of at least $750 but not more than $10,000 in connection with the transmission or other transfer of funds to any person outside the United States, and to verify the identity of senders of such transmissions or transfers. The proposed rule is intended to address the misuse of money transmitters by money launderers and is in addition to existing rule requiring currency transaction reports for amounts exceeding $10,000.

The key that brings the earlier described airport horror stories and the seemingly unrelated late afternoon conference on money laundering together is the term “revenue enhancement.” The government wants to take your money, preferably in the form of taxes. Taxes require that your income be tracked. If that doesn’t work, the law allows agents to seize and keep money when it’s derived from drug dealing. CTR’s and the deputation of these various gatekeepers are attempts to track those who function outside the system.

The situation thus may be that you may want to allow CTR’s to be filed on you, just in case the money is confiscated. Of course, this will require that the gambler having the CTR filed on him pay taxes, and that is something some gamblers avoid like the plague. Many pros pay their taxes honestly, but part of why the lifestyle is so attractive to some is that one is free of the middle-class trap. The thinking is, if one has to pay taxes on one’s winnings, one may as well get a real job.

At the Montreal Gambling Conference, Max Rubin, author of Comp City, took the microphone during the question and answer period of the “Money Laundering” seminar to ask some specific questions about what constitutes smurfing.

“Does there have to be intent to evade taxes, or intent to evade the Treasury Department?” asked Rubin.

Rubin explained that card counters often stay under the casino radar by not showing ID and using different names. Obviously, when one fills out a CTR, one is required to show ID, so big money card counters might avoid doing it when using an alias.

“I know guys who pay hundreds of thousands in taxes,” he said, “but they don’t want the casinos to know who they are. Is that a crime?”

Djinis answered: “No, it’s probably not. If the intention is to evade detection by the casino, but not evade our reporting requirements, I don’t see a crime by the customer.”

It could be a catch 22, however, because if forced, a card counter would have to prove he was a card counter, and the only way to do that may be to have CTR’s filed in a casino.

If you would like more information on the Bank Secrecy Act or federal forfeiture regulations, you can find it on the internet at:
http://www.netrunner.net/~alert/document.html. This site was an invaluable source in the writing of this article, and it is constantly being updated as regulations are gutted or amended. ♠