Archive for 100000 baccarat shoes

Baccarat Advantage: A Bogus Black Box

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on May 4, 2011 by virtuoid

A friend sent me a computer application Baccarat Advantage (baccaratadvantage.com), a black box which outputs bet placement instructions based on inputted Banker and Player hand total values.

The creator of Baccarat Advantage calls himself “Dr. Jacob Steinberg,” and claims to have achieved a positive expectation after running 1 million live shoes through his program.  Because a user of the program only accesses the program’s interface, where he enters the total hand values and receives the outputted betting instructions, the actual method of determining the bet placement is never revealed, and he can only use the application to play at online casinos, never at physical, brick-and-mortar casinos.   In addition to the purchase price, Dr. Steinberg also requires his customers to share a percentage of their winnings from using the program, and the exact purchase price depends on what percentage the customer agrees to pay.  In this way, he justifies selling the program, since he can in principle exponentially increase his income through his customers’ winnings while never actually revealing to them the exact method of his supposed holy grail.

Despite what Dr. Steinberg claims, my tests of his Baccarat Advantage objectively demonstrate that it quickly yields negative expectancies, and if he really did win a million live shoes with the method in his program, those shoes must have been unbelievably favorably biased to it.  On the surface, his procedure appears to utilize information from hand totals and not just the (mathematically doomed to fail) pattern of P/B wins.  Thus, there is a faint glimmer of card-counting potential, though the program does not fully account for the values of each card.  However, whatever his method is, my tests show that it consistently yields negative expectancies and can no better win at baccarat than any other method tested to date.

A picture of the Baccarat Advantage user interface:

Upon activating the program, a brief splash window encourages the player with an affirmative tagline, Because winning feels so good.  Play commences as follows:  At the beginning of each shoe, the user enters the first four hand totals of the first two decisions in the “Second-to-Last Hand” and “Last Hand” rows.  The program then outputs a bet placement instruction in the “Now Bet” row.  The user then presses the “Won,” “Tie,” or “Lost” button according to the result of the bet, upon which the values in the “Last Hand” row moves up to the “Second-to-Last Hand” row, clearing  the “Last Hand” row and making it available for fresh input.  He then enters the next set of hand totals in the now emptied “Last Hand” row and repeats the process.  After the end of each shoe, the “Reset” button is pressed, all the input boxes clear, and the process begins again for the next shoe.

There are two money management options: 1) Flat Betting and 2) Progression Betting.  Based on $1 units, flat betting requires a $50 bankroll, while progression betting requires a $164 bankroll.  The progression (as seen in the picture above) is a simple 7-level Martingale, padded at certain levels to cover Banker commissions.  Flat betting is described as a “slow winner,” but requiring “lower bankroll,” while progressive betting is touted as an “infallible, quick winner,” but requiring “higher bankroll.”  Either way, Dr. Steinberg claims his method consistently beats the house edge and is the only true (and easy) way to win baccarat.

For the most part, the program consistently outputs the same bet placement instructions per set of inputs.  I write, “for the most part,” because there were some minor glitches which would sometimes result in the same set of inputs resulting in different bet placement instructions.  The apparent glitches may occur when one changes an inputted value, and then back to the original value again, whereupon the opposite bet placement instruction would sometimes appear.  This is clearly an operational bug on the part of the programmer, assuming there is supposed to be a one-to-one correspondence between unique input values and output bet placement instructions.  Otherwise, the program appeared to be consistent enough for the most part to be tested against data sets of baccarat shoes.

To examine the long term performance of Dr. Steinberg’s baccarat black box, I created a script to automate the inputting and reading of the outputted bet placement instructions for 12,100 baccarat shoes.  Roughly 3-4 shoes per minute could thus be accurately inputted and analyzed, and the entire testing took place over several days and nights.  My automation script performs exactly what a human would do, entering the total hand values decision by decision, reading the outputted bet placement instructions, pressing the “Won,” Tie,” or “Lost” button according to the result of the bet, and pressing “Reset” after the end of the shoe before starting the next one.  For the testing, I used the Flat Bet mode, since no progression will be able to consistently help a method which cannot win flat betting.  For verification, I sent the data output to my friend, who double-checked and confirmed he was getting the same outputted bet placements from the program.

A sample of the data output follows:

1st column: shoe number
2nd column: decision number
3rd column: Banker hand total
4th column: Player hand total
5th column: decision P/B/T winner
6th column: Baccarat Advantage outputted bet placement

1  1 5 2 B -
1  2 1 3 P -
1  3 9 5 B P
1  4 3 8 P P
1  5 6 2 B B
1  6 5 5 T B
1  7 0 9 P -
1  8 8 7 B B
1  9 9 5 B B
1 10 0 6 P P
1 11 5 9 P B
1 12 6 6 T P
1 13 9 2 B -
1 14 6 7 P P
1 15 9 3 B P
1 16 0 5 P P
1 17 0 0 T P
1 18 2 1 B -
1 19 0 9 P P
1 20 5 8 P B
1 21 6 8 P P
1 22 7 9 P P
1 23 0 9 P P
1 24 8 1 B B
1 25 9 5 B B
1 26 8 6 B B
1 27 6 9 P B
1 28 1 9 P B
1 29 6 5 B B
1 30 3 8 P B
1 31 0 5 P B
1 32 3 9 P B
1 33 0 9 P B
1 34 8 4 B B
1 35 3 7 P B
1 36 8 6 B P
1 37 9 7 B B
1 38 3 8 P B
1 39 5 9 P B
1 40 4 6 P P
1 41 8 8 T P
1 42 3 9 P B
1 43 9 2 B B
1 44 7 5 B P
1 45 9 6 B B
1 46 0 2 P P
1 47 1 7 P P
1 48 9 0 B B
1 49 9 6 B P
1 50 8 0 B B
1 51 2 2 T P
1 52 4 7 P B
1 53 8 8 T B
1 54 9 5 B B
1 55 5 6 P P
1 56 9 6 B P
1 57 5 8 P P
1 58 4 4 T B
1 59 7 6 B B
1 60 6 5 B P
1 61 0 9 P P
1 62 1 7 P B
1 63 0 8 P P
1 64 1 6 P B
1 65 0 9 P P
1 66 8 6 B B
1 67 6 6 T B
1 68 4 6 P P
1 69 4 3 B B
1 70 0 9 P B
1 71 5 1 B B
1 72 3 4 P B
1 73 4 2 B P
1 74 4 8 P P
1 75 8 7 B B
1 76 7 8 P B
1 77 2 2 T P
1 78 9 4 B P
1 79 8 6 B P
1 80 6 6 T B
1 81 6 4 B P
1 82 3 7 P P

Notice that sometimes the program does not bet after a Tie, and sometimes it does.

The numerical and graphical results of the testing are presented in Simulation Series 31 Results.  Three sets of data were examined, each one consisting of slightly different Banker (B) and Player (P) compositions.  As the following plots show, the qualitative behavior of the Baccarat Advantage Player’s Advantages (P.A.’s, the net units won after commissions divided by the total amount bet) depend on the B/P compositions of the data set, though all are consistently negative.

Data Set 1 had a slightly lower-than-average numbers of Bankers, 50.61% Bs and 49.39% Ps (not counting Ties).  In this set, the P.A.’s of the Baccarat Advantage bet placements are always consistently worse than the expectancies for B, while the P.A.’s of the opposite of the Baccarat Advantage bet placements are always consistently better than those of P.  (Because of the lower-than-average numbers of Bs in Set 1, the expectancies for B is always more negative than that of P.)  The following plot which graphs the evolution of the P.A.’s over the numbers of shoes tested shows that in Set 1, Baccarat Advantage P.A.’s (blue for the program’s output, and red for the opposite of the program’s output) mostly lie to the outside of the Banker and Player P.A.s (yellow for B, and green for P).

Data Set 2 has slightly more Bs overall than Data Set 1, 50.69% Bs and 49.31% Ps (not counting Ties), which is closer to what are the “average” proportions.  As the following plot shows, the blue and red Baccarat Advantage P.A. lines begin to fall in-between the yellow and green Banker and Player P.A. lines.

Data Set 3 has 50.83% Bs and 49.17% Ps (not counting Ties), which is more Bs than “average,” and for the most part, the Baccarat Advantage P.A.’s are always comparable to or no better than the standard B/P expectancies.  Thus, in the plot below, the blue and red lines are mostly contained within the yellow and green lines.  In various, brief stretches, the Baccarat Advantage P.A’s became slightly more positive that that of B, and the opposite bet placement’s P.A.’s correspondingly became slightly worse than P, which is the opposite of what occurred in Data Set 1.

Notice that the line of symmetry between the opposing pairs in the above P.A. graphs is about half way between -1.0 and -1.5. This line of symmetry is due to the built-in tilt of the game in the house’s favor, and the fact that it is negative is the reason why “just bet opposite” a losing method does not win either. In a perfectly fair 50/50 game, the line of symmetry would be at exactly P.A.=0, meaning in such a zero-expectancy game in the long run, you always have equal chances of being net positive or negative, and on average, break-even. However, in baccarat, the house’s edge skews everything in the house’s favor, and you expect to always be net negative in the long run, no matter how you play. In other words, if you can’t consistently win a perfectly fair 50/50, zero-expectancy game in the long run, you have even less mathematical hope of winning a negative expectancy game in the long run.

Despite the above qualitative differences due to B and P compositions in the shoe, the resulting P.A.s are always negative, and the Baccarat Advantage method itself loses all data sets quite unceremoniously, as the following plots of the net score versus shoe clearly show:


I did not test Baccarat Advantage’s progression mode systematically, but I compared a few shoes to demonstrate that the bet placement output from the program in progression mode is exactly the same as in flat bet mode; only the bet amount differs according to a win or loss, and the progression is the straightforward 7-level Martingale.

Just for fun, I let my automation script run through a small data set in the progression betting mode.  In these runs, the required bet amounts would bust past the 7 levels of the progression every few dozen shoes, and a rather sad pop-up box would announce, “Sorry, you have lost.  Start over.”  Tracking the exact results of the 7-level progression over my testing results would have been a routine exercise, but completely not worth the time or effort.

In conclusion, my tests show that Dr. Steinberg’s Baccarat Advantage yields standard negative expectations and is quantitatively no different than any other baccarat method I have tested, except that in certain situations when the B/P compositions are above or below average, the P.A.’s of the Baccarat Advantage bet placements or its opposite are slightly more positive than expected when always betting B or P.  Unfortunately, the slight improvements in odds in these situations are not enough to be profitably exploited.

Baccarat Advantage is a black box that is at best broken and at worst bogus.

Disclaimer: The betting strategies and results presented are for educational and entertainment purposes only. Gambling involves substantial risks, and the odds are not in the player’s favor by design. The author does not state nor imply any system, method, or approach offers users any advantage, and he shall not be held liable under any circumstances for any losses whatsoever.

Baccarat Simulation Series 31 Results: Baccarat Advantage

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on May 4, 2011 by virtuoid

Results from Baccarat Simulations Series 31 are presented below.

In this series, I entered sets of 12,100; 4,100;  and 2,100 shoes (each set varying in B/P compositions) into the black-box Baccarat Advantage application and analyzed the results.

Read a full discussion of these results at the following post:
Baccarat Advantage: A Bogus Black Box.

Set 1: 12,100 Shoes (B: 50.61%, P: 49.39%)
PBT Stats:

Count % (w/T) % (only PB) Expectancy
B 451,428 45.80% 50.61% -0.013162
P 440,597 44.70% 49.39% -0.012142
T 93,623 9.50%

Simulation Results:

Method Net Score Total Bet P.A.
BaccAdv -11,870.20 858,946 -1.38%
BaccAdv R -9,862.25 858,946 -1.15%
B only -11,740.40 892,025 -1.32%
P only -10,831.00 892,025 -1.21%

Set 2: 4,100 Shoes (B: 50.69%, P: 49.31%)
PBT Stats:

Count % (w/T) % (only PB) Expectancy
B 153,433 45.90% 50.69% -0.011454
P 149,228 44.64% 49.31% -0.013893
T 31,599 9.45%

Simulation Results:

Method Net Score Total Bet P.A.
BaccAdv -3,360.05 291,442 -1.15%
BaccAdv R -3,725.80 291,442 -1.28%
B only -3,466.65 302,661 -1.15%
P only -4,205.00 302,661 -1.39%

Set 3: 2,100 Shoes (B: 50.83%, P: 49.17%)
PBT Stats:

Count % (w/T) % (only PB) Expectancy
B 78,750 46.01% 50.83% -0.008731
P 76,165 44.50% 49.17% -0.016687
T 16,242 9.49%

Simulation Results:

Method Net Score Total Bet P.A.
BaccAdv -1,578.05 149,191 -1.06%
BaccAdv R -2,212.85 149,191 -1.48%
B only -1,352.50 154,915 -0.87%
P only -2,585.00 154,915 -1.67%

Data Set: 12,100 baccarat shoes used (ref. My Baccarat Shoe Factory).

Player’s Advantage is the net units won after commissions divided by the total units bet.

BaccAdv = Baccarat Advantage bet placement (output from black-box)

BaccAdv R = Baccarat Advantage reversed bet placement (opposite of output from black-box)

B only = always betting B every decision
P only = always betting P every decision

% (w/T) = percentage of decision counting ties
% (only PB) = percentage of decision not counting ties

Always flat-betting 1 unit per betting opportunity.  (No bets on ties, and bets occurring on ties are pushed and not tallied into the total number of bets.)

__________________________________________________________

Graphs of P.A. and Net Units Won (after commissions) per Shoe:

Set 1: 12,100 Shoes (B: 50.61%, P: 49.39%):


Set 2: 4,100 Shoes (B: 50.69%, P: 49.31%):


Set 3: 2,100 Shoes (B: 50.83%, P: 49.17%):

Disclaimer: The betting strategies and results presented are for educational and entertainment purposes only. Gambling involves substantial risks, and the odds are not in the player’s favor by design. The author does not state nor imply any system, method, or approach offers users any advantage, and he shall not be held liable under any circumstances for any losses whatsoever.

Does A Harvard Education Help You Win Baccarat?

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on March 7, 2011 by virtuoid

My friend pointed out to me a couple of threads at BaccaratForums by a member stevefoxwong who claimed to have tested two methods which won both Zumma sets of shoes.  Based on his results, stevefoxwong proclaimed them as “holy grails.”  One of the methods is by “Harvard educated” Zuan Xin and his successor and classmate, David Sofer.   Xin’s method is posted at macaucasinoworld.com, which is heavily sponsored by Macau casinos.   Hidden within his collection of humorous and rather mystical anecdotes, Xin supposedly reveals the esoteric secrets of his Grand Baccarat Learning pattern of patterns method, which he claims can mathematically beat the game.  In David Sofer’s words, “intricate theoretical probability, tens of thousands of live casino shoes, and millions of computer simulated shoes were triangulated” to establish the validity and efficacy of Xin’s method.

According to Sofer,

Zuan Xin revealed the underlying mathematical structure of the game of Baccarat, its pattern of patterns, he did not invent a quote unquote system. People who study online or attend special learnings gain a complete understanding of his teachings and then they decide how and with how much they will use these teachings.

The pattern of patterns as revealed by Zuan Xin indicates that there is no such thing as a quote unquote flat betting system.

Zuan Xin being a Harvard trained applied mathematician and number theorist, those of us who follow him do not question his mathematical conclusions, and because he has provided his teachings online at no cost, he should not be mistrusted. He is retired now, I continue to write content based on his files that he gave to me, I only charge tuition when I conduct a special learning, as that requires substantial time and energy.

Billions of dollars of Baccarat losses worldwide indicate that all of these so called systems are worthless. Be a player not a gambler!

Sofer charges a mere $888 to directly transmit Xin’s special learnings to those who are not diligent enough to figure out Xin’s method for themselves at his site.   My friend was one of the diligent ones, and he set upon the task of trying to reproduce stevefoxwong‘s Zumma results.  However, he could not.   Moreover, he realized that the validity of Xin’s core assumptions stood upon a single test.   If it failed a long term simulation, then Xin’s method could not possibly win in the long term.

According to my friend, Xin’s method is based on reversion to the mean. Taking the 1s event (a single decision with no repeats on each side) as an example, Xin knows that in the long term, 1s should occur half of the time, and 1+s (events longer than 1s) should occur the other half of the time.  Hence, within a shoe, whenever the percentage of 1s to the total number of events is less than 50%, that is, less than expected, Xin believes it is worth the risk to start betting that 1s will eventually “catch up.”  For example if in a shoe, one 1s occurred, while three 1+s occurred, the 1s ratio is 25% (1/4), and so 1s are occurring less than expected, hence start betting for 1s to occur later in the shoe, and keep betting for 1s until the ratio reverts to the mean.

According to my friend, the remainder of Xin’s method simply involves similar considerations of the expected ratios of the higher-numbered events (2s, 3s, 4s, etc.), and so if the 1s test failed, the entire edifice of Xin’s house of cards collapses.

Of course, assumptions like reversion to the mean is based on gambler’s fallacy (ref. Fallacies and Illusions), and from mathematical grounds, has absolutely no hope of winning a long term simulation.   But to help objectively establish quantitative results, I performed a simulation of my friend’s crucial test of Xin’s core assumption.

In the test, I waited a certain number of hands at the start of each shoe (Wait = 5, 10, 15, 20) to begin collecting the number of 1s and 1+s events, which I used to calculate the ratio of 1s to the total number of events (1s plus 1+s).   After the mandatory wait, whenever the ratio is below a set threshold percentage value (5%, 10%, 15%, 20%, 25%, 50%), I begin betting for 1s to occur.   For money management, I use a 1,1,3,6 progression, and I stop betting if the net score in any shoe falls lower than -10u.   I treat each shoe as a closed system and start the count of events afresh upon each new shoe.

The quantitative results over 102,600 shoes are tabulated in Series 30 Results.  In a phrase, the long term expectation is always worse than the standard house vig.

A graph summarizes the trend of the results:

If Xin and Sofer indeed have positive results of Xin’s full method from “millions of computer simulated shoes,” they are not posted at his site or anywhere else that I could find. To the best of my knowledge, the results I have posted here are the only published ones of an objective test of a core assumption in Xin’s method.  I invite any of Xin’s and Sofer’s students (which number in the thousands according to Sofer) to offer feedback here about their experiences playing baccarat with Xin’s method.

I did try calling Harvard’s alumni department to try to verify whether Xin and Sofer actually attended Harvard, but as of this writing, Harvard has not yet responded to my request for information.  I will update this post if and when they do.

Until then, assuming Xin and Sofer are actually Harvard alumni, then the answer to the question, “Does a Harvard education help you win baccarat?” is apparently, “Nope.”

Disclaimer: The betting strategies and results presented are for educational and entertainment purposes only. Gambling involves substantial risks, and the odds are not in the player’s favor by design. The author does not state nor imply any system, method, or approach offers users any advantage, and he shall not be held liable under any circumstances for any losses whatsoever.

Baccarat Simulation Series 30 Results: Zuan Xin Baccarat Great Learning

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on March 7, 2011 by virtuoid

Results from Baccarat Simulations Series 30 are presented below.

In this series, I examined a core test of Zuan Xin’s Baccarat Great Learning method.  For a discussion of the results, please refer to the post Does A Harvard Education Help You Win Baccarat?

Wait 1s Ratio Threshold Player’s Advantage Net Score Total Bets
5 25% -1.29% -4,903.05 379,680
5 50% -1.23% -33,112.25 2,686,710
10 25% -1.21% -3,236.80 267,420
10 50% -1.17% -29,341.10 2,513,278
15 25% -1.41% -2,604.30 184,455
15 50% -1.14% -26,707.35 2,345,074


20 5% -2.94% -199.15 6,784
20 10% -2.71% -337.05 12,459
20 15% -2.81% -875.70 31,115
20 20% -3.03% -1,963.55 64,700
20 25% -1.16% -1,539.50 132,575
20 50% -1.12% -24,469.20 2,176,109

Using 1M Shoes, normal and reversed bet placements:Data Set: 102,600 baccarat shoes used, including Zumma 600, Zumma 1000, Wizard of Odds 1000, and Virtuoid 100,000
(ref. My Baccarat Shoe Factory).

Wait 1s Ratio Threshold Player’s Advantage Net Score Total Bets
1M Normal
20 5% -1.49% -941.95 63,140
20 10% -1.77% -2,090.55 117,891
20 15% -1.11% -3,341.15 300,314
20 20% -1.44% -9,207.25 639,218
20 25% -1.06% -13,926.80 1,319,115
20 50% -1.21% -259,467.00 21,463,289
1M Reversed
20 5% -1.05% -441.20 42,021
20 10% -0.98% -870.80 89,265
20 15% -1.50% -3,661.10 244,296
20 20% -1.10% -6,601.05 597,494
20 25% -1.15% -15,766.20 1,370,468
20 50% -1.23% -299,024.00 24,284,122

Player’s Advantage is the net units won after commissions divided by the total units bet.Data Set: 1,002,600 baccarat shoes used, including Zumma 600, Zumma 1000, Wizard of Odds 1000, and Virtuoid 1,000,000
(ref. My Baccarat Shoe Factory).

Wait:  mandatory number of decisions to wait at the start of each shoe to collect statistics

1s Ratio Threshold:  the percentage of 1s to total number of events below which to begin betting for 1s.

Money Management:  1,1,3,6 progression, -10u stop loss, begin wait at start of each shoe.

__________________________________________________________

Graphs of Net Units Won (after commissions) per Shoe:

Zuan Xin’s Baccarat Great Learning (Wait 20, 1s Threshold 5%, 10%, 25%, 50%):

Disclaimer: The betting strategies and results presented are for educational and entertainment purposes only. Gambling involves substantial risks, and the odds are not in the player’s favor by design. The author does not state nor imply any system, method, or approach offers users any advantage, and he shall not be held liable under any circumstances for any losses whatsoever.

24 Karat Fool’s Gold Beats Both Zummas

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 29, 2010 by virtuoid

In his advertisements, Lorenzo Rodriquez describes how he kept losing at baccarat using a method which cost him $5,000, how when he later tested it, it failed to win even the Zumma shoes.  This motivated him over the next 6 months to program every baccarat method he could find, but all failed to win even the Zumma shoes.  Finally, he had an epiphany, and the result was his 24 Karat Baccarat method, which he proclaims in his manual to be just short of a miracle.  His method wins both Zumma 600 and 1000, and he reportedly used it to win real money playing it at casinos.  Now, he sells his holy grail for less than fifty dollars (ref. 24karatbaccarat.com)

At least Rodriguez told the truth:  his 24 Karat Baccarat method does indeed win both Zumma 600 and Zumma 1000 shoes.

However, testing his method over 102,600 shoes shows that in the long run, Rodreiguez’s method offers no actual positive edge, yielding Player’s Advantages no better than single-side betting (ref. Series 14 Results, Series 1 Discussion).

Interestingly, the above score-vs-shoe graph shows localized stretches of positive performance which can occur over many thousands of shoes.  A most remarkable run of 12,000+ shoes from roughly shoe #19,000 to #31,000 showed a generally positive trend.  However, the overall trend is quite clearly negative.

Rodriguez’s method assumes an existing shoe bias will tend to normalize (thus committing the gambler’s fallacy).  It bets only in 3 groups of 5 decisions in the last half of the shoe.  It uses a 5-level Martingale based on 5, 10, 20, 40, and 80 units.  In my simulation, I reduced this Martingale progression to the equivalent of 1, 2, 4, 8, and 16 units.  I also used U1D2M2 and flat betting.  The results show that when flat betting is generally break-even or positive, negative progressions enhance performance, but when flat betting is negative, then negative progressions only lose money faster.  This has been a common theme in all of my simulation results.

As is true for Scott’s (eirescott) Birthday Grail method (ref. Can Betting on Birthday’s Make You Rich?), Rodriquez’s method bets relatively infrequently.  Hence, the ups and downs in the score simply become stretched out over a longer period of time, making the fluctuations more prominent on an inter-shoe chart basis, fluctuations which would be just as apparent on an intra-shoe chart basis for methods betting every decision.

This is another good example why a sufficiently large sample size is crucial to accurately access a method’s long-term performance.  Because any kind of shoe may arise during live play, a sufficiently large testing sample is needed to cover as many variations as possible.

This is also a good example why beating Zumma shoes isn’t nearly enough to establish whether a method truly has a positive edge.  The number of possible baccarat shoes is in the quintillion, and even 100,000 shoes is barely scratching the surface.

Being able to beat Zumma is a good start, but it is definitely not sufficient to declare one’s method, in Rodriguez’s own words, “just short of a miracle” (his emphasis).  It is very short of such.

Disparity Data

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , on October 23, 2010 by virtuoid

Ellis C. Davis, Jerry Patterson, and Mark Teruya, among other successful baccarat players and systems designers, all weigh disparity in their bet placement decisions.

Disparity is simply how much one side differs from another.  For example, if 20 Ps and 15 Bs have occurred in a shoe, the disparity is 5 decisions in favor of P.

Betting with the disparity is to bet with the trend, based on the assumption that the present disparity will persist, an example of the inverse gambler’s fallacy.  Betting against the disparity is to bet against the trend, based on the assumption that that a reversion to the mean is due, which is an example of the gambler’s fallacy (ref. Fallacies and Illusions).

To establish a statistical baseline for future reference, below are some basic disparity statistics from 102,600 baccarat shoes, including Zumma 600 and Zumma 1000 (ref. My Baccarat Shoe Factory).

1. The shoe frequency of the final count of Player, Banker, R, and A in every shoe.

For example from the table below, 8,888 shoes had a final count of 37 Players, while 8,726 shoes had a final count of 39 Bankers.

Final Count Player Banker R A
15 0 0 0 0
16 0 0 0 0
17 1 0 0 0
18 1 0 1 0
19 1 1 3 0
20 11 2 6 8
21 15 10 10 11
22 27 17 25 22
23 60 21 45 48
24 118 67 96 87
25 229 133 189 196
26 401 223 332 322
27 749 429 550 592
28 1,073 677 884 935
29 1,704 1,167 1,435 1,435
30 2,472 1,690 2,193 2,128
31 3,451 2,583 3,143 2,952
32 4,536 3,448 4,021 4,058
33 5,793 4,716 5,135 5,195
34 6,943 5,664 6,184 6,342
35 7,758 6,850 7,446 7,254
36 8,606 7,856 8,015 8,158
37 8,888 8,334 8,503 8,526
38 8,755 8,557 8,748 8,742
39 8,314 8,726 8,617 8,576
40 7,528 8,303 7,860 7,766
41 6,353 7,311 6,915 6,912
42 5,320 6,615 5,850 5,799
43 4,172 5,355 4,708 4,775
44 3,123 4,166 3,709 3,690
45 2,284 3,163 2,663 2,725
46 1,520 2,366 1,912 1,908
47 939 1,579 1,358 1,304
48 663 1,041 844 874
49 362 633 513 533
50 210 397 350 360
51 109 251 166 169
52 62 124 83 97
53 21 65 49 49
54 15 33 17 32
55 8 15 8 11
56 2 6 8 6
57 1 2 2 2
58 1 3 2 0
59 1 1 2 1
60 0 0 0 0
61 0 0 0 0
62 0 0 0 0
63 0 0 0 0
64 0 0 0 0
65 0 0 0 0
Total: 102,600 102,600 102,600 102,600

Next are graph of the information in the above table, which plots the shoe frequency of the final counts of Player, Banker, R, and A in 102,600 shoes.

Shoe frequency of the final counts of Player and Banker in 102,600 shoes:

Shoe frequency of the final counts of R and A in 102,600 shoes:

The distributions appear to be Gaussian, with one standard deviation corresponding to about 4 to 5 final count units.

Interestingly, the peak in the Banker’s distribution peaks at 39, which is 2 units to the right of the Player’s, which peaks at 37.  This reflects how the baccarat drawing rules slightly favor Banker over Player decisions.  No such bias appears between R and A.

2.  The shoe frequency of the final count disparity between Player and Banker, and R and A, in every shoe.

In the following table, the final count disparity for PB is defined as the Player’s final count minus the Banker’s, and that for RA is R’s minus A’s.  For example, 4,753 shoes had a PB disparity of -1, which means in those shoes, there was 1 more Banker at the end of the shoe than Player; while 4,384 shoes had a PB disparity of +1, where 1 more Player than Banker occurred.

Final Count Disparity PB RA
-45 0 0
-44 0 0
-43 0 0
-42 0 0
-41 1 1
-40 0 0
-39 0 0
-38 1 0
-37 1 0
-36 2 0
-35 2 3
-34 9 6
-33 4 3
-32 8 4
-31 7 12
-30 20 15
-29 15 15
-28 43 27
-27 41 42
-26 84 61
-25 115 84
-24 165 112
-23 180 164
-22 233 221
-21 338 271
-20 448 340
-19 567 443
-18 664 583
-17 874 760
-16 1,098 922
-15 1,314 1,076
-14 1,553 1,304
-13 1,862 1,583
-12 2,160 1,841
-11 2,408 2,170
-10 2,792 2,443
-9 3,119 2,707
-8 3,386 3,111
-7 3,727 3,353
-6 3,971 3,703
-5 4,191 3,933
-4 4,420 4,177
-3 4,661 4,370
-2 4,648 4,442
-1 4,753 4,597
0 4,632 4,677
1 4,384 4,626
2 4,332 4,619
3 4,267 4,281
4 3,991 4,189
5 3,717 3,985
6 3,472 3,770
7 3,038 3,375
8 2,820 3,058
9 2,416 2,748
10 2,066 2,405
11 1,809 2,120
12 1,618 1,841
13 1,308 1,550
14 1,087 1,322
15 873 1,158
16 696 835
17 552 732
18 410 598
19 326 482
20 257 333
21 173 257
22 155 202
23 81 152
24 71 124
25 54 88
26 43 49
27 12 41
28 21 23
29 12 19
30 9 17
31 4 4
32 2 10
33 2 2
34 1 3
35 2 2
36 1 3
37 0 0
38 1 0
39 0 1
40 0 0
41 0 0
42 0 0
43 0 0
44 0 0
45 0 0
Total: 102,600 102,600

Next are graphs of the information in the above table, which plots the shoe frequency of the final count disparities of Player, Banker, R, and A in 102,600 shoes.

Shoe frequency of the final count disparities of Player and Banker in 102,600 shoes:

Shoe frequency of the final count disparities of R and A in 102,600 shoes:

The distributions appear to be Gaussian, with one standard deviation corresponding to about 7 to 8 final count disparity units.

The peak in the PB disparity graph is shifted to the left to -1 rather than being centered at 0.  Again, this reflects Banker’s expected greater frequency compared to Player’s.  No such bias appears in the RA disparity.

Interestingly, in this set of 102,600 shoes, only 3 had a final Player count less than 20, and only 1 had a final Banker count less than 20.  No shoes had any counts less than 17 or greater than 59.  For the final count disparity, no shoe had more than 41 Bankers over Players or 41 As over Rs.  Similarly, no shoe had more than 38 Players over Bankers or 31 Rs over As.

Disclaimer: The betting strategies and results presented are for educational and entertainment purposes only. Gambling involves substantial risks, and the odds are not in the player’s favor by design. The author does not state nor imply any system, method, or approach offers users any advantage, and he shall not be held liable under any circumstances for any losses whatsoever.

My Baccarat Shoe Factory

Posted in Life with tags , , , , , , , , , , , , , , , , , , , , , , , , on October 2, 2010 by virtuoid

Preparing to perform large scale modeling of baccarat methods, I wrote programs to first analyze existing baccarat shoe data, as well as generate my own.

The existing baccarat shoe data are from the popular Zumma 600 (600 live shoes) and Zumma 1000 (1000 live shoes) books, as well as the Wizard of Odds (1000 simulated shoes using a virtual 8-deck shoe).

In addition, I wrote my own program to simulate an 8-deck shoe, allowing me to generate a practically limitless number of realistic baccarat shoes. In my program, after a shuffle procedure thoroughly randomizes the shoe, cards are dealt according to baccarat drawing rules. In the same manner as the Wizard of Odds procedure, cards are dealt until less than 6 cards remain in the shoe. Extensive checking of the resulting output verifies my program produces realistic baccarat shoes.  To form a substantial, preliminary data set, I used my program to generate 100,000 unique baccarat shoes.

To provide an extra degree of confidence that my generated shoes were realistically simulating what one might encounter when playing a live baccarat game at a casino, I analyzed the ratios of successive SAP and FOE event frequencies in all of the data sample sets (Zumma, Wizard of Odds, and my simulated shoes). SAP events are normal Player/Banker events, while FOE events are derivatives of SAP events. Because they are derivatives, FOE events offer an extra layer of testing sensitivity for the data sample.

Based on the probabilities of event occurrences in a random distribution, the ratio of each successive event should be 1/2.

That is:

the number of 1s should be 1/2 the total number of events,
the number of 2s should be 1/2 the 1s,
the number of 3s should be 1/2 the 2s,
the number of 4s should be 1/2 the 3s,
etc …

My analysis shows that in all data sets (Zumma 600, Zumma 1000, Wizard of Odds 1000, and my simulated shoes Virtuoid 1000), the actual ratios of successive events agrees with what is expected in a random distribution.

Note: The scatter at the higher numbered events is due to a relative scarcity of occurrences. Moreover, I limited the highest number of events graphed to 12, even though the highest event number in the data set is 16. Events 13-16 occurred too infrequently to form a statistically sufficient set.

These results suggest the following:

- Zumma live shoes exhibit event frequency distributions expected in a random data set.

- Wizard and Virtuoid simulated shoes using a virtual shoe exhibit event frequency distributions expected in a random data set.

- There is no evidence of shoe shuffle control in the Zumma 600 or Zumma 1000 data sets. Intentional shuffle control would bias the event frequencies and show up as significant departures from what is theoretically expected.

Thus, one of the following two statements must be true:

1) Zumma recorded shoes from casinos which did not artificially control the shuffle.

OR …

2) Zumma did not record shoes from real, physical casinos.

To elaborate, my analysis shows that both Zumma data sets exhibit characteristics which are consistent with a random distribution.

So, one can conclude either one of two things:

1. If one believes Zumma is telling the truth that its sample was collected from real casinos, then the results suggest that those casinos were not intentionally controlling the shuffle, but offering a truly fair and random game.

2. If one doubts Zumma is telling the truth that its sample was collected from real casinos, and one believes that casino shuffles are controlled to be biased and not random, then since Zumma data sets actually exhibit random characteristics, one can use the results to suggest that Zumma did not collect its data from real casinos.

My results in and of themselves cannot confirm which of the above two is true. But one statement is true, and the other is false, and it all depends on your assumptions about casino shuffle control.

If you believe Statement 1 above, then the simulated, virtual shoes by Wizard and myself are just as good as live shoes from a statistical standpoint, since their event frequencies are consistent with what is expected in a random distribution.

If you believe Statement 2 above, then live shoes would be expected to have more biases than simulated shoes, and the biases should be revealed in an analysis of the ratio of successive event frequencies.

Of course, even if Zumma did collect its data from real casinos, my analysis does not conclusively say whether or not other casinos intentionally control the shuffle. The SAP and FOE events of a particular casino would have be analyzed on a case-by-case basis to quantitatively determine whether it is offering a fair, random game.

Legally speaking, all casinos are supposed to offer perfectly fair games, but there are some who insist they do not. (I had written about the idea of shuffle control in these posts: Shuffle Control: Why It’s Bad for the House and Beating Random.)

With my new Baccarat Shoe Factory, I generated 100,000 unique baccarat shoes in preparation for large-scale testing of baccarat methods.

I also performed tests of the ratios of SAP and FOE event frequencies to verify my generated shoes conformed statistically to what is expected in a random distribution. Because of the significantly larger sample, I plot events up to 20, compared to only 12 for Zumma and Wizard of Odds.

As before, scatter at the higher events is due to relatively fewer occurrences.  I limit the analysis to events of 20 or less, even though there were a few 21-25 events in both the SAP and FOE, as shown below in the numerical data table.

Numerical statistics from the 100,000 shoe data set:

(P=Player, B=Banker, T=Ties, R and A are derivatives of P and B)

Total P: 3,738,579 44.6207% (44.6274% theoretical)
Total B: 3,841,096 45.8443% (45.8597% theoretical)
Total T: 798,901 9.5350% ( 9.5156% theoretical)
Total P+B+T: 8,378,576
Total R: 3,789,162 49.9911%
Total A: 3,790,513 50.0089%
SAP Events SAP Count SAP Ratios
1s 1,948,858 0.5071
2s 959,265 0.4922
3s 474,340 0.4945
4s 232,981 0.4912
5s 115,632 0.4963
6s 56,605 0.4895
7s 27,973 0.4942
8s 13,858 0.4954
9s 6,736 0.4861
10s 3,243 0.4814
11s 1,646 0.5076
12s 821 0.4988
13s 435 0.5298
14s 199 0.4575
15s 96 0.4824
16s 51 0.5313
17s 33 0.6471
18s 17 0.5152
19s 10 0.5882
20s 2 0.2000
21s 0
22s 1
23s 0
24s 0
25s 2
Total SAP Events: 3,842,804
FOE Events FOE Count FOE Ratios
1s 1,920,943 0.5066
2s 948,873 0.4940
3s 468,155 0.4934
4s 230,283 0.4919
5s 113,571 0.4932
6s 56,087 0.4938
7s 27,415 0.4888
8s 13,517 0.4931
9s 6,486 0.4798
10s 3,307 0.5099
11s 1,653 0.4998
12s 823 0.4979
13s 410 0.4982
14s 192 0.4683
15s 100 0.5208
16s 56 0.5600
17s 37 0.6607
18s 11 0.2973
19s 4 0.3636
20s 2 0.5000
21s 2
22s 1
23s 1
24s 1
25s 0
Total FOE Events: 3,791,930

My analysis verifies that my virtual 8-deck shoes are being sufficiently shuffled to produce characteristically random baccarat decisions with averages agreeing with theoretically calculated expectancies, making them statistically and practically equivalent to the Zumma and Wizard of Odds data sets.  Thus, the results of testing baccarat methods when using Zumma, Wizard of Odds, or my own data should realistically reflect the  results one might get when playing at physical casinos offering fair games in the real-world.

Follow-up Shoe Disparity Analysis: Disparity Data.

Follow-up:  Separate P and B events analysis over 2361 live shoes, Zumma 600+1000 live shoes, and one million computer generated shoes:  P and B Events Statistics: A Comprehensive Comparison

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