My Baccarat Shoe Factory

Zumma live shoes, and Wizard of Odds and Virtuoid simulated shoes all have event frequencies characteristic of random distributions.

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

121 replies on “My Baccarat Shoe Factory”

[…] My next level of programs enabled me to generate a practically unlimited number of realistic baccarat shoes with statistical characteristics and expectancies agreeing with theory. (Reference: My Baccarat Shoe Factory.) […]

Use of actual lBaccarat data (not computer generated simulated live data, would be the only way to properly test baccarat strategies without allowing unknown factors to influence the results. You cannot test and check if data is statistically significant against unknown factors by definition.

Use real casino data — albeit difficult to source. Avoid computer-based data, that you think simulates live data… since all factors in drawing cards and outcomes thereof are not necessarily known… or covered by statistical testing chi-squares.

Thanks for your opinion, BaccPlayer.

What you suggest is that live shoes from casinos are statistically different in terms of frequencies of events and Player-Banker expectations.

However, my analysis indicates no such differences exist.

While I respect your belief, which is what people like Ellis believe, no objective evidence exists to support it.

On the contrary, all the objective evidence supports the fact that live shoes from casinos have statistical properties which are identical to those generated from randomly generated virtual shoes, and both agree perfectly with theoretical expectations.

Based on the objective evidence, I am confident my data base adequately represents what would be encountered in live play, and thus my simulation results are relevant and reliable.

But if you happen to have a significant bank of live data, I would be very happy to include them into my data base.

Here – I performed a detailed statistical analysis of P and B events frequencies in 2361 manually collected live shoes from land-casinos, the Zumma 600 & 1000 live shoes, and 1 million computer generated shoes. They all show the same statistics and are from that perspective indistinguishable. That is, there is absolutely no objective evidence that live casino shoes are different than my randomly generated shoes. Ref: P and B Events Statistics: A Comprehensive Comparison

English is not my primary language, but I could understand it when using the google translator. Amazing publish, you can keep them coming! Cheers!

About whether or not Zumma used live results or not,I have read there was 41,698 decisions from 600 shoes.This works out to 69.50 decisions per shoe.There for how many decks were used?With an average of 82 hands per 8 deck shoe!Thanks again for all you great work.


Thanks for your comment. Your numbers look about right.
Perhaps the difference lies in the number of burnt cards, as well as where the cut card is placed?

[…] However, as I performed statistical tests of live and my computer generated shoes, I could find nothing to distinguish one from the other. Please refer to the following studies in which I performed detailed analysis and comparisons of Zumma 600+1000 (supposedly gathered from physical casinos), 2361 Live Shoes (all of which were personally collected by my friend and most of which were shuffled by SM), and my computer generated shoes:

P and B Events Statistics: A Comprehensive Comparison

My Baccarat Shoe Factory

I’ve performed many other tests, too, and I’m too lazy to dig up the results right now, lol. But in all my studies, I could find no signature in live SM or hand-shuffled shoes which would indicate they are not random and not for all intents and purposes identical to my computer generated, completely random shoes. […]

Do you offer data. I have both Zummas. I’m interested in your generated shoes in a simple .txt format of Ps and Bs only run in a single column.


Great, thanks. I’ll reply with the latest concept I’ve tested. You may not want to bother with it – but it beats the Z-1600. It is based on “retracements” and only bets P to avoid commissions. The general concept is the Fibonacci retracements of technical analysis would work without human intervention – likely – and that naturally occuring events will behave “naturally” re these retracements. I have tested this with the slightest retracement level of 20%.

@Scott – I just sent you the data. That’s an interesting concept you are exploring. Thanks for sharing.

What program did you use to analyze the various methods you investigate here against the shoe results? It seems like a complicated business trying to tell a program what to look for in more complicated methods.


Thanks for your question. I custom coded everything from scratch. Any mechanical system can be coded and simulated. I’ve even coded systems which were so complex that few humans if any could possibly play them live at the tables. They were meant to be used by players on computers betting at online casinos, such that they could use a computer to monitor and analyze the shoes in real time as they unfolded.

Human ingenuity is limitless, but unfortunately, I haven’t been able to find one practical method that yields a decent positive expectation in the long run.

Would you be interested in testing my system? I’ve manually (and painstakingly) tested it against three random shoes in the Wizard of Odds’ 1000 shoe results and played it on a few dozen actual live shoes. The results have been shockingly good so far and I’m wondering if it is indeed a fluke or if I have something that beats random. (Sorry if Ellis thinks I’m stupid.)

Virtuoid, wow, I always wished a programmer would get involved and really analyze all the different systems out there. Could you please send me a copy of these 100,000 shoes. If possible, I’d prefer them in order with only a space separating each shoe. If not possible, I will be happy with whatever you can send me. Thanks in advance!

Just a Question, Do you use for baccarat statistics? is it the same as zumma and other real live results with out counting the tie

Hi, I would also really love a copy of the 100,000 shoes. I want to test the probabilities of certain things happening. Thank you for your time


Congratulation for you analyse. I would like to verify the % of a winning shoe that start with a 2S Bank or Player.

Did you verify it ?

Could you send me the 100 000 shoes, so i can verify it

Bests regards

A Ross

Hi Blog owner, I will like to thank you because – I believe without your blog, I would have tested my wimpy systems and lost great deal of money. I haven’t give up on the dream but through your blog, I understand that I must not be naive and only if I could eliminate the possibility of being a broke then I could consider going back.

You stated that the 1s is more than the 2s and the 2s or more adding up with the rest will be equal to the 1s thus whether will 1s become 2s is absolutely 50/50. I do not doubt the stats that you posted. Anyway by far this is the only one we could trust.

The streak of 2s and above – Logically the single streak will be more than the double and so on… just like the 1s and 2s. Is it possible on your side to effortlessly confirm this using your stats?

Imagine this – Some guys had sparked a dream of being a professional baccarat player. He had came up with a crappy system which he thinks is flawless. Now he is building his bankroll for the big day. In the process, he stumble across your blog.


Thanks, AC …

Yes, I, too, was once in your position, dreaming the same dream you did. Only after learning the hard way by losing real money (to this day, those losing experiences still hurt!) did I finally performed my simulations to test these systems. And only after doing this a couple of years did the truth finally sink in: you cannot systematically beat baccarat in the long run.

Yes, your proposed test is one I have already done, and the result is as expected: there is no systematic advantage by considering different ratios of event frequencies.

I hope you will be able to put your 3 years savings to better use, and thank you for letting me know I made a difference in your life.


How many shoes would you confidently say would prove a system works or not?

Thanks virtuoid!

Depends on the method’s betting frequency.

For example, some methods bet very infrequently, whereas others bet all decisions. So, you can’t make an apples-to-apples comparison if simply using “shoes” as the criteria. To make the comparison meaningful, you should use the total number of actual bets instead.

For example, estimating 70 decisions per shoe, for a method that bets every decision, then, that method’s long term expectancy will be quite clear after 10,000 shoes (or 700,000 bets). (Probably only a few thousand shoes is sufficient, but after 10,000 shoes, the long term expectancy will be very obvious and not subject to variance.)

But if a method bets only one-quarter of the shoe on average, then you would need to run 4 x 10,000 = 40,000 shoes to yield an equivalent number of decisions.

Etc …

The only reason why I had to test methods over such large data sets is because many of them don’t bet every decision in a shoe. In those cases, it just takes “longer” (in terms of number of shoes to get an equivalent number of bets) to determine the true long term expectancy.

Hello Dave,

Thank you very much for the valuable information on baccarat statistics and for posting the results of the systems you tested.

Like many others, I also test systems using zumma 600 & 1K and wizard of odds 1K 8-deck, but these limited shoes provides us with unreliable results.

If you have the time, I would like to have a copy of your virtuoid 100k shoes, a sample this large will be a really big help. I will email the results to you if are interested.

Thanks for your generosity,

Hi, Virtuoid…..
Can you email me the results from 100K baccarat shoes as well. Want to test a system.
Thank you in advance!

I too need a large enough sample size and 100K seems like it would be enough to PROVE whether or not a system is legit or not. I have one id like to test out but have been just playing online with live dealers so its going very slowly to test a large enough sample size. Thanks for all your work, virtuiod!

Hi Virtuod,

Many thanks for your wonderful work here. I have been following your site for the past month, and what I can say is that you put a lot of efforts and passion on your work. Would it be possible if you can email my your 100K baccarat shoes. I have one system I would like to test.

Hello Dave,

Thank you very much for the valuable information on baccarat and
sharing the results of the systems you tested.Your blog is indeed a very helpful resource for knowing more about the game.I have one system I would like to test ,would you mine sharing the shoe data you have from zumma 600, 1000, 2600 real shoe and your virtuoid 100,000, 1M computer generated shoe ?

Again I really appreciate the time you have taken to write this wonderful blog and for your analysis.

Best Regards.

Richard Nguyen

Hi, Great blog! Would you mind sending me a copy of the 100K Shoe data… I would like to analyse it…

Many thanks for your time.


Hi Dave,
I can’t believe this is the first time I’ve come across your site. Your passion & dedication toward the subject matter clearly shines through your work. I’m similarly passionate about topics that deal with gambling – In fact I just started a site this month to present such information to readers in an ‘easy reading’ way.

Could I request for your 100k simulation as well? I want to test a method and I’m hoping to publish an article on it soon. I’ll credit you and drop a link as well 🙂

Thank you so much for your hard work. I’m going to have a fabulous weekend going through all your articles!

I am trying to create a program like yours but need some help, I have an idea that might be great. I work at a casino in California and haft to set at a baccarat table all night “I know so painful” !!, but I have a great Idea but need someone to know how to program it. I have put this up on some programming sites and they are asking 2300 to 2800 to build this program. Am I getting ripped off or not. Please email me back and I will give you more information but I do not want to put this out for others to try or steal my method.


Hello Virtuoid! I’m wondering if it’s possible for you to send me a copy of the 100K Shoe data as I would like to analyse it.

Thanks in advance, and hoping to hear from you soon.


Yeah, that’s why a computer is needed to determine accurate long term statistics.

Again thanks a lot for the 100k shoe date.

Do you by any chance mind sending me the others: zumma 600, 1000, 2600 real shoe and 1M computer generated shoe?


Hi, may I have a copy of the 100k shoe simulation? I have a system that I would like to test. I played 4 shoes in Vegas and made $2500 per shoe with no loss.



Hey Dave, I would also love to the 100K shoes that you generated. Data for real shoes is very lacking, and this data set would be invaluable to me. Ridiculous what some people are trying to charge online for very limited amounts of data. I very much appreciate the work you have done here. You have confirmed my feelings that there is probably no consistent way to beat Baccarat in the long run.

Hi Dave,

Amazing work you’re doing here on your blog. You’ve educated me in a way other sites and forums have not. While I’ve had a little bit of success with a couple of methods, the downturns have been stomach turners.

Can you email the shoe data you have accumulated? I see you have Zumma 600 – 1000, 2361 real shoe, 100,000 shoe and 1M shoe data. I’d love to be able to find a way to run simulations of my own with all this info.

Thanks for helping in my research with your blog. It’s greatly appreciated!

Best Regards,

Mr. Tony
Can you please forward me the data? (
Many thanks for your help.

Hi Eric,

Sent you the data.

Trudeau is a notorious con-man. I think he’s finally serving time now.

Personally, I wouldn’t waste my time on testing his (or anyone else’s) method. They are all long term negative.


Dear Mr. Dave
Pls need your help sent me your real and simulation data shoes,
hopefully from your data i can find good system.

Stay tuned … I’m working on programming a simulator app that will allow you to generate and test your own baccarat shoes.

Hi Dave, any word on your shoe generating/system tester app?This is such a fantastic idea. Really appreciate your blog and your non biest data you provide to the baccarat community. I’m sure once someone does crack baccarat we can count on you to give it your honest approval.


Hi Steve,
The app is still under development.
Thanks for your interest.

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