Best scenario based on productivity vs probabilities minimizing risk


New Member
Hello guys, I am running some tests on "trying" to beat a casino game called baccarat. Believe me when I say that I have been working on this project for many months at this point. Without getting in details on a system or how to (if it really works) or it is even possible (that is not the point of this post), I will go directly to my simulation results which is what I really want to discuss and where I need to be sure that I am focusing/doing the right mathematical/statistical/logical thing. Having the following two scenarios and based on more than 12K shoes:



*the ocurrences are based on different "cases" where I will stop playing a shoe or even discard it without playing (the ones in 0), i.e. for case A after winning 20 units and going below that level (for case B 40 units)

As you can see scenario B produces more in net units, almost 10K more (45K in total); also it give us 1 more unit (4 in total) per shoe on average. On first thought, in the long run this looks better than A.

But here comes my doubt...
1. Isn't it better or even lower in risk to look or insure a higher % of occurences of your top case (the one where you win more on average... 21 units 49%)?
2. Moreover if we consider to play 2 tables at the same time, wouldn't it be better to have more possibilities/probabilities/ocurrences of getting one of the shoes from my top case?

I will put you a 3rd scenario based on A but with 2 more cases to stop playing a shoe; I guess the % of ocurrences are more distributed:


Based on all the above and I hope it is clear enough, which one do you think is the best/optimal scenario? (definitely consider minimizing risk and maximizing profit).

Thanks in advance for your time and any advice/thoughts/light! that you can provide.

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J - I've played a lot of blackjack and hold'em, but never baccarat. Not sure how the game is played or what your system is doing. But here are my general suggestions.
1) Read a little of Ed Thorp's work on blackjack for inspiration
2) Clearly define the hypothesized situation when the player has an advantage over the house. (Thorp said this was when the deck has a disproportionate amount of 10's and Faces)
3) Get good at coding, try R since its free and lots of youtube videos to teach how to use.
4) Test your hypothesis
5) If your results are conclusive, PM me and we'll go to Vegas ;)


New Member
Hi Archidamus, first of all thank you for your reply. I definitely know very well both games that you mentioned. About baccarat, not sure it is necessary to understand the game to answer my question but in summary and for anybody else that would like to know...


...each shoe has 8 decks and there are 3 possible main bets: Player (pays 100% of your bet), Banker (pays %95, the other 5% goes to the house as commission) and Tie (pays 8 times your bet). All clients bet to whatever they want, dealer puts two cards on the player and two cards on the banker, based on the sum and combination of cards the dealer may put a third card on each. At the end the one that is closest to 9 wins (face cards and tens value is cero btw), if there was a tie (same result for player and banker) in the hand and you bet to the banker or player, it is consider a push. There is a slightly (minimum) edge for the banker (due to the house rules when getting a third card); that explains the 5% commission if you bet on it. If you want stats, in the long run you will get these results:

Total player wins ratio = 0.447496
Total banker wins ratio = 0.456076
Total tie wins ratio = 0.096428
Average hands per shoe = 65 (depending on the cut and burned cards at start)

About your suggestions:
1. I am already an AP ;) but thanks for the book recommendation.
2. Sure that is only one!
3. Heard about it, haven't tried it before, will take a look thanks. Now I have already developed my own simulator, as I mentioned, several months of work here my friend...
4. Already done.
5. We are here! Analyzing the results of my simulations...

...and back to my original question which I think it is more logical/mathematical/statistical (and I guess could be applied to other projects), I have mentioned 3 possible scenarios A, B and C. Based on more than 10K shoes (consider that a sample), B produces 10K more units than the others and 1 more unit per shoe on average which I think is something to consider, BUT, looking inside each scenario, the "case" in which I win more on average has more % of ocurrences in A and C. Moreover as I mentioned, if I am planning to play (online) 2 different shoes at the same time, isn't it better to have more probabilities of my "winner" case on my side?

In the three scenarios based on my simulations I win, but which one is the optimal considering productivity, probabilities and risk, anyone?

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J, Thanks for the clarifying information. I think your question is a little statistics and a little industrial engineering/Optimization.

As for making the comparison for the 3 systems I would run a few million iterations and get as best approximations of the true probabilities of winning. 12k shoes might seem like a lot, but what I've experienced in Monte Carlo simulations is that you end up needing 100x the iterations. The rule of thumb is that for every 100x interations ran, you gain one more decimal point of exactness in your estimates.

Also, consider analyzing the statistics for each shoe in the 3 different cases. I would create a histogram using the units won/lost per shoe and look at the mean/median/mode/variance/ and skew. A picture is worth 1k words. If the distributions fit something like a longnormal or gamma distribution you can do some cool stuff with it, like closed form calculations.

As for Risk, I am not sure if you are willing to adjust your system betting parameters. The kelly criterion might be applicable to you here if you have good estimates on the winning and losing probabilities. Also, by running more iterations than you think you need, you can get some good ideas on the risk. Like, if you start with 1K bank roll whats the probability of loosing it all.

Once you've gotten a high degree of confidence in the probabilities and the risk, then I would do some calculations as if I was an industrial engineer at a manufacturing plant. How long does it take to play each hand? How many hands do you apply this system(and bet more I assume)? What have been the max draw downs in each of the scenarios? You could also run the simulations with a time aspect, example dealing takes 8 seconds, each new card tkes 3 seconds, moving chips takes this long, yadda yadda. I would using a stopwatch and do some time studies of actual games in the enviroment youll be in.

This does sound pretty cool. I wish the best of luck to you and hope the online casinos don't catch on to you to quickly.


New Member
Hey A! sorry for getting back to u after so many days, but I was on vacations for one week totally "disconnected" of the world. First of all, thank you very much for taking the time to respond and give such valuable ideas/tips.

1. 12K is my initial sample composed by 1.5K played shoes by me (which is my most valuable data because I know for sure that they are real), and then the rest are random generated shoes (actually I have more than 100K) from 2 different "respectful" sources supposedly considering all the game parameters (so I assume that they are my closest approach to the word real). I totally agree that the numbers may vary depending on the sample size but I have to make decisions with what I have at this point. I do consider that 100K is a decent sample and my numbers are similar to the ones that I shared with the 12K shoes.
2. The histogram recommendation is great and I haven't done it. This may give me the answer* that I am looking for.
3. I have definitely considered bankroll management and I have all that already handled. But thanks again for the good advice.
4. Excellent point and this is a must. It is what I call "sessions simulations" (what I shared at my original post was "shoes simulations") and also has a high importance. My results are pretty good here and I feel very confident and optimistic with them after running 10 simulated years with consistent average numbers. As I mentioned before and if I am right, I already win in all scenarios but I was looking for the "optimal".

*I have made some adjustments to my system and unless the histogram gives me something to reconsider, I have already made a decision. I will go with this more balanced scenario:


At first it looks like it produces less than the others but actually the units per shoe on average (3) is almost the same. So here comes the main reason of choosing this one: "the occurrences". I have come to the conclusion that it is better to have more probabilities (49%) of seeing my winning "case". Moreover if during my sessions simulations (and also in a real life scenario) we will get a total random shoe. Apart from that, having 38% of -7 units per shoe on average as the second case with more probabilities, gives me a more balanced and lower risk scenario (compared to the others). All this also considering that I am going to play (mainly) two tables at the same time. So with the appropriate bankroll/bet management and session parameters (that I have already defined and tested), I think this is the way to go.

About "somebody" catching me hehe, no worries, I am not even counting cards**, I am just playing with their own rules, no cheating in any way and believe me when I say that they (each house) are going to return me all the money that I invested/lost all these years + interests without even knowing how :cool:.

Thank again Archidamus for all your good recommendations, I really appreciate them.


**"they" wanted to make everybody believe (even themselves) that it is cheating or against the law or against the rules, when it is just pure ability!
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