gigolo2002ph
gigolo2002ph
Joined: Jan 22, 2014
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January 22nd, 2014 at 6:56:21 AM permalink
Hi Wizard,

I have a question with regards to the probability of winning for a Banker, Player and Tie.
Below are the combinations in each market. May I know how did you compute the no. of combinations in each event?
Is there any method or did you used a simulation software or a program to calculate all the possible combinations?
Thanks in advance and more power to your site. :)

Combinations Markets
2,292,252,566,437,888 - Banker
2,230,518,282,592,256 - Player
475,627,426,473,216 - Tie
AceTwo
AceTwo
Joined: Mar 13, 2012
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January 28th, 2014 at 12:45:46 PM permalink
The total number of 'combinations' if you add the above is 4.998.398.275.503.360
This is calulated as Permut(416,6) in excel.
These are permutations (order matters) of chosing 6 cards out of 416 for 8 deck game.
Even though in Bacarat some hands go to 4 cards, some to 5 cards and some to 6 cards to do the calculation you take into account the 6 cards and if in a particular hand that would stop at 4 cards all permutations that include the 5th and 6th card count for that.
The individual number of permutations that result in Banker, Plaayer and Tie are calculated using a combinatorial software that goes through every single particular permutation and chekcs whether it is banker player or tie.
And actually the software does not have to go through 5 Quadrillion permutations but a much smaller number since when a hand finishes at 4 cards all resulting 6 card permutations from that are counted. And there are also otehr tricks in the programming that can reduce the number of iterations to a relatively smaller number and the calculation can be done in a split second.
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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January 28th, 2014 at 3:19:25 PM permalink
If you consider the cards as number 1 to 9 and 10 (which counts as 0) then there are 55 possibilities for the first two cards in the player's hand. Similarly in the banker's hand. This gives 3025 possible starting positions. From there you work out which ones need more cards (obviously some don't) and then either given the player's third card or stands whether the dealer stands ad work through those. Thus some starting hands will have 100 possible outcomes and others much less. Having decided which cards were used and the number of decks, you can calculate the number of permutations. Sadly excel won't run to that many significant digits, but I got similar answers.

This is the type of thought process needed when working out these things - how can I make the number of calculations fewer.
teliot
teliot
Joined: Oct 19, 2009
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January 28th, 2014 at 3:39:24 PM permalink
Quote: gigolo2002ph

Hi Wizard,

I have a question with regards to the probability of winning for a Banker, Player and Tie.
Below are the combinations in each market. May I know how did you compute the no. of combinations in each event?
Is there any method or did you used a simulation software or a program to calculate all the possible combinations?
Thanks in advance and more power to your site. :)

Combinations Markets
2,292,252,566,437,888 - Banker
2,230,518,282,592,256 - Player
475,627,426,473,216 - Tie

I iterate through all possible six-card sequences with six nested for loops, each from 0 to 9, and consider all six-tuples (a,b,c,d,e,f). I evaluate the result of each of those (Player/Banker/Tie), and then compute the number of ways that six-tuple can occur. I keep track of the totals with three long long int variables. I have a function long long int getNumber(a,b,c,d,e,f), and another function int getResult(a,b,c,d,e,f) (returns 0, 1, 2). It's fairly trivial programming, less than 200 lines of code. My results match Mike's. I modify this code for side-bet analysis.

It takes about 3 milliseconds to run. This is the way Mike does it as well, I am almost certain.

For those side-bets or game variants where individual cards matter (rank and suit), I modify the program to iterate through every card. Then I have six loops from 0 to 51, so the size of the iteration is 52^6, which is considerably slower. On my computer running 1 thread, it takes about 2 hours.
Poetry website: www.totallydisconnected.com
Tanko
Tanko
Joined: Apr 22, 2013
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January 30th, 2014 at 4:25:14 AM permalink
While playing Baccarat against the Interblock machines at Resorts World, I noticed many of the winning hands were naturals, so I wrote down the results of the next twenty shoes that I played.

I found that for each individual shoe in this small sample, a consistent 44% of the winning hands were naturals.

In one shoe, eleven of the first fifteen hands were naturals.

Ten 9's and one 8.

Fifty percent of the winning hands in that shoe were naturals.

Many of these winning hands in my sample were natural eights losing to natural nines.

Does anyone know what the expected percentage of hands won by naturals is?
gr8player
gr8player
Joined: Mar 2, 2013
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January 30th, 2014 at 6:53:50 AM permalink
Hello, Tanko, I trust all is well with you.

The naturals appear to me as just one of many "anomalies" pertaining to those Interblock machines at Resorts World in NYC.

I live but 20 minutes drive from there, as opposed to 2 1/2 hrs from AC, but I just can't bet any real dollars into those Baccarat "machines". I just have no trust in their results.

As such, I'm relegated to play only live-dealer games. Too often I've felt like a fool playing those machines, where Goodness only knows how they arrive at each hand's results...and that's a feeling that I just won't allow, especially while gambling.

Stay well.
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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January 30th, 2014 at 3:54:52 PM permalink
Quote: teliot

...It's fairly trivial programming, less than 200 lines of code....takes about 3 milliseconds to run.

Please forgive me for asking the obvious (also I haven't read the obvious book if there is one), but what programming language would you recommend (I'm guessing it's c or similar) and how does one run it on a PC. Personally I use scripting under HTML, so could write the code but haven't yet found the best engine to run such code quickly. Many thanks.
teliot
teliot
Joined: Oct 19, 2009
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January 30th, 2014 at 4:06:50 PM permalink
Quote: charliepatrick

Please forgive me for asking the obvious (also I haven't read the obvious book if there is one), but what programming language would you recommend (I'm guessing it's c or similar) and how does one run it on a PC. Personally I use scripting under HTML, so could write the code but haven't yet found the best engine to run such code quickly. Many thanks.

Hi, usually I write code mainly in C or C++. Sometimes in Java. I have a dedicated x86 (Alienware) running Ubuntu Linux where I run these programs. For C/C++, I use the gcc or g++ compilers, and compile with -Ofast (not that I fully understand optimization).

Scripting is possible, but will be painfully slow. You might as well learn a real language if you are going to be doing combinatorial analysis. The programming doesn't use any advanced concepts. Because you know scripting, you can easily learn enough if you self-study for a few weeks.

Cheers,

Eliot
Poetry website: www.totallydisconnected.com
charliepatrick
charliepatrick
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January 30th, 2014 at 4:28:28 PM permalink
Thanks - I used to code in mainframe, so hopefully it should be fairly easy to pick-up the basics. Also thanks for the other things to look into.
teliot
teliot
Joined: Oct 19, 2009
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January 30th, 2014 at 4:48:20 PM permalink
Quote: charliepatrick

Thanks

My pleasure. The world could use a lot more people who know how to analyze casino games.
Poetry website: www.totallydisconnected.com

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