Darmafi
Darmafi
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December 18th, 2022 at 12:34:49 PM permalink
Assuming you wanted to test whether or not the online blackjack game (computerized, not live dealer) you were playing was conforming to the expected probabilities, what information, specifically, would need to be gathered to form a determination one way or the other?

Game Rules as provided by the operator:

- 6 decks shuffled after each round
- S17
- DAS, LS
- 3 splits for 4 hands
- BJ 3:2
SOOPOO
SOOPOO
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December 18th, 2022 at 2:38:15 PM permalink
Quote: Darmafi

Assuming you wanted to test whether or not the online blackjack game (computerized, not live dealer) you were playing was conforming to the expected probabilities, what information, specifically, would need to be gathered to form a determination one way or the other?

Game Rules as provided by the operator:

- 6 decks shuffled after each round
- S17
- DAS, LS
- 3 splits for 4 hands
- BJ 3:2
link to original post



It would be a massive undertaking. I’ll give one simple example. Every 100th hand you are dealt an 11 and of course double down. And for that hand the dealer always draws to a 21. And you never draw to a 21. How do you program to look for that?

Or every 50th hand you are automatically dealt either 13, 14, 15, or 16?

Etc…..
heatmap
heatmap
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December 18th, 2022 at 2:53:20 PM permalink
Quote: Darmafi

Assuming you wanted to test whether or not the online blackjack game (computerized, not live dealer) you were playing was conforming to the expected probabilities, what information, specifically, would need to be gathered to form a determination one way or the other?

Game Rules as provided by the operator:

- 6 decks shuffled after each round
- S17
- DAS, LS
- 3 splits for 4 hands
- BJ 3:2
link to original post



Apparently states use this list of tests which help understand if a random number generator is conforming

This is my states laws taken from this page
https://www.pacodeandbulletin.gov/Display/pacode?file=/secure/pacode/data/058/chapter810a/s810a.5.html&searchunitkeywords=die%2Chard&origQuery=die%20hard&operator=OR&title=058%20RECREATION

Quote:

§ 810a.5. Random number generator standards.
(a) The random number generator must be cryptographically strong at the time of submission for approval. When more than one instance of a random number generator is used in an interactive gaming system, each instance must be separately evaluated and certified. When each instance is identical but involves a different implementation within a game/application, each implementation shall also be separately evaluated and certified. Any outcomes from the random number generator used for game symbol selection/game outcome determination must be shown, by data analysis and a source code read, to:

(1) Be statistically independent, unless the submission has been approved for a persistent-state outcome determination.

(2) Be fairly distributed (within statistically expected bounds) over their range.

(3) Pass various recognized statistical tests.

(4) Be cryptographically strong.

(b) Random number generators must adhere to standards in § 461a.7 (relating to slot machine minimum design standards).

(c) The gaming laboratory may employ the use of various recognized tests to determine whether or not the random values produced by the random number generator pass the desired confidence level of 95%. These tests include the following:

(1) Chi-square test.

(2) Equi-distribution (frequency) test.

(3) Gap test.

(4) Overlaps test.

(5) Poker test.

(6) Coupon collectors test.

(7) Permutation test.

(8) Kolmogorov-Smirnov test.

(9) Adjacency criterion tests.

(10) Order statistic test.

(11) Runs tests (patterns of occurrences should not be recurrent).

(12) Interplay correlation test.

(13) Serial correlation test potency and degree of serial correlation (outcomes should be independent of the previous game, unless the submission has been approved for a persistent-state outcome determination).

(14) Tests on subsequences.

(15) Poisson distribution.

(d) The scaling method may not compromise the cryptographic strength of the random number generator. The scaling method must preserve the distribution of the scaled values. For example, if a 32-bit random number generator with a range of the set of integers in the closed interval (0, 232-1) were to be scaled to the range of the set of integers in the closed interval (1, 6) so that the scaled values can be used to simulate the roll of a standard six-sided die, then each integer in the scaled range should theoretically appear with equal frequency. In the example given, if the theoretical frequency for each value is not equal, then the scaling method is considered to have a bias. Thus, a compliant scaling method must have bias equal to zero.

(e) If the interactive gaming system utilizes hard-based random number generators, there must be dynamic/active, real-time monitoring of the output with a sample size large enough to allow for reasonably high statistically powerful testing so that game play is disabled when an output testing failure is detected.

(f) If the interactive gaming system utilizes a software-based random number generator, it must adhere to all of the following:

(1) The period of the random number generator, in conjunction with the methods of implementing the random number generator outcomes, must be sufficiently large to ensure that all game independent outcome combinations/permutations are possible for the given game/application, unless the submission has been approved for a persistent-state outcome determination.

(2) The methods of seeding/reseeding must ensure that all seed values are determined in a manner that does not compromise the cryptographic security of the random number generator.

(3) To ensure that random number generator outcomes cannot be predicted, adequate background cycling/activity must be implemented in between games. Whenever a game outcome is made up of multiple mapped random number generator values, background cycling/activity must be implemented during the game (that is, in between the selection of each mapped random number generator value) to ensure that the game outcome is not comprised of sequential mapped random number generator outcomes. The rate of background cycling/activity must be sufficiently random in and of itself to prevent prediction.

Darmafi
Darmafi
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December 18th, 2022 at 3:39:10 PM permalink
Rather than analyzing specific hands, wouldn’t it be sufficient to compare the results expected in a fair-game with the results obtained from the casino in question?

Rough example: after 1000 rounds of flat betting $10 per hand the expected loss should be somewhere between $300 and $500. If your actual results are -$2000 or greater, you have reason to suspect foul play.

Would something like this “work” and what would the specific parameters be?
aceside
aceside
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December 18th, 2022 at 3:44:19 PM permalink
I think this is rather easy to find out. Theoretically, you are supposed to be dealt one Blackjack every 21.057 hands. If this number is correct, the game is fair.
Darmafi
Darmafi
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December 18th, 2022 at 3:52:20 PM permalink
I feel like that would be too specific of a test because the issue might not be with the BJ percentages. It could be any number of modifications to game play.
Darmafi
Darmafi
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December 18th, 2022 at 4:03:00 PM permalink
Quote: heatmap

Quote: Darmafi

Assuming you wanted to test whether or not the online blackjack game (computerized, not live dealer) you were playing was conforming to the expected probabilities, what information, specifically, would need to be gathered to form a determination one way or the other?

Game Rules as provided by the operator:

- 6 decks shuffled after each round
- S17
- DAS, LS
- 3 splits for 4 hands
- BJ 3:2
link to original post



Apparently states use this list of tests which help understand if a random number generator is conforming

This is my states laws taken from this page

Quote:

§ 810a.5. Random number generator standards.
(a) The random number generator must be cryptographically strong at the time of submission for approval. When more than one instance of a random number generator is used in an interactive gaming system, each instance must be separately evaluated and certified. When each instance is identical but involves a different implementation within a game/application, each implementation shall also be separately evaluated and certified. Any outcomes from the random number generator used for game symbol selection/game outcome determination must be shown, by data analysis and a source code read, to:

(1) Be statistically independent, unless the submission has been approved for a persistent-state outcome determination.

(2) Be fairly distributed (within statistically expected bounds) over their range.

(3) Pass various recognized statistical tests.

(4) Be cryptographically strong.

(b) Random number generators must adhere to standards in § 461a.7 (relating to slot machine minimum design standards).

(c) The gaming laboratory may employ the use of various recognized tests to determine whether or not the random values produced by the random number generator pass the desired confidence level of 95%. These tests include the following:

(1) Chi-square test.

(2) Equi-distribution (frequency) test.

(3) Gap test.

(4) Overlaps test.

(5) Poker test.

(6) Coupon collectors test.

(7) Permutation test.

(8) Kolmogorov-Smirnov test.

(9) Adjacency criterion tests.

(10) Order statistic test.

(11) Runs tests (patterns of occurrences should not be recurrent).

(12) Interplay correlation test.

(13) Serial correlation test potency and degree of serial correlation (outcomes should be independent of the previous game, unless the submission has been approved for a persistent-state outcome determination).

(14) Tests on subsequences.

(15) Poisson distribution.

(d) The scaling method may not compromise the cryptographic strength of the random number generator. The scaling method must preserve the distribution of the scaled values. For example, if a 32-bit random number generator with a range of the set of integers in the closed interval (0, 232-1) were to be scaled to the range of the set of integers in the closed interval (1, 6) so that the scaled values can be used to simulate the roll of a standard six-sided die, then each integer in the scaled range should theoretically appear with equal frequency. In the example given, if the theoretical frequency for each value is not equal, then the scaling method is considered to have a bias. Thus, a compliant scaling method must have bias equal to zero.

(e) If the interactive gaming system utilizes hard-based random number generators, there must be dynamic/active, real-time monitoring of the output with a sample size large enough to allow for reasonably high statistically powerful testing so that game play is disabled when an output testing failure is detected.

(f) If the interactive gaming system utilizes a software-based random number generator, it must adhere to all of the following:

(1) The period of the random number generator, in conjunction with the methods of implementing the random number generator outcomes, must be sufficiently large to ensure that all game independent outcome combinations/permutations are possible for the given game/application, unless the submission has been approved for a persistent-state outcome determination.

(2) The methods of seeding/reseeding must ensure that all seed values are determined in a manner that does not compromise the cryptographic security of the random number generator.

(3) To ensure that random number generator outcomes cannot be predicted, adequate background cycling/activity must be implemented in between games. Whenever a game outcome is made up of multiple mapped random number generator values, background cycling/activity must be implemented during the game (that is, in between the selection of each mapped random number generator value) to ensure that the game outcome is not comprised of sequential mapped random number generator outcomes. The rate of background cycling/activity must be sufficiently random in and of itself to prevent prediction.


link to original post



Well, we apparently have something in common. I’ve contacted PGCB several times over the course of a year to get the results (or at least a summary) of their most recent audit(s) but I never even received a reply. No luck searching their website either.

I can’t understand why the audit results would not be publicly available.
aceside
aceside
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December 18th, 2022 at 4:27:58 PM permalink
Quote: Darmafi

I feel like that would be too specific of a test because the issue might not be with the BJ percentages. It could be any number of modifications to game play.
link to original post


The thing is all other modifications are minor and should not change the house edge very much.
Talldude90
Talldude90
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December 18th, 2022 at 4:50:29 PM permalink
I'm no longer a mathlete. However I'm pretty certain given the variance of the game you can see how long it would take to get within a certain % of the EV of the game. You can even use the statistics to tell you in what percentile you are falling away from the average given x number of bets and y deviance from expected value... Dunno how many hands, I'd expect the number to not be small, like not 1 or 2 gaming sessions.
DRich
DRich
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December 18th, 2022 at 4:53:08 PM permalink
Quote: Darmafi



Well, we apparently have something in common. I’ve contacted PGCB several times over the course of a year to get the results (or at least a summary) of their most recent audit(s) but I never even received a reply. No luck searching their website either.

I can’t understand why the audit results would not be publicly available.
link to original post



My assumption would be if the Gaming Control found something way out of the statistical norms you would hear about it. The property would have to address it in the public forum. Most state Gaming Control board meetings are open to the public if you are interested enough in attending.

This website has agendas and minutes for the meetings: https://www.pgc.pa.gov/InformationResources/MediaReportsSurveys/Pages/CommissionersBoardMeetingReportsandMinutes.aspx
At my age, a "Life In Prison" sentence is not much of a deterrent.
heatmap
heatmap
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December 18th, 2022 at 5:59:36 PM permalink
https://www.pacodeandbulletin.gov/Display/pacode?file=/secure/pacode/data/058/chapter1112a/s1112a.1.html&searchunitkeywords=probabilities&origQuery=probabilities&operator=OR&title=058%20RECREATION

Quote:

Randomness—The observed unpredictability and absence of pattern in a set of elements or events that have definite probabilities of occurrence.

avianrandy
avianrandy
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December 19th, 2022 at 1:47:37 AM permalink
Quote: Darmafi

Assuming you wanted to test whether or not the online blackjack game (computerized, not live dealer) you were playing was conforming to the expected probabilities, what information, specifically, would need to be gathered to form a determination one way or the other?

Game Rules as provided by the operator:

- 6 decks shuffled after each round
- S17
- DAS, LS
- 3 splits for 4 hands
- BJ 3:2
link to original post

what I would be concerned with is the expected probability of getting paid if you were to win. This site has a sister site latest casino bonuses (lcb) or something like that. The 6 deck continuous shuffle thing is tough...the other rules pretty good. Where is this casino home base? Aruba, Switzerland?
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