Determining the Fairness of Online Blackjack
Game Rules as provided by the operator:
- 6 decks shuffled after each round
- S17
- DAS, LS
- 3 splits for 4 hands
- BJ 3:2
Quote: DarmafiAssuming 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…..
Quote: DarmafiAssuming 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.
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?
Quote: heatmapQuote: DarmafiAssuming 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 pageQuote:§ 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.
Quote: DarmafiI 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.
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The thing is all other modifications are minor and should not change the house edge very much.
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
Quote:Randomness—The observed unpredictability and absence of pattern in a set of elements or events that have definite probabilities of occurrence.
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?Quote: DarmafiAssuming 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
