Lab Testing BMM TestLabs Las Vegas, NV June 18 - 2 0 , 201 9
Overview of a Gaming Floor Audit
Name of presenter(s) June 2018
Topics of discussion
• What’s involved in a Gaming Floor Audit • Identifying risk to your Gaming Floor • Gaming Devices & Associated Equipment • Class II Player Interfaces • Class III Gaming Devices • Monitoring & Control Systems • Progressive Controllers & Systems • Kiosks • Promotional Systems
• Software & Verification
What is a gaming floor audit?
• It is a process to check and ensure that the machines and/or tables are setup and operating in a manner expected by the operator, regulator and the public. • When should an audit be conducted? – New games to the floor – Annual audits per MICS & regulation – Disputes/issues
Identifying risk on the gaming floor
• Risk can be found within a modern gaming floor, due to many reasons – Technology – Cheating or exploits – Maintenance – Etc.
What’s involved in a Gaming Floor Audit
• Operational downtime & manpower • Physical inspection of machines • Logical inspection of machines • Report review and comparison • Security/Surveillance review
What’s involved in a Gaming Floor Audit
• Operational downtime & manpower – Planning – Resources
What’s involved in a Gaming Floor Audit
• Physical Inspections
– Cabinet or table hardware. – Peripherals – Informational – Critical areas – Communication hardware
What’s involved in a Gaming Floor Audit
• Logical Inspections
– Software configurations – Software/firmware versions
– Software Verification – Metering/Accounting – Communication – Artwork / Information
What’s involved in a Gaming Floor Audit
• Report Review & Comparison – Accounting information – Significant events
What’s involved in a Gaming Floor Audit
• Security & Surveillance – Seals – Locks
– Camera coverage – *Mind the Gap*
What’s involved in a Gaming Floor Audit
• Monitoring & Control Systems – Server Rooms – Environmental controls – Backup and recovery plans – More tomorrow
What’s involved in a Gaming Floor Audit
• Progressives
– System based progressives – Controllers – Signage – Software – Accounting
What’s involved in a Gaming Floor Audit
• Kiosks – Promotional, Voucher/ticket, Jackpot – Software – Acceptance and Issuance – Exterior – Communications
Software Verification
• Program Storage Media – Hard disk – CF / CFast – SATADOM • Signature Algorithms – CDCK – Kobetron – SHA1 / HMAC-SHA1 – MD5
Software Verification
• Signature Methods / Tools – Kobetron GI-4000 – Kobetron Verify+ – BMM Signatures – GAT • Other useful equipment
– EPROM reader/burner – Forensic media readers – Windows 10 = Caution!
Conducting a Gaming Floor Audit
Name of presenter(s) June 2018
Topics of discussion
• Developing a gaming floor audit plan • When to conduct a gaming floor audit • Development of checklists and procedures
When to conduct a gaming floor audit?
• New machine installs • Machine moves • Software / machine conversions • Annual machine audit requirements
Developing a Gaming Floor Audit Plan
• Time to conduct the audit • Selection of machines • Selection of personnel
• Equipment required • Estimated downtime • Preliminary paperwork • Audit • Review reports and determine outcomes
Checklists and Procedures
Online Accounting System Audit
Nichole Karr, Senior IT Audit Manager June 27, 2018
Topics of discussion
• Overview of accounting system and components • What is an accounting system audit • Identifying risk to your accounting system • Data integrity • Developing an accounting system audit plan • When to conduct an accounting system audit
Online Accounting Systems
Online Accounting Systems are organized sets of computerized accounting methods, procedures, and controls established to gather, record, classify, analyze, summarize, interpret, and present accurate and timely financial data used by all levels of employees and management in a casino environment.
Type of Accounting Systems
In the casino industry, a variety of accounting systems are utilized each day (depending on jurisdictions): • Slots
• Table Games • Cage & Credit • Bingo • Keno • Race & Sports
Components of an Accounting System
There are five (5) components that make up an accounting system:
• Source Documents (markers, vouchers, jackpot/fills, table fills/credits)
• Input devices (computers, bar code scanners, slot machines, kiosk)
• Information processors (computers and software programs)
• Information Storage (servers, hard drives)
• Output Devices (Printers, monitors)
Accounting System Audit
Auditing is a systematic and independent examination.
Accounting System Audit
The system audits consist of an evaluation of the components which comprise that system, with examination and testing of:
• Confirming that systems are appropriately recording and reporting all transactions.
• Validating the correctness of the systems calculations
• Assessing the data integrity of the system
• Verifying that confidential data is not exposed to unauthorized individuals
• Verifying logging of system access and changes to system data
Identifying Risk to Accounting Systems
Accounting systems are fundamental when it comes to casino operations.
In the casino industry financial data followed by customer data are what drives every decision make managers, owners, regulators.
The information that is captured by the casino’s accounting system is so important that it puts it at a high risk of being lost or stolen.
Types of Risks with Accounting Systems
There are four general types of risks associated with information technology systems, regardless if they are in development or in use.
• Strategic Risk – Risk of choosing inappropriate technology.
• Operating Risk – the risk of doing the right things in the wrong way.
• Financial Risk – the risk of having financial resources lost or stolen.
• Information Risk – risk of loss of data integrity, incomplete transactions or hackers.
Data Integrity
Data integrity is the completeness, accuracy and consistency of stored data, without any alteration.
Compromised data is little help to companies and major issues can arise from sensitive data loss. For this reason, maintaining data integrity is a core focus of any casino environment.
Data security (act of protecting the data) is one of several measures which can be employed to maintain data integrity.
Data Integrity
• Data is expected to be: Attributable, Legible, Contemporaneous, Original, Accurate • Validate computer systems • Implement audit trails • Implement error detection software • Secure records with limited system access • Maintain backup & recovery procedures • Protect the physical & logical security of systems • Properly train users & maintain training records
Accounting System Audit Plan
• Less physical, more logical • Inspect servers, software verification • Review reports • Review audit logs
When to conduct a system audit?
• Initial installation & configuration • After game installs, conversions, moves • During/After any new components added • System updates/upgrades • Annually
Promotional System Audits
Nichole Karr, Senior IT Audit Manager June 2018
Topics of discussion
• What is a Promotional System Audit? • Identifying risk to promotional systems • Risk mitigation
What is a Promotion System Audit?
• Subset of an Accounting System Audit • Customer Service vs. Data & System Integrity • Reconciliation between promotion and accounting system.
Risks to Promotional Systems
• Employee Theft/Collusion • Patron Cheating • Hacking • Configuration / Setup of promotions
Risks to Promotional Systems
Tallahassee – A rind of employees and a supervisor at Gulfstream Park Casino manipulated computer software in the summer of 2007 to steal nearly $290k in slot machine winnings by using cards that allowed them to play for free , according to a state investigation. The casino caught another employee, host S. Dorman, with 17 promotional cards – free play cards usually issued as customer appreciation rewards or marketing tools. Investigators also initially suspected the casino’s vice president of gaming of circumventing internal controls to authorize the fraudulent free play cards .
Risk Mitigation
• User Roles - Segregation of Duties • System Access • Promotional Activity logs/Audit Trails • Daily Audits by Income Control/Accounting • Periodic reviews by Gaming Regulators
Class II Systems & Audits
June 2018
Topics of discussion
• Latest Changes to 25 CFR Part 547 • How Class II systems determine outcome & track accounting • Developing a Class II audit plan
Changes
Major changes from 2008 to 2012 to 2018 • No minimum probability requirements – manufacturers and ITL required to disclose game math to TGRA • Grandfather period increased to 10 years from November 2008, and now removed and replaced with Audit requirements • Remote access requirements moved to Part 543 • Removed UL and FCC testing requirements • References to entertaining displays removed
New Grandfathering
• Grandfather systems are now to be called systems manufactured prior to November 2008. • Changes still must maintain or improve compliance with full Class II requirements • 10% of all previous “grandfather” equipment
must be audited annually. May count towards the entire annual floor audit.
How Class II systems work
• Central Determination – Game of Bingo, Pull-tabs, or Lotto • Ball draw performed by a server and provided to each terminal/client • Bingo/Lotto cards either provided by server or generated by each terminal/client • Results often maintained on the server, not on each terminal/client. • Terminal/clients may store accounting, performance and events.
Class II System Audits
From Part 543: • Should include other external standards such as GAAP, GAAS, etc. • Accounting • Internal Audit • Annual requirements
Accounting
• Record gaming activity from an accounting system to identify and track all revenues, expenses, assets, liabilities, and equity • Record all markers, IOU’s, returned checks, held checks, or other instruments • Record journal entries prepared by the gaming operation and/or any independent accountants
Accounting
• Prepare income statements and balance sheets • Prepare appropriate ledgers to support balance sheets • Review segregated functions, duties, and responsibilities • Review minimum bankroll calculations • Review preservation of financial records and supporting documentation
Internal Audit
• Bingo
– Supervision – Bingo cards and sales – Draw – Prize payout – Cash & equivalent controls – Technologic aids to the play of Bingo – Operations – Vouchers/Tickets – Revenue audit procedures
Internal Audit
• Pull-tabs
– Supervision – Pull-tab inventory & sales – Winning pull-tabs – Pull-tab operating funds – Statistical records – Revenue audit procedures
Internal Audit
• Card games – Supervision
– Exchange or transfers – Playing cards – Shill funds – Reconciliation of card room bank – Posted rules – Progressive pots and pools
Internal Audit
• Information Technology – Supervision
– Class II logical & physical controls – Independence – Physical & logical security – User controls – Installations and/or modifications – Remote access controls – Incident monitoring and reporting – Data backups – Software downloads
Internal Audit
• Gaming promotions • Player tracking procedures • Complimentary services or items • Patron deposit accounts • Lines of credit • Drop and count standards • Cage, vault, cash & equivalent procedures • Accounting standards
UNDERSTANDING MATH ANALYSIS FOR PAYOUT PERCENTAGES AND ODDS
JUNE LIGHT – DIRECTOR MATHEMATICS, BMM TESTLABS
Overview
Why is Class II Math important?
How is Class II Math is evaluated? • Understanding of PAR • What is a PAR Sheet • Primary Uses • Terminology/Components of a PAR Sheet • Volatility • PAR Sheet evaluation
Purpose of Class II Math Evaluations
Two Primary Purposes:
1. Verify that all jurisdictional requirements are met (i.e. min/max RTP, Odds)
2. Ensure that the manufacturer’s stated math calculations are correct (i.e. RTP, volatility) WHY?
Minimum Math Requirements
25 CFR § 547.4
(a)Fairness. No Class II gaming system may cheat or mislead users. All prizes advertised must be available to win during the game. A test laboratory must calculate and/or verify the mathematical expectations of game play, where applicable, in accordance with the manufacturer stated submission. The results must be included in the test laboratory’s report to the TGRA. At the request of the TGRA, the manufacturer must also submit the mathematical expectations of the game play to the TGRA.
Minimum Math Requirements
25 CFR § 547.4
(a)Fairness. No Class II gaming system may cheat or mislead users. All prizes advertised must be available to win during the game.
Why is Class II Math important?
25 CFR § 547.4
(a)Fairness. No Class II gaming system may cheat or mislead users. All prizes advertised must be available to win during the game. A test laboratory must calculate and/or verify the mathematical expectations of game play, where applicable, in accordance with the manufacturer stated submission. The results must be included in the test laboratory’s report to the TGRA. At the request of the TGRA, the manufacturer must also submit the mathematical expectations of the game play to the TGRA.
Why is Class II Math important?
25 CFR § 547.4
(a)Fairness. No Class II gaming system may cheat or mislead users. All prizes advertised must be available to win during the game. A test laboratory must calculate and/or verify the mathematical expectations of game play, where applicable, in accordance with the manufacturer stated submission. The results must be included in the test laboratory’s report to the TGRA. At the request of the TGRA, the manufacturer must also submit the mathematical expectations of the game play to the TGRA.
Why is Class II Math Important?
25 CFR § 547.16
(c) Odds notification. If the odds of winning any advertised top prize exceeds 100 million to one, the Player Interface must display: “Odds of winning the advertised top prize exceeds 100 million to one” or equivalent.
What does PAR stand for?
Several Different Acronyms
• Percentage of Actual Return • Pay Table And Reel Strips • Player Average Return • Probability Accounting Report
What is a PAR sheet?
What is a PAR sheet? • Details how the math of a bingo game (or similar) is designed • Prize Schedule, Bingo Patterns, and Game Information • Hit rates, progressive info, and top awards • Game volatility and performance characteristics Typically 2 Types: • Detailed PAR sheets - demonstrate how each mathematical calculation was derived in the game • Operator/Summary PAR sheets - summarize the key aspects of the product
Primary Uses for PAR sheets
Regulatory Uses
• Verifies that the Top Award is compliant • Prize Schedule, Bingo Patterns, and Game Information • Testing and Certification of the product
Operational Uses
• Analyze slot performance (Theo vs. Actual) • Game performance over time • Setup and configuration of the product
Strategic Uses
• Segment marketing • (Re)Configuration of the games to maximize revenue
Terminology / Components of a PAR sheet
General Game information – Game theme name, Prize Schedule, Bingo Patterns, and Game Information RTP – Return to player, two main types: theoretical and actual Theoretical RTP - The % of all wagers paid back to the player in a complete game cycle Actual RTP - The % of all wagers actually paid back to players on a particular game, calculated by (money out/money in)
Theoretical House Edge – the amount the house will theoretically receive, typically calculated by 100% - Theoretical RTP
Odds (expressed as 1 in number) – How many times a particular combination (either prize or award) occurs over the cycle of the game. Ex. If a specified prize can occur 500 times from a game cycle of 10,000 then the odds are 1 in 21 (20+1)
Terminology / Components of a PAR sheet
Cycle - The number of all possible unique bingo game outcomes
Probability - The probability that of an outcome occurring (inverse of the odds)
Expected Value (EV) - The probability of an event multiplied by the award for that event
Hits – the number of occurrences of a bingo pattern within the game cycle
Hit Rate – The amount of games expected to trigger a particular outcome
Volatility
Game Volatility: Winning/losing behavior over a period of time, varies by how the game math is structured Example: Dice game, three different pay tables, same RTP (not craps) pays for rolling a pair of dice
Paytable 1
Paytable 2
Paytable 3
Outcome Hits
Pay
Total Pay EV
Outcome Hits
Pay
Total Pay EV
Outcome Hits
Pay
Total Pay EV
2
1
1
1 2.78%
2
1
0
0 0.00%
2
1
3
3 8.33%
3
2
1
2 5.56%
3
2
0
0 0.00%
3
2
2
4 11.11%
4
3
1
3 8.33%
4
3
0
0 0.00%
4
3
1
3 8.33%
5
4
1
4 11.11%
5
4
0
0 0.00%
5
4
0
0 0.00%
6
5
1
5 13.89%
6
5
0
0 0.00%
6
5
0
0 0.00%
7
6
0
0 0.00%
7
6
5
30 83.33%
7
6
0
0 0.00%
8
5
1
5 13.89%
8
5
0
0 0.00%
8
5
0
0 0.00%
9
4
1
4 11.11%
9
4
0
0 0.00%
9
4
0
0 0.00%
10
3
1
3 8.33%
10
3
0
0 0.00%
10
3
1
3 8.33%
11
2
1
2 5.56%
11
2
0
0 0.00%
11
2
1
2 5.56%
12
1
1
1 2.78%
12
1
0
0 0.00%
12
1
15
15 41.67%
Total
36
RTP
83.33%
Total
36
RTP
83.33%
Total
36
RTP
83.33%
Winning
30
Winning
6
Winning
12
Combinations
Combinations
Combinations
Win Rate
83%
Win Rate
17%
Win Rate
33%
Volatility Index
Expected performance of the machine based on the number of games played. Based on a confidence interval. Allows you to compare actual performance to theoretical performance.
PAYTABLE 1 90% Volatility Index
95% Volatility Index
Games
Min % Max %
Games
Min % Max %
1,000
80.57% 100.23%
1,000
78.72% 102.08%
10,000 87.29% 93.51%
10,000
86.70% 94.09%
100,000 89.41% 91.38%
100,000
89.23% 91.57%
1,000,000 90.09% 90.71%
1,000,000 90.03% 90.77%
10,000,000 90.30% 90.50%
10,000,000 90.28% 90.51%
PAR Sheet Evaluation - Bingo
Bingo Prize Schedule
PAR Sheet Evaluation - Bingo
PAR Sheet Evaluation - Bingo
Bingo Prize Schedule
PAR Sheet Evaluation - Bingo
PAR Sheet Evaluation - Bingo
PAR Sheet Evaluation - Bingo
PAR Sheet Evaluation - Bingo
• (c) Odds notification. If the odds of winning any advertised top prize exceeds 100 million to one, the Player Interface must display: “Odds of winning the advertised top prize exceeds 100 million to one” or equivalent.
Bingo Math
• The math behind bingo is important. • How can it be used on the floor?
PAYTABLE 1 90% Volatility Index
95% Volatility Index
Games
Min % Max %
Games
Min % Max %
1,000
80.57% 100.23%
1,000
78.72% 102.08%
10,000
87.29% 93.51%
10,000
86.70% 94.09%
100,000 89.41% 91.38%
100,000
89.23% 91.57%
1,000,000 90.09% 90.71%
1,000,000
90.03% 90.77%
10,000,000 90.30% 90.50%
10,000,000 90.28% 90.51%
Final Thoughts
PAR Sheets are a powerful operational tool • Monitor performance • Know what to expect from the machine Strategic use of PAR Sheets may require the assistance of data analytics and experimentation • What type of play am I getting on my games now? • Are my games high volatility or low volatility • What type of customers do I have? • What type of games do my customers prefer to play? • How does floor traffic play into this?
Understanding Math Analysis Payout Percentages and Odds
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In the beginning
It was a simpler time…
• Consideration • Risk • Reward
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What is?
RTP – Return to player, two main types: theoretical and actual • Theoretical RTP – The percent(%) of all wagers paid back to the player in a complete game cycle • Actual RTP – The percent(%) of all wagers actually paid back to players on a particular game, calculated by (money out / money in)
Odds (expressed as 1 in number) • How many times a particular combination (either prize or award) occurs over the cycle of the game. Example: If five (5) “Wild” symbols can occur 500 times from a game cycle of 10,000 then the odds are 1 in 21
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Why is Slot Math important?
Jurisdictional Requirements (RTP) • Each game shall theoretically payout a minimum of eighty percent (80%) during the expected lifetime of the game (i.e. progressives, bonus systems, merchandise, etc. shall not be included in the percentage payout if they are external to the game).
• The calculation of minimum payout percentage excludes the cash equivalent value of any merchandise or other thing of value that cannot be converted into cash by the gaming establishment but may include the acquisition cost to the gaming licensee of the merchandise or other thing of value.
company confidential
Why is Slot Math important?
Jurisdictional Requirements (odds) • The highest single advertised payout on each gaming device shall occur, statistically, at least once in 50,000,000 games. This does not apply to multiple awards won together on the same game play where the aggregate prize is not advertised. This odds rule shall not apply to games which make it possible for a player to win the highest win, multiple times through the use of free games. This rule does apply to each wager that wins the maximum award. If the highest advertised award can occur within a bonus or free game feature, the odds calculation shall include the odds of obtaining the bonus round including the odds to achieve the top award.
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Other Requirements
• Inge S. Telnaes
• US Patent Number 4,448,419 • Electronic gaming device utilizing a random number generator for selecting the reel stop positions.
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Other Requirements
Game Volatility
• Game volatility is the expression used to describe the frequency of prize payouts based on the hit table. A low volatile game provides the player with a steady flow of smaller prizes whereas a game with high volatility typically gives the player higher value and more erratic prizes. • Some jurisdictions restrict games based on volatility by requiring the minimum payout percentage to be achieved in X games based on an assumed number of plays per year. • Ontario § 20.2.1 - The intent of the following standards are to avoid potentially large deviations of a game’s actual payback from its theoretical payback, and to achieve the minimum required payback within the game’s expected lifetime.
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Other Requirements
Ontario 20.3 Award Odds • 20.3.1 The top award must not have odds exceeding 17 million : 1. All other awards and accumulated awards displayed on the gaming equipment must not have odds exceeding 34 million : 1.
New Jersey 13:69E‐1.28A • Standards for the approval of a slot machine game • (c) Slot machines shall not offer a play with odds greater than 100 million to 1.
Nevada Reg 14 Tech Standards • 2.070 Jackpot Odds. If the odds of hitting any advertised jackpot that is offered by a gaming device exceeds 100 million to one, the odds of the advertised jackpot must be prominently displayed on the award glass or video display.
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Other Requirements
13:69E-1.28A Standards for the approval of a slot machine game • (d) The theoretical RTP of a slot machine game shall not decrease by more than one-hundredth of a percentage point with an increased wager unless the aggregate total of the decreases in theoretical RTP for plays offered by the slot machine game is no more than one-half of one percent.
Straight Flush 5 Coin wager
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Other Requirements
13:69E-1.28A Standards for the approval of a slot machine game What’s not included in calculating RTP: (e) The following shall not be included as a payout when determining the theoretical RTP of a slot machine: A payout of merchandise or thing of value; (in-lieu-of exceptions)
A complimentary; or A limited time payout.
Cash in lieu of merchandise must equal the minimum value for the RTP.
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Other Requirements
13:69E-1.28A Standards for the approval of a slot machine game
• (i) When a slot machine offers a play which permits a patron to risk an award or make a subsequent wager as an extension of a game outcome, the slot machine shall: • Only allow the patron to risk an award if the award can be increased as a result of continued play; and • Disclose the optimal strategy or provide mathematically sufficient information for the patron to derive optimal strategy if the choice affects the theoretical RTP of the slot machine.
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Volatility
Game Volatility • Winning/losing behavior over a period of time, varies by how the game math is structured Example: Dice game, three different pay-tables, same RTP (not craps) pays for rolling a pair of dice
Pay table 1
Pay table 2
Pay table 3
Outcome Hits
Pay
Total Pay
EV
Outcome Hits
Pay
Total Pay EV
Outcome Hits
Pay
Total Pay EV
2
1
1
1 2.78%
2
1
0
0
0.00%
2
1
3
3
8.33%
3
2
1
2 5.56%
3
2
0
0
0.00%
3
2
2
4
11.11%
4
3
1
3 8.33%
4
3
0
0
0.00%
4
3
1
3
8.33%
5
4
1
4 11.11%
5
4
0
0
0.00%
5
4
0
0
0.00%
6
5
1
5 13.89%
6
5
0
0
0.00%
6
5
0
0
0.00%
7
6
0
0 0.00%
7
6
5
30
83.33%
7
6
0
0
0.00%
8
5
1
5 13.89%
8
5
0
0
0.00%
8
5
0
0
0.00%
9
4
1
4 11.11%
9
4
0
0
0.00%
9
4
0
0
0.00%
10
3
1
3 8.33%
10
3
0
0
0.00%
10
3
1
3
8.33%
11
2
1
2 5.56%
11
2
0
0
0.00%
11
2
1
2
5.56%
12
1
1
1 2.78%
12
1
0
0
0.00%
12
1
15
15
41.67%
Total
36
RTP
83.33%
Total
36
RTP
83.33%
Total
36
RTP
83.33%
Winning
30
Winning
6
Winning
12
Combinations
Combinations
Combinations
Win Rate
83%
Win Rate
17%
Win Rate
33%
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Volatility Index
• Expected performance of the machine based on the number of games played based on a confidence interval. Allows you to compare actual performance to theoretical performance.
PAYTABLE 1 90% Volatility Index
95% Volatility Index
Games
Min % Max %
Games
Min % Max % 78.72% 102.08% 86.70% 94.09%
1,000 80.57% 100.23% 10,000 87.29% 93.51% 100,000 89.41% 91.38% 1,000,000 90.09% 90.71%
1,000
10,000
100,000 89.23% 91.57% 1,000,000 90.03% 90.77%
10,000,000 90.30% 90.50%
10,000,000 90.28% 90.51%
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Volatility Spreadsheet
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What does PAR stand for?
Several Different Acronyms • Percentage of Actual Return • Pay Table and Reel Strips • Player Average Return • Probability Accounting Report
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Terminology
PAR Sheets • Contains game theme name, number of lines, reel strip layout, winning combinations, symbol count RTP • Return to player, two main types: theoretical and actual • Theoretical RTP - The % of all wagers paid back to the player in a complete game cycle • Actual RTP - The % of all wagers actually paid back to players on a particular game, calculated by (money out/money in) House Edge • the amount the house will theoretically receive, typically calculated by 100% - RTP Odds (expressed as 1 in number) • How many times a particular combination (either prize or award) occurs over the cycle of the game. Ex. If 5 “Wild” symbols can occur 500 times from a game cycle of 10,000 then the odds are 1 in 21
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Terminology
Cycle • The number of all possible unique game outcomes Probability • The probability that of an outcome occurring (inverse of the odds) Expected Value (EV) • The probability of an event multiplied by the award for that event Hits • the number of occurrences of a combination within the game cycle Hit Rate • The amount of games expected to trigger a particular outcome Optimal Strategy • used to describe a strategy for playing games that will return the highest payback, typically used for video card type games
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General Math Characteristics
What are the core mathematical characteristics? 1. RNG outcomes used to determine reel-strip stops. 2. Awards are based on reel-strip combinations matching the pay-table. 3. Additional features (bonuses, free games, etc.) are treated as part of a single game (variable pay winning combinations) 4. Progressives may or may not be separate from the base game 5. Game volatility determined by pay table probabilities 6. Game RTP determined by overall pay table (including features), and corresponding probabilities of each award 7. Hit frequency is the ratio of all winning combinations to total combinations
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Items Included for Math Evaluations
Math items used for review includes: • Artwork • Game Description • Help Screens • Source Code (math portion, or the entire game) • PAR Sheets
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PAR Sheets
What purposes do PAR Sheets serve? • Game Numerical Analysis Summary • Return To Player Percentage (RTP%) • Volatility • Odds for prizes/awards • Hit Frequency • Display Information • Reel Strip Information •
Game Rules (Advertised Game Rules, etc.) • Bonus Feature Description/Mathematics (If Applicable) • Free Games • Bonus Games • Progressive Information (If Applicable) • The contribution rate.
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PAR Sheet Review
PAR Sheet Review includes the verification of: • Cycle – typically no regulated limits, per se • Return to Player (i.e.. 90%) or the House Hold • Odds of top award (e.g. 1 in 50,000,000) • Live game Correlation (Poker, Baccarat, Black Jack) • Pays match the help screens • Math implementation into the source code (reel strips, pay tables, pay and bonus features) • Other game math requirements depending on technical standards
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PAR Sheet Example
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PAR Sheet Example – Base Game
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PAR Sheet Example – Base Game
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PAR Sheet Example – Base Game
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PAR Sheet Example – Base Game
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PAR Sheet Example – Bonus #1
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PAR Sheet Example – Bonus #1
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PAR Sheet Example – Bonus #1
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PAR Sheet Example – Bonus #1
• Average Contribution of Bonus • = (Prob. of Triggering Bonus) * (Avg. # FS) * (Avg. Multiplier) * (Bonus Game EV)
• = (0.000438099) * (15) * (1) * (306.531220%) = 2.014%
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PAR Sheet Example – Bonus #2
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PAR Sheet Example – Odds
• Top Award Odds
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PAR Sheet Example – Odds
• Top Award Odds
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PAR Sheet Example – Odds
• Top Award Odds
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PAR Sheet Example – Odds
• Top Award Odds
• 1 in 22,322,517
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Poker Calculations
• Jacks or Better
Hand
Prize
Royal Flush
300
Straight Flush Four of a Kind
50 25
Full House
7 5 4 3 2 1 0
Flush
Straight
Three of a Kind
Two Pair
Jacks or Better
Others
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Poker Calculations
How to calculate the RTP of this game? • Start with all possible initial five (5) card hands. • There are approximately 2.5 million. • For each of the initial nine (9) hands evaluate all possible ways to play the hand (1 deck = 32 ways).
If starting hand is As Qs Js 7s 2h 1._ _ _ _ _ (discard all cards) – 1 way 2.As _ _ _ _ (discard 4) – 5 ways 3.As Qs _ _ _ (discard 3) – 10 ways 4.As Qs Js _ _ (discard 2) – 10 ways 5.As Qs Js _ 2h (discard 1) – 5 ways 6.As Qs Js 7s 2h (discard 0) – 1 ways
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Poker Calculations
How to calculate the RTP of this game? • For each of the ways, count how many times each hand in the pay-table can be achieved to obtain the hits. • Example: As Qs Js 7s 2h
Jacks or Better
Held Cards
RF SF 4K FH Fl
Str
3K 2P
Other
__ __ __ __ __ 3 26 344 2,124 3,463 6,547 31,502 71,802 157,584 1,260,544
As Qs Js __ __ 1
35 15
9
27
348
646
As Qs Js 7s __
9
9
29
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Poker Calculations
How to calculate the RTP of this game?
Outcome
Prize
Hits
Probability
EV
Royal Flush
300
34,233,681
0.000021
0.006183
Straight Flush
50
174,621,153
0.000105
0.005256
Four of a Kind
25
3,925,527,663
0.002363
0.05908
Full House
7
19,122,223,647
0.011512
0.080582
Flush
5
18,901,530,366
0.011379
0.056895
Straight
4
18,879,205,390
0.011365
0.045462
Three of a Kind
3
123,582,572,007
0.074398
0.223194
Two Pair
2
214,420,059,063
0.129083
0.258166
Jacks or Better
1
357,649,448,799
0.215308
0.215308
All Other
0
904,413,121,331
0.544466
0
RTP 0.950126
Totals
1,661,102,543,100
1
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Additional Requirements
Relevant Technical Requirements • GLI-11 v3.0 § 4.5.4 Live Game Correlation . Unless otherwise denoted in the game artwork, where the gaming device offers a game that is recognizable as a simulation of a live casino game such as poker, blackjack, roulette, etc., the same probabilities associated with the live game shall be evident in the simulated game. For example, the odds of getting any particular number in roulette where there is a single zero (0) and a double zero (00) on the wheel, shall be 1 in 38; the odds of drawing a specific card or cards in poker shall be the same as in the live game.
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Additional Requirements
Relevant Technical Requirements • GLI-11 v3.0 § 4.8.1 Software Requirements for Percentage Payout . a) Gaming devices that may be affected by player skill shall meet the requirements of this section when using an optimal method of play that provides the greatest return to the player over a period of continuous play.
Note: At the discretion of the regulatory agency, the independent test laboratory can apply an alternative approach to return percentage calculations.
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Best Method for Math Evaluations
Theoretical vs. Simulations results • Theoretical calculation: • Pros • Exact theoretical results
• The formulas/calculations can be verified
• Cons • Not always feasible when game rules/logic are complex • Time consuming when game rules/logic are complex
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Best Method for Math Evaluations
Theoretical vs. Simulations results • Simulation (matches game implementation): • Pros • Verify theoretical results • Faster/easier than calculations • Cons • Results have a variance
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Review
Par Sheet Formulas: • Cycle • The total number of possible outcomes of the base game. • Prize Probability • The number of specific occurrences out of all possible outcomes. • Odds • Given all of the possible outcomes with regards to a specific occurrence. • Expected Value (EV) • The expected value of an individual prize or group of prizes. • RTP • The sum of the expected values of all prizes.
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Review
Math implementation into Source Code: • Verify the following are implemented in the source code properly: • Reel Strips • Weighted tables • Basic rules of the game
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