2. HOW TO PLAY CASINO OVER UNDER
Place an ante and bonus (optional) to get one card face up.
After seeing the card, either fold and lose the ante or match the amount of your ante and
place those chips in the spot marked over 23 or under 18. Aces are always worth 11.
The three card total resolves all wagers. The base over under ante and declaration pay even
money and the bonus pays in accordance with the paytable being used.
BEST FEATURES
Best hands/hour pace in table games.
Players pick it up in seconds and it doesn’t take them long to get comfortable playing.
The house can determine the exact HA they desire by modifying the number of decks
and/or modifying the pay table.
Thus far almost all players have played the base game and the bonus together as opposed
to just playing the base over/under game alone.
Dealers are efficiently trained with ease.
3. Which is the best game for beginners?
Casino Over Under® is less intimidating. The game was purposefully created in a way that
no player can possibly make a mistake that could cost another player a win.
Although both games are easy, Casino Over Under® is much easier to play optimally.
More winning = Happier players!
There are fewer decisions in Casino Over Under® and unlike Blackjack most of the
decisions in Casino Over Under® are no-brainers.
Since the values of the cards are the same with the exception of aces always being 11,
Casino Over Under® is a great counting game that will prepare players to eventually play
Blackjack.
The Ultimate Starter Game
It makes no sense for players to get fed to the wolves by playing Blackjack as their first
experience.
MGM Resorts already intelligently does a fantastic job of prepping their new players by
offering classes. Why not have a beginner game for them to get their feet wet?
If a person puts skis on for the first time they aren’t going straight to the intermediate
course after their first course on the basics. Rather, they go to the bunny slope because it
is less intimidating and easier. Casino Over Under® wishes to be the bunny slope of the
table games industry.
4. APPEALING TO MILLENNIALS
CASINO OVER UNDER®IS A GREAT WAY TO ATTRACT MILLENNIALS
Casino Over Under® was first released as an app and has been downloaded tens of
thousands of times in over 50 countries world-wide. Having it offered in MGM Resorts
casinos will give millennials a game they are familiar with. Also, it will undoubtedly
increase the credibility of the brand dramatically which will help both Casino Over Under®
and MGM Resorts.
Presently, the mobile app version of the game has an overall rating of 4.8 out of 5.0.
Although Millennials have gambled it has been mostly on fantasy sports and sports
gambling as opposed to traditional pit games. Casino Over Under® is essentially the
over/under wager from sports as a card game.
It’s been said that Millennials appreciate transparency. Casino Over Under® is a simple
game that clearly shows them where their money is coming and going.
Many casinos have added clubs and restaurants to attract Millennials. Casino Over Under®
is the ultimate game for such an atmosphere given its simplicity.
5. Casino Over Under® has an account/page on all eleven of the social media sites listed in
this chart including 47,100 followers on Twitter alone.
Implementing Casino Over Under® into your MGM Resorts casinos will quickly cause a
domino-type reaction that should increase footfall in little time. Casino Over Under®’s
already potent social media presence will increase exponentially being associated with such
a brand which should in turn snowball to the benefit of both Casino Over Under® and
MGM Resorts by attracting Millennials.
6. World Headquarters
600 Airport Road
Lakewood, NJ 08701
Phone (732) 942-3999
Fax (732) 942-0043
www.gaminglabs.com
Worldwide Locations
World Headquarters
Lakewood, New Jersey
U.S. Regional Offices
Colorado
Nevada
International Offices
GLI Africa
GLI Asia
GLI Australia Pty Ltd
GLI Austria GmbH
GLI Europe BV
GLI Italy
GLI South America
January 26, 2016
Mr. Jason Kobal, President
Casino Over Under LLC
12169 West Linebaugh
Tampa, Florida 33626
Scope of Evaluation: Mathematical Analysis of Over/Under (Gaming
Laboratories International, LLC Proposal
#LO-20151112-02 dated November 12, 2015)
REF: LO-00-CVU-16-01
Evaluating Location
GLI-1/GLI-2
Nevada Registration Number: 31668-01
Dear Mr. Kobal,
As per Casino Over Under LLC’s request, please find Gaming
Laboratories International, LLC’s (GLI) analysis of the table game,
Over/Under to be submitted to and reviewed by the Nevada Gaming
Control Board for determination as to its suitability.
Game Description
Over/Under is a game played with six standard 52-card decks,
accommodating up to six players. At the beginning of each round,
each player makes a mandatory Ante wager. Each player may also
place an optional Bonus wager up to the amount of the Ante wager.
After all wagers have been placed, the dealer will deal one face-up
card to all players. Each player may fold, place an Under wager, or
place an Over wager. The Under wager and Over wager must be the
same size as the Ante wager. If the player folds, the Ante wager is lost
and the Bonus wager remains in play. The dealer will then deal two
additional cards to each player. The player’s score is calculated by
summing up the point values of all three cards. Cards two though ten
award their face value in points, face cards award ten points and Aces
award eleven points.
7. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Page 2 of 8
If the player has placed the Under wager and the player’s score is less than 17.5, the
player is paid 1 to 1 on both the Ante and Under wagers. Otherwise, the Ante and Under
wagers are lost.
If the player has placed the Over wager and the player’s score is greater than 23.5, the
player is paid 1 to 1 on both the Ante and Over wagers. Otherwise, the Ante and Over
wagers are lost.
After the Over and Under wagers have been resolved, the Bonus wager is resolved based
on the player’s score. The Bonus wager paytable is provided here in Table 1.
Table 1. Over/Under Bonus Paytable A
Score Pays
6 or 33 50 to 1
7 or 32 10 to 1
8 or 31 5 to 1
9 or 30 4 to 1
10 or 29 3 to 1
11 or 28 2 to 1
12 or 27 1 to 1
13 to 26 Loss
Mathematical Analysis
The mathematical analysis of Over/Under was performed analytically. A computer
program was developed to loop through all initial player hands and record the final score
hits based on the score of the first card. For each initial card score, the optimal strategy
was determined. Table 2 summarizes the optimal strategy.
8. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Page 3 of 8
Table 2. Over/Under Base Game Optimal Strategy
First Card Score Optimal Strategy
2 Place Under Wager
3 Place Under Wager
4 Place Under Wager
5 Place Under Wager
6 Place Over Wager
7 Place Over Wager
8 Place Over Wager
9 Place Over Wager
10 Place Over Wager
11 Place Over Wager
Using the optimal strategy and the results from the program, the probabilities of winning
while following optimal strategy were calculated. The results can be found in Table 3
below. The Return to Player (RTP) and House Edge (HE) for the optimal strategy are in
summarized Table 4.
Table 3. Over/Under Base Game Probabilities of Winning
Initial Score Probability
2 0.56561
3 0.48196
4 0.39508
5 0.30049
6 0.28528
7 0.35449
8 0.43093
9 0.51358
10 0.60195
11 0.69655
Table 4. Over/Under Base Game RTP/HE Summary
Figure Percentage
RTP 98.95%
HE Per Total Wager 1.05%
HE 2.10%
The RTP is calculated as the ratio of the player’s average winnings with respect to the
average units wagered per game. HE per total wager is the ratio of the average wagers
that the player has lost with respect to the average units wagered per game. HE is the
ratio of the average wagers that the player has lost with respect to the initial bet.
9. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Page 4 of 8
Using the results from the program detailed above, the RTP of the Bonus wager was
calculated. Table 5 summarizes the results for the Bonus wager. Table 6 shows the Bonus
wager RTP and HE.
Table 5. Over/Under Bonus Wager Probabilities
Outcome Probability
6 or 33 0.00081
7 or 32 0.00661
8 or 31 0.02579
9 or 30 0.04533
10 or 29 0.04222
11 or 28 0.05170
12 or 27 0.06233
13 or 26 0.76520
Table 6. Over/Under Bonus Wager RTP/HE Summary
Figure Paytable A
RTP 94.39%
HE 5.61%
Summary
Individuals who decide to play Over/Under will observe an RTP of 98.95%,
corresponding to a HE of 2.10% and an HE per total bet of 1.05%, when using optimal
strategy. The optimal strategy is to place the Under wager when the score of the initial
card is five or less, and to place the Over wager when the score of the initial card is
greater than or equal to six.
Since the Bonus wager has a positive house edge, it is never in the player’s interest to
place the Bonus wager. The Bonus wager has an RTP of 94.39%, which corresponds to a
HE of 5.61%.
Concerns Identified:
The following concerns were raised during the evaluation of the aforementioned
game. The details are as follows:
· NONE
10. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Page 5 of 8
Conclusion
Gaming Laboratories International, LLC attests that it has reviewed the mathematics
of the game as submitted by Casino Over Under LLC and has performed an independent
review of the game play to confirm that the submission documents are accurate.
Please refer to the attached Terms and Conditions which apply to the information
being provided herein.
Should you have any questions or need any additional information, please feel
free to contact our office.
Sincerely,
GAMING LABORATORIES INTERNATIONAL, LLC
Christine M. Gallo
Vice President of Technical Compliance and Quality Assurance
Enclosure
ko
11. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Page 6 of 8
Terms and Conditions
This Report is issued solely for the benefit of the Recipient for the specific
jurisdiction referenced in this Report, and may not be relied upon for any reason by any
person or entity other than the Recipient including, but not necessarily limited to, the
manufacturer and/or developer of the items (a “Third Party”) which are the subject of this
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12. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Page 7 of 8
The certification established by this Report applies exclusively to tests conducted
using current and retrospective methods developed by Gaming Laboratories
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13. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Page 8 of 8
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CONSTRUED TO IMPLY ANY ENDORSEMENT OR WARRANTY REGARDING
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RESPONSIBILITY OF THE RECIPIENT AND GLI EXPRESSLY DISCLAIMS ANY
LIABILITY WHATSOEVER IN CONNECTION WITH SUCH THIRD PARTY
RIGHTS AND REMEDIES. GLI AND THE RECIPIENT ACKNOWLEDGE AND
AGREE THAT THE SERVICES PROVIDED BY GLI HEREUNDER COULD NOT
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notices implemented or issued by the NGCB.
15. Mr. Jason Kobal
Over/Under
LO-00-CVU-16-01-394
January 26, 2016
GLI-1/GLI-2
Appendix I, Page 2 of 2
Nevada Test Cases Evaluated and Test Results:
Test Cases Relating to Return Percentage:
Test Case Version Test Results
14.040.1 1.0 Pass À
À Please note that the test case listed above is related to Gaming Devices and
may factor into determination of suitability for Nevada.
16. June 29, 2015
Mathematical analysis
of
Over/Under
prepared for
Jason Kobal
by
Joseph Shipman, Ph.D.
Shipman Game Consulting
P.O. Box 443, Rocky Hill, NJ 08553
609-216-2182
ShipmanGameConsulting@gmail.com
17. Introduction
Over/Under is a new casino table game, played using a shoe containing standard decks of cards,
in which players, after seeing the first card of a 3-card hand, bet that it will have a point total
over or under given targets. Players may also make an optional side bet which pays based on the
3-card total, before any cards are dealt. This report analyzes the House Edge and Optimal
Strategy for various versions of the game, including a detailed card counting analysis for one
particular version.
Rules of Play
The game begins with players making an Ante bet and, if they choose, an optional Bonus bet,
which may not exceed the amount of the Ante bet. The dealer gives each player one card, face-
up, from a shoe (an 8-deck shoe is used for the mathematical analysis, but the game can also be
played with other sizes of shoe). After receiving this card, players may choose to fold, losing
their Ante bet, or to make a Raise bet equal in size to the Ante bet. The Raise bet is placed in
either an "Over" or an "Under" betting area. Players are then each dealt two more cards.
The 3-card total point value of a player's hand is the sum of the pips on the numbered cards 2
through 10, plus 11 for each Ace and 10 for each face card (in other words, the same as
Blackjack scoring except Aces are always "high"). The "Over target" and "Under target"
numbers, which may be whole numbers or fractional numbers such as 17 1/2, are displayed on
the table felt or on a placard.
Players choosing "Over" are paid even money on their Ante and Raise bets if their total exceeds
the "Over" target number, lose their Ante and Raise bets if their total is less than the target
number, and push both bets if their total equals the target (which is only possible if the target is a
whole number, fractional targets never push).
Similarly, players choosing "Under" are paid even money on their Ante and Raise bets if their
total is less than the "Under" target number, lose their Ante and Raise bets if their total exceeds
the target number, and push both bets if their total equals the target (which is only possible if the
target is a whole number).
Players who folded their Ante bet but made a Bonus bet are still given their 2nd and 3rd cards so
that the Bonus bet may be settled.
If players made the optional Bonus bet, it is paid according to one of the following two pay
tables:
18. Bonus Pay Table A
6 or 33 50 to 1
7 or 32 10 to 1
8 or 31 5 to 1
9 or 30 4 to 1
10 or 29 3 to 1
11 or 28 2 to 1
12 or 27 1 to 1
13 through 26 -- Loss
Bonus Pay table B
6 or 33 50 to 1
7 30 to 1
8 20 to 1
9 15 to 1
32 10 to 1
10 5 to 1
11 4 to 1
12 3 to 1
31 2 to 1
13 or 26-30 1 to 1
12 through 25 -- Loss
19. Analysis
This game was analyzed in an Excel spreadsheet using combinatorial mathematics and
probability. Several different sets of targets were used (all numbers are for an 8-deck shoe), but
the first configuration is the recommended one:
Target Score House Edge
Over Under Optimal Strategy Average bet (% of Ante) (% of Total Bet)
23 1/2 17 1/2 Under 5, Over 6 2 1.96% 0.98%
23 16 Under 4, Over 5 2 3.72% 1.86%
24 1/2 19 Under 6, Over 7 2 5.43% 2.72%
23 15 1/2 Under 3, Fold 4, Over 5 1.92 6.72% 3.50%
25 19 1/2 Under 6, Over 7 2 7.27% 3.64%
23 1/2 17 Under 5, Over 6 2 7.44% 3.72%
24 18 Under 6, Over 7 2 8.01% 4.01%
25 1/2 20 Under 7, Over 8 2 8.65% 4.32%
24 18 1/2 Under 6, Over 7 2 1.36% 0.68%
25 1/2 20 1/2 Under 8, Over 9 2 0.68% 0.34%
The Bonus bet has a House Edge of 5.29% for Pay Table A, and 3.73% for Pay Table B.
Card Counting Analysis
Because the game is played from a shoe, the composition of the cards changes over time. A
player who "counts cards" and adjusts his initial bet size or his strategy accordingly has the
possibility of gaining an advantage. 12,200 random 8-deck shoes were generated, and the 23 1/2
/ 17 1/2 game configuration, which is one of the most favorable ones for the player, was used.
Players were assumed to know the exact composition of the shoe at each stage, and to start play
at the beginning of the shoe (if players are allowed to jump in at any point without the shoe being
shuffled, they may gain an arbitrarily large advantage). Seven strategies were analyzed:
20. Card Counting Strategy 1 (pay table A or B):
Do not change bet size, but play the bonus bet only if it is profitable to do so
Strategy 2:
Play only the base game, bet 1 unit when the shoe is unprofitable and 2 units when profitable.
Strategy 3 (pay table A or B):
Play the base game, betting 1 unit when the shoe is unprofitable and 2 units when profitable, and
play the bonus game using a separate count whenever it is profitable.
Strategy 4 (pay table A or B):
When the bonus game is more profitable than the AVERAGE base game is unprofitable, play
both games betting 2 units, otherwise play only the base game betting 1 unit (this strategy is
easier to play than Strategy 3 because it only requires keeping one kind of count).
Strategy 5:
Play only the base game, bet 1 unit when the shoe is unprofitable and 5 units when profitable.
Strategy 6 (pay table A or B):
Play the base game, betting 1 unit when the shoe is unprofitable and 5 units when profitable, and
play the bonus game using a separate count whenever it is profitable.
Strategy 7 (pay table A or B):
When the bonus game is more profitable than the AVERAGE base game is unprofitable, play
both games betting 5 units, otherwise play only the base game betting 1 unit (this strategy is
easier to play than Strategy 6 because it only requires keeping one kind of count).
Note that although strategy 3 (6) is more mathematically effective than strategies 2 (5) and 4 (7),
it is much more difficult to carry out, because the player must keep track of two separate
"counts". There is a very small correlation (a correlation coefficient of approximately 0.1)
between the House Edge in the base game and the House Edge in the Bonus game. For the base
game, the player can capture most of the advantage with a simple count that gives 2,3,4,5,6,7 a
weight of +1 and 9,10,J,Q,K,A a weight of -1. For the Bonus game, the best count weights
middle-value cards positively and high and low cards negatively.
Interestingly, although Pay Table A is better for the House normally, it is more vulnerable to
card counting than Pay Table B.
The following results were obtained:
21. Average card counter advantage from beginning
of shoe (as percent of unit bet)
Strategy 1A 1B 2 3A 3B 4A 4B 5 6A 6B 7A 7B
Bet
ratio 1 1 2 2 2 2 2 5 5 5 5 5
Pay
Table A B none A B A B none A B A B
Counts 1 1 1 2 2 1 1 1 2 2 1 1
Decks in
0
-
1.96%
-
1.96%
-
1.96%
-
1.96%
-
1.96%
-
1.96%
-
1.96%
-
1.96% -1.96% -1.96% -1.96%
-
1.96%
1
-
1.93%
-
1.94%
-
1.87%
-
1.81%
-
1.84%
-
1.93%
-
1.95%
-
1.59% -1.46% -1.53% -1.86%
-
1.94%
2
-
1.90%
-
1.92%
-
1.81%
-
1.54%
-
1.62%
-
1.75%
-
1.89%
-
1.11% -0.44% -0.71% -1.21%
-
1.69%
3
-
1.66%
-
1.75%
-
1.58%
-
0.90%
-
1.18%
-
1.17%
-
1.66%
-
0.30% 1.38% 0.56% 0.42%
-
1.20%
4
-
1.37%
-
1.55%
-
1.32%
-
0.14%
-
0.64%
-
0.44%
-
1.32% 0.61% 3.57% 2.05% 2.48%
-
0.43%
5
-
0.99%
-
1.29%
-
0.99% 0.82% 0.03% 0.48%
-
0.84% 1.73% 6.25% 3.84% 5.01% 0.68%
6
-
0.59%
-
0.99%
-
0.70% 1.91% 0.83% 1.54%
-
0.21% 2.93% 9.41% 6.05% 8.09% 2.34%
7 0.26%
-
0.32%
-
0.08% 3.95% 2.42% 3.54% 1.15% 4.98% 15.00% 10.09% 13.52% 5.74%
The following conclusions may be drawn from this data (which uses the very player-favorable 23 1/2 - 17 1/2
configuration):
1) If the player does not change his bet size, the only way to beat the game is to jump in to the middle of a
favorable shoe, and the dealer may continue to deal 3/4 of the way through the shoe (or 7/8 of the way if he is
willing to allow a small advantage comparable to the one obtained from card counting in Blackjack).
2) If the player can bet 1x or 2x but does not play the bonus game or jump in the middle of the shoe, it is also
not possible to beat the game by card counting, even if the dealer goes 7/8 of the way through the shoe.
3) If the player can bet 1x or 2x and plays with Pay Table B, the shoe must be shuffled after 6 decks (5 if the
player is very skilled and can keep 2 incompatible simultaneous counts). With 1x-2x bets and pay table A, the
shoe should be shuffled after 4 decks.
4) If the player can bet 1x or 5x then the shoe must be shuffled halfway through (4 decks out of 8) even if no
bonus bets are made (the resulting advantage is comparable to the advantage from card-counting in Blackjack).
If Pay Table B is used with a 5x bet multiple then the shoe may still be shuffled after 4 decks, unless the player
is a very skilled expert who can keep two incompatible counts at the same time, in which case the shoe must
be shuffled after 3 decks. If Pay table A is used with a 5x bet multiple then the shoe must be shuffled after 3
decks regardless, because the bonus count alone can beat the game if you go to 4 decks (2.48% player
advantage).