Comprehensive Analysis of Caveman Keno: RTP, Hit Frequency, Volatility

This report provides a comprehensive analysis of Caveman Keno, a variation of the classic keno game, focusing on the Return to Player (RTP) percentage, hit frequency, and volatility index. The analysis covers different pick scenarios (2 to 10 numbers) and evaluates the potential earnings and bonuses for players. The study determines that the RTP ranges from 61.13% to 68.03%, indicating the portion of wagered amounts players can expect to get back over time. The volatility indices reveal that significant positive returns (bonuses) are more likely when players choose picks 6 through 10, suggesting that these options offer a fairer or more rewarding gameplay experience. The report includes detailed tables showcasing the calculations and results for various pick scenarios, offering insights into the game's fairness and potential advantages for players. This assignment is available on Desklib, a platform offering a wide range of study tools and resources for students.

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Contents
Introduction.................................................................................................................................................3
Analysis.......................................................................................................................................................3
Conclusion...................................................................................................................................................6
References...................................................................................................................................................8

Introduction
A keno is a form of gamble that is played in casinos or online. A known rule of the game
is such that a participant is allowed to pick between two to ten numbers, ranging from one to
eighty. Computer then randomly picks twenty numbers, ranging from one to eighty. The
participant can win according to a pay table and according to how many of his/her chosen
numbers are matched by the twenty numbers drawn by computer.
In our particular scenario, a participant has to pick two to ten numbers, ranging from one to
eighty, as in regular keno. Computer then randomly picks three numbers among the numbers the
participant has not chosen. These three numbers are then marked with eggs. The computer will then
choose twenty numbers, ranging from one to eighty just like it could be the case in a normal keno game.
The participant may win depending on the number of the participant's choices that match the twenty
numbers chosen by the computer just like in the case of a normal keno. The participant will get a
multiplier according to the number of eggs that match the twenty balls chosen. The usual multipliers are
one for zero or one match, three for two matches, and six for three matches. The player's win will be
the sum of the wins of the regular keno pay table and the multiplier wins.
Analysis
Return to play is the percentage of the amount of money that a gambling machine
pays back over time (Ziming & Haward, 2009). It is calculated as an average based on at least
1000 plays. It tells how low or high a games’s payout is (Gobet, Fernad, Schiller, & Marvin,
2014). Return to player is calculated by: the total amount returned to the players divided by the
total amount bet by the players (McGrath, Barrett, Stewart, & McGrath, 2012).

The total amount bet by players is calculated as the sum of each initial bet round per
player for the audited period while the amount returned to player is defined as the net amount
won by a player in a round (Natallie & Shawn, 2008).
Hit frequency is the number of times a machine will stop in a winning combination
(Orford, Wardle, Griffiths, & Mark, 2013). In other words, it is the total number of wins that one
expects in a single bet/gamble (Shamsutdinova, 2011). Volatility index on the other hand is the
advantage of that the gambler gains. It is the difference between the bonuses and the return to
player.
Pick 2
Catch Pays Combination Return
2 10 190 1900
Total 3160 1900
RTP 60.13%
60.13%
Pick 3
Catch Pays Combination Return
2 3 11400 34200
3 16 1140 18240
Total 82160 52440
63.83%
Pick 4
Catch Pays Combination Return
2 1 336300 336300
3 5 68400 342000
4 75 4845 363375
Total 1581580 1041675
65.86%
Pick 5
Catch Pays Combination Return
2 1 6501800 6501800

3 2 2017800 4035600
4 13 290700 3779100
5 80 15504 1240320
Total 24040016 15556820
64.71%
Pick 6
Catch Pays Combination Return
3 2 39010800 78021600
4 6 8575650 51453900
5 70 930240 65116800
6 150 38760 5814000
Total 300500200 200406300
66.69%
Pick 7
Catch Pays Combination Return
3 1 555903900 555903900
4 3 165795900 497387700
5 14 27442080 384189120
6 270 2325600 627912000
7 1,000 77520 77520000
Total 3176716400 2142912720
67.46%
Pick 8
Catch Pays Combination Return
3 1 6226123680 6226123680
4 2 2362591575 4725183150
5 5 530546880 2652734400
6 68 68605200 4665153600
7 200 4651200 930240000
8 1,000 125970 125970000
Total 28987537150 19199434830
66.23%
Pick 9
Catch Pays Combination Return
4 1 26461025640 26461025640
5 6 7560293040 45361758240
6 50 1326367200 66318360000
7 125 137210400 17151300000
8 500 7558200 3779100000
9 1,000 167960 167960000
Total 2.319E+11 1.5924E+11

68.67%
Pick 10
Catch Pays Combination Return
4 1 2.42559E+11 2.42559E+11
5 5 84675282048 4.23376E+11
6 10 18900732600 1.89007E+11
7 77 2652734400 2.04261E+11
8 250 222966900 55741725000
9 500 10077600 5038800000
10 1,000 184756 184756000
Total 1.64649E+12 1.12017E+12
Pick 2 Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
Keno RTP%
61.30
%
63.83
%
65.86
%
64.71
%
66.69
% 67.46% 66.23% 68.67% 68.03%
Keno Hit
Freq. 0.613
1.914
8
2.634
517
3.235
609
4.001
454
4.72197
9287
5.29867
2938
6.18005
0445
6.80336
6751
Keno Pulls /
Hit 6.13
12.12
707
52.69
035
62.12
37
152.0
553
845.138
3336
844.475
9995
1154.98
2761
1253.86
0492
Bonus RTP
% 10
6.333
333 20 19.2 38
178.979
6783 159.375
186.888
8889 184.3
Bonus Hit
Freq. 3.065
4.042
356
13.17
259
12.42
474
25.34
254
120.734
0477
105.559
4999
128.331
4179
125.386
0492
Bonus
Pulls / Hit
1.878
845
2.580
102
8.675
852
8.040
321
16.90
117
81.4433
8175
69.9156
5821
88.1216
2625
85.3047
2783
Game Total
RTP%
14.94
%
12.96
%
41.85
%
39.67
%
80.24
% 381.16% 334.85% 403.34% 394.99%
Volatility
Index
-
46.36
%
-
50.87
%
-
24.01
%
-
25.05
%
13.55
% 313.70% 268.62% 334.67% 326.96%
Conclusion
The results shows the percentages of the potential earnings or the return to players. From
the table, it is clear that the return to player ranges between 61.13% to 68.03% (Shamsutdinova,
2011). This implies that if one plays the game, they are likely to get back these portions of their
amounts used in gambling. The individual return to player values are shown in the table in the

analysis section. Therefore, it is prudent to say that the game is fair enough since the total
amount used in gambling does not go into waste.
The volatility indices shows the advantage of the gambler/player. The percentages show
the percentage bonuses that the player is likely to earn if they take part in the game. It is clear
that for pick 2, pick 3, pick 4 and pick 5, a player is likely to get no bonuses. However, for pick
6, pick 7, pick 8, pick 9 and pick 10, a player is likely to get significant (positive return). This is
an indication that the game is fair or worth playing only when it involves pick 6, pick 7, pick 8,
pick 9 and pick 10.

References
Gobet, Fernad, Schiller, & Marvin. (2014). Problem Gambling || Cognitive Models of Gambling
and Problem Gambling. 32.
McGrath, D. S., Barrett, S. P., Stewart, S., & McGrath, P. R. (2012). A Comparison of Gambling
Behavior, Problem Gambling Indices, and Reasons for Gambling Among Smokers and
Nonsmokers Who Gamble: Evidence from a Provincial Gambling Prevalence Study.
Journal of Nicotine & Tobacco Research, 7.
Natallie, V. M., & Shawn, R. C. (2008). A Canadian Population Level Analysis of the Roles of
Irrational Gambling Cognitions and Risky Gambling Practices as Correlates of Gambling
Intensity and Pathological Gambling. 18.
Orford, J., Wardle, H., Griffiths, & Mark. (2013). hat proportion of gambling is problem
gambling? Estimates from the 2010 British Gambling Prevalence Survey. International
Gambling Studies, 16.
Shamsutdinova, D. V. (2011). Prevention of modern teenager's computer excessive gambling. 6.
Ziming, X., & Haward, S. (2009). How Do Gamblers End Gambling: Longitudinal Analysis of
Internet Gambling Behaviors Prior to Account Closure Due to Gambling Related
Problems. 14.