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Cleopatra Keno

Introduction

Cleopatra Keno is a video keno variant in which the player wins 12 free games if the last ball drawn contributes to a player win. All wins in free games are doubled. Free games do not earn additional free games.

Pay Tables

 

Following are some common pay tables for Cleopatra Keno. The return is in the bottom row.

Pay Table 1

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 - - - - - - -
1 0 - - - - - - -
2 3 1 - - - - - -
3 19 5 3 2 1 - - -
4 0 45 24 5 3 3 2 1
5 0   240 42 7 10 5 3
6 0     410 118 65 12 5
7 0       500 250 108 35
8 0         1,000 200 206
9 0           1,000 1,000
10 0             2,000
Return 94.03% 95.25% 95.05% 95.03% 95.07% 95.09% 95.04% 95.02%
 

Pay Table 2

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 - - - - - - -
1 0 - - - - - - -
2 3 1 - - - - - -
3 19 5 3 2 1 - - -
4 0 43 24 5 3 3 2 1
5 0   230 40 7 10 5 3
6 0     410 111 65 12 5
7 0       500 210 100 35
8 0         1,000 200 175
9 0           1,000 1,000
10 0             2,000
Return 94.03% 94.22% 94.17% 94.03% 94.08% 94.12% 94.19% 94.13%
 

Pay Table 3

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 - - - - - - -
1 0 - - - - - - -
2 3 1 - - - - - -
3 18 5 3 2 1 - - -
4 0 39 23 5 3 3 2 1
5 0   225 37 7 10 5 3
6 0     390 97 60 10 5
7 0       500 200 100 30
8 0         1,000 200 160
9 0           1,000 1,000
10 0             2,000
Return 92.11% 92.16% 92.08% 92.10% 92.09% 92.08% 92.14% 92.00%
 

Pay Table 4

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 - - - - - - -
1 0 - - - - - - -
2 3 1 - - - - - -
3 17 5 3 2 1 - - -
4 0 35 22 5 3 3 2 1
5 0   220 34 6 10 5 3
6 0     375 95 56 10 5
7 0       500 180 80 25
8 0         1,000 200 150
9 0           1,000 1,000
10 0             2,000
Return 90.19% 90.10% 89.99% 90.28% 90.14% 90.15% 90.02% 90.01%
 

Pay Table 5

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 - - - - - - -
1 0 - - - - - - -
2 3 1 - - - - - -
3 16 5 3 2 1 - - -
4 0 31 21 5 3 3 2 1
5 0   220 30 6 10 5 3
6 0     375 80 50 10 5
7 0       500 180 65 25
8 0         1,000 200 100
9 0           1,000 1,000
10 0             2,000
Return 88.27% 88.04% 88.34% 88.27% 88.01% 87.99% 88.44% 88.58%
 

Analysis

 

This section shall analyze Pay Table 4 above.

The next table shows the number of combinations for each possible number of picks and catches.

 

Cleopatra Keno — CombinationsExpand

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 34220 487635 5461512 50063860 386206920 2558620845 14783142660 75394027566
1 35400 684400 9752700 109230240 1001277200 7724138400 51172416900 295662853200
2 11400 336300 6501800 92650650 1037687280 9512133400 73379314800 486137960550
3 1140 68400 2017800 39010800 555903900 6226123680 57072800400 440275888800
4 0 4845 290700 8575650 165795900 2362591575 26461025640 242559401700
5 0 0 15504 930240 27442080 530546880 7560293040 84675282048
6 0 0 0 38760 2325600 68605200 1326367200 18900732600
7 0 0 0 0 77520 4651200 137210400 2652734400
8 0 0 0 0 0 125970 7558200 222966900
9 0 0 0 0 0 0 167960 10077600
10 0 0 0 0 0 0 0 184756
Total 82160 1581580 24040016 300500200 3176716400 28987537150 231900297200 1646492110120

 

The next table shows the probability for each possible number of picks and catches, before considering the bonus.

 

Cleopatra Keno — Probability of WinningExpand

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0.41650438 0.30832143 0.22718421 0.16660175 0.12157425 0.08826624 0.06374784 0.0457907
1 0.4308666 0.43273183 0.40568609 0.36349473 0.31519251 0.26646411 0.22066559 0.17957138
2 0.13875365 0.21263547 0.27045739 0.30832143 0.32665405 0.32814562 0.31642614 0.29525678
3 0.01387537 0.04324789 0.08393505 0.12981955 0.17499324 0.21478623 0.24610922 0.26740237
4 0 0.00306339 0.01209234 0.02853792 0.05219097 0.0815037 0.11410518 0.1473189
5 0 0 0.00064492 0.00309564 0.0086385 0.01830259 0.03260148 0.05142769
6 0 0 0 0.00012898 0.00073208 0.00236671 0.00571956 0.01147939
7 0 0 0 0 0.0000244 0.00016046 0.00059168 0.00161114
8 0 0 0 0 0 0.00000435 0.00003259 0.00013542
9 0 0 0 0 0 0 0.00000072 0.00000612
10 0 0 0 0 0 0 0 0.00000011
Total 1 1 1 1 1 1 1 1

 

The next table shows the contribution to the return for each possible number of picks and catches, before considering the bonus.

 

Cleopatra Keno — Before Bonus ReturnExpand

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
2 0.41626095 0.21263547 0 0 0 0 0 0
3 0.23588121 0.21623946 0.25180516 0.2596391 0.17499324 0 0 0
4 0 0.10721873 0.26603144 0.14268959 0.1565729 0.2445111 0.22821036 0.1473189
5 0 0 0.14188343 0.10525171 0.05183103 0.18302586 0.1630074 0.15428306
6 0 0 0 0.04836935 0.06954728 0.13253596 0.05719558 0.05739697
7 0 0 0 0 0.01220128 0.02888193 0.04733427 0.04027858
8 0 0 0 0 0 0.00434566 0.00651849 0.0203129
9 0 0 0 0 0 0 0.00072428 0.00612065
10 0 0 0 0 0 0 0 0.00022442
Total 0.65214216 0.53609365 0.65972003 0.55594975 0.46514573 0.59330052 0.50299039 0.42593549

 

The next table shows the probability of winning the bonus for each possible number of picks and catches, before considering the bonus.

 

Cleopatra Keno — Bonus ProbabilityExpand

Catch Pick 3 Pick 4 Pick 5 Pick 6 Pick 7 Pick 8 Pick 9 Pick 10
0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
2 0.01387537 0.02126355 0 0 0 0 0 0
3 0.0020813 0.00648718 0.01259026 0.01947293 0.02624899 0 0 0
4 0 0.00061268 0.00241847 0.00570758 0.01043819 0.01630074 0.02282104 0.02946378
5 0 0 0.00016123 0.00077391 0.00215963 0.00457565 0.00815037 0.01285692
6 0 0 0 0.0000387 0.00021962 0.00071001 0.00171587 0.00344382
7 0 0 0 0 0.00000854 0.00005616 0.00020709 0.0005639
8 0 0 0 0 0 0.00000174 0.00001304 0.00005417
9 0 0 0 0 0 0 0.00000033 0.00000275
10 0 0 0 0 0 0 0 0.00000006
Total 0.01595667 0.02836341 0.01516996 0.02599312 0.03907497 0.0216443 0.03290772 0.0463854

 

The next table shows the return for each combinations of picks and catches, according to Pay Table 1 above.

 

Cleopatra Keno — Return

Pick Return Before Bonus Bonus Return Total Return
3 0.652142 0.249744 0.901887
4 0.536094 0.364931 0.901024
5 0.659720 0.240190 0.899910
6 0.555950 0.346821 0.902771
7 0.465146 0.436213 0.901359
8 0.593301 0.308198 0.901498
9 0.502990 0.397254 0.900245
10 0.425935 0.474172 0.900108

 

So, the bottom line is that this particular pay table returns 90% of money bet.

Calculator

 

Calculate the odds for any pay table with my Cleopatra Keno calculator.

Written by: Michael Shackleford