• Appendices
  • Slots Analysis
  • Miscellaneous

Cleopatra and the legend of her beauty sit at the pinnacle of this mystery and intrigue. Gaming developer, IGT, puts together all that you know and love about Egypt and Cleopatra into a five-reel, 20-line slot machine game that will take you away into this ancient land of superstitions and secrets. Basic Game Experience for Cleopatra. Cleopatra Plus Slots. Cleopatra, who was the last active pharaoh of Egypt, is one of the most famous names in Ancient History. She was a strong, powerful leader who ruled Egypt for 21 years, and now she’s had an online casino slot game, Cleopatra Plus, made in her honour by IGT (International Gaming Technology). Range of Games: It’s important that you can play the classic IGT slots for real money, like Cleopatra and White Orchid, but it’s just as important that you can play the latest releases by IGT. Our recommended casinos have an updated catalogue of IGT slots, so you don’t need to miss out on anything.

Introduction

In my continued effort to pull the veil of secrecy away and show how slot machines work, I offer the following deconstruction of the popular IGT game Cleopatra. This is a simple five-reel video slot with a free spin bonus.

The version this analysis is based on is the one that can be played for free at FreeCasinoGames.net.

The Reel Strips

Our friends at Casino Guru were kind enough to provide the reel strips for the game at Vegas Slots Online. I believe they pieced them together from a lot of playing, the same way I did other slot deconstructions, like the one of Lionfish.

The way video slots like this one work is to choose a random number for each reel, from 1 to the number of positions in the reel, and map the random number to the corresponding position on the reel. In other words each position on a given reel is equally likely. The number of each symbol on each reel is carefully chosen to achieve a desired return. Following are the reel strips for Cleopatra. Note that reel 5 is longer than first four reels.

Cleopatra Reel Strips

PositionReel 1Reel 2Reel 3Reel 4Reel 5
1eyeQKKgold
2QJ9910
310goldeyeeyeJ
4goldQ10Aflower
5JAgoldflowerK
6ACleopatraKJ10
7crook and flailQJscarabCleopatra
810JCleopatra10K
9QeyeQcrook and flail9
10flower910Jscarab
119Qgoldgold10
1210gold9Qeye
13SphinxKJeyeA
14QscarabscarabJJ
15JJA10Sphinx
16Cleopatraflower10crook and flail9
17Q10crook and flailAA
18AscarabAQcrook and flail
19flower9KSphinxQ
20KSphinxscarab10A
21scarabA9Kcrook and flail
22Qcrook and flail10gold10
23eye10flowerJeye
24KKQcrook and flailQ
25crook and flailflower99gold
2610Jcrook and flailA9
27scarabQKflowerCleopatra
289eyeeye9J
29goldJ9Aflower
3010crook and flailSphinxCleopatraQ
31K
32eye
33J
3410
35gold
36Q
37crook and flail
389
39scarab
40A
419
Gold

For an example, consider this screenshot above. Assume that the random number chosen is associated with the symbol appearing in the top row. This configuration would occur if the random numbers chosen were as follows:

  • Reel 1: 2
  • Reel 2: 19
  • Reel 3: 7
  • Reel 4: 5
  • Reel 5: 14
In the event the random number chosen is last or second to last on the reel, then the reel would wrap around, with position 1 following the last position on the reel.

Symbol Frequency

The next table shows the total number of each symbol on each reel.

Cleopatra Symbol Distribution

SymbolReel 1Reel 2Reel 3Reel 4Reel 5
Cleopatra11112
Scarab22212
Flower22122
Gold22223
crook and flail22233
eye22223
A22244
K22423
Q55224
J25244
1052435
922535
Sphinx11111
Total3030303041

Pay Table

The pay table is easily seen from the rule screens, which I also show in the table below. Cleopatra is wild and may substitute for any symbol except the Sphinx. In addition, one or more Cleopatra symbols will double any win, except wins based only on Cleopatras. In the event the player qualifies for two possible wins on the same pay-line, because it started with two to four wilds, the game will choose the higher of the two wins. In that event results in a tie, I count it as an all Cleopatra win in the tables of winning combinations later on. For example, Cleopatra - Cleopatra - K - Q -J, which can be scored as 10 for either two Cleopatras or a doubled three kings, is counted as two Cleopatra win.

Cleopatra Pay Table

Symbol5 pays4 pays3 pays2 pays
Cleopatra10000200020010
Scarab750100252
Flower750100252
Gold400100150
crook and flail25075100
eye25050100
A12550100
K1005050
Q1002550
J1002550
101002550
91002552

The Sphnix is a scatter pay. This means the player is paid according to the number that appear on the screen anywhere. The player is paid a multiple of his total amount bet and the number of diver symbols. Following is the scatter pay table.

  • 5 Pays: 100
  • 4 Pays: 20
  • 3 Pays: 5
  • 2 Pays: 2

Line Pay Math

Winning Combinations — Non-Doubled

The next table shows the number of combinations for each possible win when no wilds are involved in the win, except all wild wins. In other words, wins that are not multiplied. Cells are left blank if they don't produce a win.

Non-Doubled Line Pay Combinations — Not Doubled

Symbol5 in a row4 in a row3 in a row2 in a rowTotal
Cleopatra2391,11819,51620,675
Scarab162969,184132,840142,336
Flower162964,428137,760142,500
Gold485768,8569,480
crook and flail728648,5289,464
eye485768,8569,480
A1281,1208,2009,448
K961,15217,71218,960
Q4003,50055,35059,250
J3202,80020,50023,620
106004,08042,64047,320
93002,04021,320118,080141,740
Total2,04617,339206,692408,196634,273

Winning Combinations — Doubled

The next table shows the number of combinations for each possible win when at least one Cleopatra involved in the win, except all wild wins. In other words, wins that are doubled.

Doubled Line Pay Combinations — Doubled

Symbol5 in a row4 in a row3 in a row2 in a rowTotal
Scarab1961,62820,664132,840155,328
Flower1961,59114,391137,760153,938
Gold3522,23219,926-22,510
crook and flail4632,88019,18822,531
eye3522,23219,92622,510
A6763,43018,45022,556
K5643,60026,56830,732
Q1,5267,73560,88570,146
J1,2706,47531,77539,520
101,8928,02447,97057,886
91,1845,16829,848118,080154,280
Total8,67144,995309,591388,680751,937

Be warned that the math is tedious and error-prone to calculate these combinations by hand. If you're up to the challenge and you can code, then I recommend coding five nested loops and cycle through all 30^4*41=33,210,000 possible outcomes.

The next table shows the probability of each possible win for the non-doubled wins. The lower right cell shows a hit frequency per line of 1.85% for non-doubled wins.

Probabilities — Non-Doubled

Non-Doubled Line Pay Probabilities

Symbol5 in a row4 in a row3 in a row2 in a rowTotal
Cleopatra0.000000060.000001170.000033660.000587650.00062132
Scarab0.000000480.000008910.000276540.004000000.00427654
Flower0.000000480.000008910.000133330.004148150.00428148
Gold0.000001450.000017340.000266670.00026667
crook and flail0.000002170.000026020.000256790.00025679
eye0.000001450.000017340.000266670.00026667
A0.000003850.000033720.000246910.00024691
K0.000002890.000034690.000533330.00053333
Q0.000012040.000105390.001666670.00166667
J0.000009640.000084310.000617280.00061728
100.000018070.000122850.001283950.00128395
90.000009030.000061430.000641980.003555560.00419753
Total0.000061610.000522100.006223790.012291360.01851515

Probabilities — Doubled

The next table shows the probability of each possible win for the doubled wins. The lower right cell shows a hit frequency per line of 2.11% for doubled wins.

Doubled Line Pay Probabilities

Symbol5 in a row4 in a row3 in a row2 in a rowTotal
Scarab0.000005900.000049020.000622220.004000000.00462222
Flower0.000005900.000047910.000433330.004148150.00458148
Gold0.000010600.000067210.000600000.00060000
crook and flail0.000013940.000086720.000577780.00057778
eye0.000010600.000067210.000600000.00060000
A0.000020360.000103280.000555560.00055556
K0.000016980.000108400.000800000.00080000
Q0.000045950.000232910.001833330.00183333
J0.000038240.000194970.000956790.00095679
100.000056970.000241610.001444440.00144444
90.000035650.000155620.000898770.003555560.00445432
Total0.000261100.001354860.009322220.011703700.02102593

Returns — Non-Doubled

The next table shows the product of each winning probability and what it pays for non-doubled wins. Each cell is the product of the probability of winning and the win. The lower right cell shows that the player can expect to win 8.17% of his bet per spin from non-doubled line pays.Slot

Non-Doubled Line Pay Returns

Symbol5 in a row4 in a row3 in a row2 in a rowTotal
Cleopatra0.0006020.0023490.0067330.0058770.012609
Scarab0.0003610.0008910.0069140.0080000.014914
Flower0.0003610.0008910.0033330.0082960.011630
Gold0.0005780.0017340.0040000.004000
crook and flail0.0005420.0019510.0025680.002568
eye0.0003610.0008670.0026670.002667
A0.0004820.0016860.0024690.002469
K0.0002890.0017340.0026670.002667
Q0.0012040.0026350.0083330.008333
J0.0009640.0021080.0030860.003086
100.0018070.0030710.0064200.006420
90.0009030.0015360.0032100.0071110.010321
Total0.0084550.0214540.0524000.0292840.081684

Returns — Doubled

The next table shows the product of each winning probability and what it pays for doubled wins. Each cell is the product of the probability of winning, the win, and 2. The lower right cell shows that the player can expect to win 40.89 % of his bet per spin from doubled line pays.

Doubled Line Pay Returns

Cleopatra Free Slot Games
Symbol5 in a row4 in a row3 in a row2 in a rowTotal
Scarab0.0088530.0098040.0311110.0160000.065768
Flower0.0088530.0095810.0216670.0165930.056693
Gold0.0084790.0134420.0180000.039921
crook and flail0.0069710.0130080.0115560.031534
eye0.0053000.0067210.0120000.024020
A0.0050890.0103280.0111110.026528
K0.0033970.0108400.0080000.022237
Q0.0091900.0116460.0183330.039169
J0.0076480.0097490.0095680.026965
100.0113940.0120810.0144440.037919
90.0071300.0077810.0089880.0142220.038121
Total0.0823040.1149800.1647780.0468150.408877

Returns — Combined

The final line pay table shows the combined return between doubled and non-doubled wins for each type of win. The lower right cell shows that the player can expect to win 52.05% of his bet per spin from line pays.

Combined Line Pay Returns

Cleopatra gold free slot games
Symbol5 in a row4 in a row3 in a row2 in a rowTotal
Cleopatra0.0006020.0023490.0067330.0058770.015560
Scarab0.0092140.0106960.0380250.0240000.081934
Flower0.0092140.0104730.0250000.0248890.069576
Gold0.0090580.0151760.0220000.046234
crook and flail0.0075130.0149590.0141230.036596
eye0.0056610.0075880.0146670.027916
A0.0055710.0120140.0135800.031165
K0.0036860.0125750.0106670.026927
Q0.0103940.0142800.0266670.051341
J0.0086120.0118560.0126540.033123
100.0132010.0151520.0208640.049217
90.0080340.0093160.0121980.0213330.050881
Total0.0907590.1364350.2171770.0760990.520470

Scatter Pay

The Sphinx is known as a 'scatter pay' symbol. It pays based on the number that appear anywhere on the screen. They do not have to be left aligned or on the same pay-line. Scatter pay wins are based on the total amount bet, as opposed the bet per pay-line.

The following table shows the probability and contribution to the return for each number of scatter pays. The bottom row shows a hit frequency on the scatter pay of 7.36% and a contribution to the total return of 17.51%.

Scatter Pay — Fixed Wins

ScattersPaysCombinationsProbabilityReturn
51002430.0000071000.000732
42011,8260.000356200.007122
35228,9060.00689350.034463
222,204,4960.06638020.132761
Total1272,445,4710.0736370.175078

Bonus

If the player gets three or more scatter symbols, then he will play a bonus round. The bonus round consists of an initial 15 free spins. Free spins use the same reel stripping as initial spins. All wins, except for five Cleopatras, are tripled. If the player gets three or more scatter symbols in a free spin, then he will get an additional 15 free spins.

As shown in the scatter section above, the probability of three or more scatters is 0.007256, or 1 in 138. After considering the probability if re-triggering the bonus in a free spin, the final number of free spins averages 16.832022. The rules say there is a cap of 180 free spins but that probability of that is truly negligible.

We can see from the final return table that the return from line pays is 0.586609. From the scatter section, we see the return from scatter pays is 0.175078. If it weren't for the rule of the jackpot (five Cleopatras) not tripling, the value per free spin would be 3×(0.520470+0.175078) = 2.086643. We need to subtract from that two times the value of the jackpot, because the jackpot is not tripled, which is 2× 0.000602 = 0.001204. Thus, the value of a free spin is 2.086643 - 0.001204 = 2.085439.

Multiplying the average number of free spins and the average win per free spin gives us the average bonus win of 16.832022 × 2.085439 = 35.102153.

The overall return from the bonus is the bonus probability times the average bonus win, which equals 0.007256 × 35.102153 = 0.254704.

Summary of Return

The final table below shows the return of each win category in Cleopatra. The lower right cell shows a total return for the game of 95.025%. The rule screens on the online game claim a return of 95.02% (perhaps they round down). Now you understand where it comes from.

Cleopatra Summary

Type of WinReturn
Line pays in initial spins52.047%
Scatter pays in initial spins17.508%
Bonus25.470%
Total95.025%

Hit Frequency and Standard Deviation

The following table shows the hit frequency and standard deviation for all possible number of paylines bet from 1 to 20. The standard deviation is expressed two ways, as follows:

  • Total standard deviation: This is the total standard deviation if betting one credit per line.
  • Relative standard deviation: This is the ratio of total standard deviation to the amount bet. In other words, the standard deviation relative to the total amount bet.
The table below is based on a 20 random simulations, one for each number of lines bet, of 100 million spins in each simulation. The data was kindly provided by Casino Guru.

Hit Frequency and Standard Deviation

3 Reel Cleopatra Slot

PaylinesHit
Frequency
Total
Std. Dev.
Relative
Std. Dev.
111.36%13.4513.45
214.92%19.329.66
318.56%25.378.46
421.66%31.087.77
524.70%36.027.20
625.62%39.796.63
726.55%43.816.26
829.36%48.436.05
931.81%53.265.92
1032.52%57.425.74
1133.20%61.095.55
1233.87%65.785.48
1334.63%69.885.38
1435.26%75.005.36
1535.86%79.105.27
1635.86%84.375.27
1735.87%89.565.27
1835.84%93.165.18
1935.85%98.595.19
2035.88%103.515.18

Internal Links

Play Cleopatra Free Slots

  • My main slot machine page.
  • Deconstructing Jackpot Party analysis of the video slot machine.
  • Deconstructing Megabucks.
  • Deconstructing the Atkins Diet slot machine. (PDF)
  • Analysis of Lucky Larry's Lobstermania.
  • Deconstructing Hexbreaker.
  • Deconstructing Lionfish.

Acknowledgements

Cleopatra Free Slot Games Free

  • Casino Guru for the reel strips as well as the data for calculating the standard deviation and hit frequency.
  • FreeCasinoGames.net for the free game, from which my screenshots were taken.

Cleopatra 2 Free Slot Games

Written by: Michael Shackleford