Cleopatra Free Slot Games

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

Position	Reel 1	Reel 2	Reel 3	Reel 4	Reel 5
1	eye	Q	K	K	gold
2	Q	J	9	9	10
3	10	gold	eye	eye	J
4	gold	Q	10	A	flower
5	J	A	gold	flower	K
6	A	Cleopatra	K	J	10
7	crook and flail	Q	J	scarab	Cleopatra
8	10	J	Cleopatra	10	K
9	Q	eye	Q	crook and flail	9
10	flower	9	10	J	scarab
11	9	Q	gold	gold	10
12	10	gold	9	Q	eye
13	Sphinx	K	J	eye	A
14	Q	scarab	scarab	J	J
15	J	J	A	10	Sphinx
16	Cleopatra	flower	10	crook and flail	9
17	Q	10	crook and flail	A	A
18	A	scarab	A	Q	crook and flail
19	flower	9	K	Sphinx	Q
20	K	Sphinx	scarab	10	A
21	scarab	A	9	K	crook and flail
22	Q	crook and flail	10	gold	10
23	eye	10	flower	J	eye
24	K	K	Q	crook and flail	Q
25	crook and flail	flower	9	9	gold
26	10	J	crook and flail	A	9
27	scarab	Q	K	flower	Cleopatra
28	9	eye	eye	9	J
29	gold	J	9	A	flower
30	10	crook and flail	Sphinx	Cleopatra	Q
31	K
32	eye
33	J
34	10
35	gold
36	Q
37	crook and flail
38	9
39	scarab
40	A
41	9

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

Symbol	Reel 1	Reel 2	Reel 3	Reel 4	Reel 5
Cleopatra	1	1	1	1	2
Scarab	2	2	2	1	2
Flower	2	2	1	2	2
Gold	2	2	2	2	3
crook and flail	2	2	2	3	3
eye	2	2	2	2	3
A	2	2	2	4	4
K	2	2	4	2	3
Q	5	5	2	2	4
J	2	5	2	4	4
10	5	2	4	3	5
9	2	2	5	3	5
Sphinx	1	1	1	1	1
Total	30	30	30	30	41

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

Symbol	5 pays	4 pays	3 pays	2 pays
Cleopatra	10000	2000	200	10
Scarab	750	100	25	2
Flower	750	100	25	2
Gold	400	100	15	0
crook and flail	250	75	10	0
eye	250	50	10	0
A	125	50	10	0
K	100	50	5	0
Q	100	25	5	0
J	100	25	5	0
10	100	25	5	0
9	100	25	5	2

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

Symbol	5 in a row	4 in a row	3 in a row	2 in a row	Total
Cleopatra	2	39	1,118	19,516	20,675
Scarab	16	296	9,184	132,840	142,336
Flower	16	296	4,428	137,760	142,500
Gold	48	576	8,856	9,480
crook and flail	72	864	8,528	9,464
eye	48	576	8,856	9,480
A	128	1,120	8,200	9,448
K	96	1,152	17,712	18,960
Q	400	3,500	55,350	59,250
J	320	2,800	20,500	23,620
10	600	4,080	42,640	47,320
9	300	2,040	21,320	118,080	141,740
Total	2,046	17,339	206,692	408,196	634,273

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

Symbol	5 in a row	4 in a row	3 in a row	2 in a row	Total
Scarab	196	1,628	20,664	132,840	155,328
Flower	196	1,591	14,391	137,760	153,938
Gold	352	2,232	19,926	-	22,510
crook and flail	463	2,880	19,188	22,531
eye	352	2,232	19,926	22,510
A	676	3,430	18,450	22,556
K	564	3,600	26,568	30,732
Q	1,526	7,735	60,885	70,146
J	1,270	6,475	31,775	39,520
10	1,892	8,024	47,970	57,886
9	1,184	5,168	29,848	118,080	154,280
Total	8,671	44,995	309,591	388,680	751,937

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

Symbol	5 in a row	4 in a row	3 in a row	2 in a row	Total
Cleopatra	0.00000006	0.00000117	0.00003366	0.00058765	0.00062132
Scarab	0.00000048	0.00000891	0.00027654	0.00400000	0.00427654
Flower	0.00000048	0.00000891	0.00013333	0.00414815	0.00428148
Gold	0.00000145	0.00001734	0.00026667	0.00026667
crook and flail	0.00000217	0.00002602	0.00025679	0.00025679
eye	0.00000145	0.00001734	0.00026667	0.00026667
A	0.00000385	0.00003372	0.00024691	0.00024691
K	0.00000289	0.00003469	0.00053333	0.00053333
Q	0.00001204	0.00010539	0.00166667	0.00166667
J	0.00000964	0.00008431	0.00061728	0.00061728
10	0.00001807	0.00012285	0.00128395	0.00128395
9	0.00000903	0.00006143	0.00064198	0.00355556	0.00419753
Total	0.00006161	0.00052210	0.00622379	0.01229136	0.01851515

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

Symbol	5 in a row	4 in a row	3 in a row	2 in a row	Total
Scarab	0.00000590	0.00004902	0.00062222	0.00400000	0.00462222
Flower	0.00000590	0.00004791	0.00043333	0.00414815	0.00458148
Gold	0.00001060	0.00006721	0.00060000	0.00060000
crook and flail	0.00001394	0.00008672	0.00057778	0.00057778
eye	0.00001060	0.00006721	0.00060000	0.00060000
A	0.00002036	0.00010328	0.00055556	0.00055556
K	0.00001698	0.00010840	0.00080000	0.00080000
Q	0.00004595	0.00023291	0.00183333	0.00183333
J	0.00003824	0.00019497	0.00095679	0.00095679
10	0.00005697	0.00024161	0.00144444	0.00144444
9	0.00003565	0.00015562	0.00089877	0.00355556	0.00445432
Total	0.00026110	0.00135486	0.00932222	0.01170370	0.02102593

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

Symbol	5 in a row	4 in a row	3 in a row	2 in a row	Total
Cleopatra	0.000602	0.002349	0.006733	0.005877	0.012609
Scarab	0.000361	0.000891	0.006914	0.008000	0.014914
Flower	0.000361	0.000891	0.003333	0.008296	0.011630
Gold	0.000578	0.001734	0.004000	0.004000
crook and flail	0.000542	0.001951	0.002568	0.002568
eye	0.000361	0.000867	0.002667	0.002667
A	0.000482	0.001686	0.002469	0.002469
K	0.000289	0.001734	0.002667	0.002667
Q	0.001204	0.002635	0.008333	0.008333
J	0.000964	0.002108	0.003086	0.003086
10	0.001807	0.003071	0.006420	0.006420
9	0.000903	0.001536	0.003210	0.007111	0.010321
Total	0.008455	0.021454	0.052400	0.029284	0.081684

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

Symbol	5 in a row	4 in a row	3 in a row	2 in a row	Total
Scarab	0.008853	0.009804	0.031111	0.016000	0.065768
Flower	0.008853	0.009581	0.021667	0.016593	0.056693
Gold	0.008479	0.013442	0.018000	0.039921
crook and flail	0.006971	0.013008	0.011556	0.031534
eye	0.005300	0.006721	0.012000	0.024020
A	0.005089	0.010328	0.011111	0.026528
K	0.003397	0.010840	0.008000	0.022237
Q	0.009190	0.011646	0.018333	0.039169
J	0.007648	0.009749	0.009568	0.026965
10	0.011394	0.012081	0.014444	0.037919
9	0.007130	0.007781	0.008988	0.014222	0.038121
Total	0.082304	0.114980	0.164778	0.046815	0.408877

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

Symbol	5 in a row	4 in a row	3 in a row	2 in a row	Total
Cleopatra	0.000602	0.002349	0.006733	0.005877	0.015560
Scarab	0.009214	0.010696	0.038025	0.024000	0.081934
Flower	0.009214	0.010473	0.025000	0.024889	0.069576
Gold	0.009058	0.015176	0.022000	0.046234
crook and flail	0.007513	0.014959	0.014123	0.036596
eye	0.005661	0.007588	0.014667	0.027916
A	0.005571	0.012014	0.013580	0.031165
K	0.003686	0.012575	0.010667	0.026927
Q	0.010394	0.014280	0.026667	0.051341
J	0.008612	0.011856	0.012654	0.033123
10	0.013201	0.015152	0.020864	0.049217
9	0.008034	0.009316	0.012198	0.021333	0.050881
Total	0.090759	0.136435	0.217177	0.076099	0.520470

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

Scatters	Pays	Combinations	Probability	Return
5	100	243	0.000007	100	0.000732
4	20	11,826	0.000356	20	0.007122
3	5	228,906	0.006893	5	0.034463
2	2	2,204,496	0.066380	2	0.132761
Total	127	2,445,471	0.073637	0.175078

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 Win	Return
Line pays in initial spins	52.047%
Scatter pays in initial spins	17.508%
Bonus	25.470%
Total	95.025%

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

Paylines	Hit Frequency	Total Std. Dev.	Relative Std. Dev.
1	11.36%	13.45	13.45
2	14.92%	19.32	9.66
3	18.56%	25.37	8.46
4	21.66%	31.08	7.77
5	24.70%	36.02	7.20
6	25.62%	39.79	6.63
7	26.55%	43.81	6.26
8	29.36%	48.43	6.05
9	31.81%	53.26	5.92
10	32.52%	57.42	5.74
11	33.20%	61.09	5.55
12	33.87%	65.78	5.48
13	34.63%	69.88	5.38
14	35.26%	75.00	5.36
15	35.86%	79.10	5.27
16	35.86%	84.37	5.27
17	35.87%	89.56	5.27
18	35.84%	93.16	5.18
19	35.85%	98.59	5.19
20	35.88%	103.51	5.18

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.

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Written by: Michael Shackleford