Deconstructing Cleopatra

Introduction

In an effort to unveil the mysteries surrounding slot machines, I present an analysis of the widely known IGT game Cleopatra, which features a straightforward five-reel video slot with a bonus for free spins.

This review focuses on the gameplay version that is available to play for free at FreeCasinoGames.net .

The Reel Strips

Our friends at Casino Guru graciously provided the game's reel strips at Vegas Slots Online. I believe they assembled them from extensive gameplay, similar to my previous analyses on other slot machines, including the one about Lionfish .

Video slots operate by selecting a random number for each individual reel, ranging from 1 to the total count of positions available on that reel, and then mapping this random number to the specific position on the reel. Essentially, each position has an equal chance of being selected. The distribution of symbols on each reel is meticulously planned to ensure a specific return rate. Below are the reel strips for Cleopatra, with a note that reel 5 has more positions than the first four reels.

Take a look at the screenshot above for an illustration. Let’s say the random number chosen corresponds to the symbol displayed in the top row. This specific setup would take place if the random numbers selected were as follows:

• Reel 1: 2
• Reel 2: 19
• Reel 3: 7
• Reel 4: 5
• Reel 5: 14

Should the random number fall on the last or second-to-last position on a reel, that reel will wrap around, meaning the first position follows after the last position.

Symbol Frequency

The subsequent table lists the total quantity of each symbol present on each reel.

Pay Table

You can easily view the pay table on the rule screens, which I've also included in the table below. Cleopatra acts as a wild symbol, substituting for all other symbols except the Sphinx. Additionally, landing one or more Cleopatra symbols will double any winnings, except for wins that consist solely of Cleopatra symbols. If a player qualifies for two potential wins on the same pay-line, stemming from two to four wilds, the game will award the greater of the two outcomes. In situations where a tie occurs, I classify it as a Cleopatra victory in the winning combinations tables that follow. For instance, the combination Cleopatra - Cleopatra - K - Q - J, which could be valued at 10 for either two Cleopatras or a tripled set of three kings, is documented as a two Cleopatra win.

The Sphinx serves as a scatter pay symbol. This means that the player receives a payout corresponding to the number of Sphinx symbols displayed anywhere on the screen, instead of needing them to align on a single pay-line. The payout is calculated as a multiple of the total bet amount based on the number of scatter symbols achieved. Below is the scatter payout table.

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

Line Pay Math

Winning Combinations — Not Multiplied

The following table provides the combinations for each possible win that does not involve wild symbols in the payout, save for wins solely derived from wilds. In simpler terms, wins that are not increased by a multiplier. Cells indicating no wins are left blank.

Winning Combinations — Doubled

The next table illustrates the combination counts for each possible win involving at least one Cleopatra symbol in the payout, apart from wins solely constituted by wilds. In other words, these are the multiplied winning combinations.

Be aware that calculating these combinations manually can be laborious and prone to mistakes. If you're feeling adventurous and possess programming skills, I recommend using five nested loops to iterate through all 30^4*41=33,210,000 outcomes.

The upcoming table presents the likelihood of each possible win for non-multiplied payouts. The bottom right cell reveals a hit rate of 1.85% for these non-multiplied wins.

Probabilities — Non-Doubled

Probabilities — Doubled

The following table shows the likelihood of each potential win for multiplied payouts. The lower right cell demonstrates a hit rate of 2.11% for wins that involve multipliers.

Returns — Non-Doubled

The next table provides the product of each winning probability with its respective payout for non-multiplied wins. Each cell reflects the product of the win probability and its payout. The lower right cell indicates that a player can expect to earn 8.17% of their bet amount per spin from non-multiplied line wins.

Returns — Doubled

The next table illustrates the product of each winning probability with its payout combined with a multiplier for multiplied wins. Each cell represents the result of multiplying the probability of winning by the win amount and 2. The lower right cell reveals that a player can anticipate a return of 40.89% of their bet per spin from multiplied line payouts.

Returns — Combined

The final table regarding line pays consolidates the returns from both multiplied and non-multiplied wins across each winning category. The bottom right cell reflects that a player can expect a total return of 52.05% of their bet per spin from line payouts.

Scatter Pay

The Sphinx functions as a 'scatter pay' symbol, rewarding the player based on the number of instances appearing anywhere on the screen. Unlike regular wins, these do not need to align left or match up on a single pay-line. Scatter wins are calculated based on the entire bet amount, not limited to the bet per pay-line.

The subsequent table outlines the probability and return contributions for various amounts of scatter wins. The last line reveals a hit frequency of 7.36% for scatter pays, contributing 17.51% to the overall return.

Bonus

When a player collects three or more scatter symbols, they gain access to a bonus round. This bonus features an initial set of 15 free spins, utilizing the same reel structure as the regular spins. All payouts, excluding five Cleopatras, are tripled. If the player achieves three or more scatter symbols during a free spin, they are awarded an additional 15 free spins.

As indicated previously in the scatter section, the likelihood of landing three or more scatters is 0.007256, which translates to roughly 1 in 138 chances. After factoring in the probability of re-triggering the bonus during a free spin, the average total number of free spins rounds up to approximately 16.832022. The rules state there is a maximum of 180 free spins, although the probability of reaching that threshold is virtually insignificant.

The final return table demonstrates that the line pays yield a return of 0.586609. From the scatter section, we note the scatter pays provide a return of 0.175078. Without the restriction of the jackpot (five Cleopatras), which doesn't receive a tripled payout, the value per free spin would calculate to 3×(0.520470+0.175078) = 2.086643. We must deduct from this amount two times the jackpot's value because it does not receive the tripling, calculated as 2×0.000602 = 0.001204. Therefore, the actual value of a free spin equates to 2.086643 - 0.001204 = 2.085439.

By multiplying the average number of free spins by the average payout per free spin, we arrive at the average bonus win of 16.832022 × 2.085439 = 35.102153.

To determine the overall return from the bonus, we multiply the bonus probability by the average bonus win, yielding 0.007256 × 35.102153 = 0.254704.

Summary of Return

The concluding table below summarizes the return for each winning category within Cleopatra. The lower right cell indicates the game's total return stands at 95.025%. The online game’s rules suggest a return of 95.02%, potentially due to rounding down. This explanation clarifies the source of that figure.

Frequency of Hits and Standard Deviation

The following table illustrates the hit frequency and standard deviation across all potential numbers of paylines wagered, ranging from 1 to 20. The standard deviation is expressed in two distinct formats:

• Total standard deviation: This reflects the overall standard deviation when wagering one credit for every payline.
• Relative standard deviation: This represents the ratio of the total standard deviation to the overall amount wagered. Essentially, it indicates the standard deviation in relation to the total stake.

The table below is derived from 20 random simulations — one for each number of lines wagered — each consisting of 100 million spins. The gathered data was generously provided by Casino Guru.

Internal Links

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

Acknowledgements

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

Written by: Michael Shackleford