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Slot Machine Appendix 6 - Red White & Blue Analysis
In the past I feared to show a concrete example on this page, not wanting to violate copyright laws. However, in the Netherlands, information on the reel stripping and probabilities of each win are sometimes posted on small cards on the machine. A fan of the site sent me the information provided on an IGT "Red White & Blue" machine.
First, let me present the pay table. For those who are not familiar with the game, a 3-bar is in blue, a 2-bar is in white, and a 1-bar is in red.
Pay Table for Red White & Blue
|Win||1 Coin||2 Coins||3 Coins|
|Red 7, white 7, blue 7||2400||4800||10000|
|Red 7, red 7, red 7||1199||2400||5000|
|White 7, white 7, white 7||200||400||600|
|Blue 7, blue 7, blue 7||150||300||450|
|Any 3 sevens||80||160||240|
|1 bar, 2 bar, 3 bar||50||100||150|
|3 bar, 3 bar, 3 bar||40||80||120|
|2 bar, 2 bar, 2 bar||25||50||75|
|Any red, any white, any blue||20||40||60|
|1 bar, 1 bar, 1 bar||10||20||30|
|Any 3 bars||5||10||15|
|Any 3 reds||2||4||6|
|Any 3 white||2||4||6|
|Any 3 blues||2||4||6|
|Blank, blank, blank||1||2||3|
After the player makes a bet and presses the spin button, the machine selects three random numbers, one for each reel. These are chosen from a random number generator that is constantly drawing random numbers at a rate of thousands per second. The numbers chosen at the moment the play is initiated are the ones used to determine the final outcome. In other words the outcome is predestined the moment you press the spin button.
In the case of Red White & Blue, each random number has 64 equally likely outcomes. Each random number is mapped to a stop position on what is called a "Lookup Table." The following is my estimate of what the Red White & Blue lookup table looks like, based on the total number of stops per symbol per reel, provided to me.
Lookup Table for Red White & Blue
|Stop Number||Reel 1||Reel 2||Reel 3|
|1||2 bar||2 bar||2 bar|
|2||2 bar||2 bar||2 bar|
|3||2 bar||blank||2 bar|
|6||3 bar||3 bar||3 bar|
|10||blank||white 7||white 7|
|11||white 7||blank||white 7|
|12||white 7||blank||white 7|
|13||white 7||blank||white 7|
|14||white 7||1 bar||white 7|
|15||white 7||1 bar||white 7|
|16||white 7||1 bar||white 7|
|20||1 bar||blank||1 bar|
|21||1 bar||blue 7||1 bar|
|22||1 bar||blue 7||1 bar|
|23||blank||blue 7||1 bar|
|24||blank||blue 7||1 bar|
|26||blue 7||blue 7||blank|
|27||blue 7||blue 7||blank|
|28||blue 7||blank||blue 7|
|31||blue 7||2 bar||blank|
|32||blank||2 bar||2 bar|
|35||2 bar||3 bar||blank|
|36||2 bar||3 bar||blank|
|43||blank||red 7||red 7|
|50||blank||3 bar||3 bar|
|51||3 bar||3 bar||3 bar|
|52||3 bar||3 bar||blank|
|55||blank||2 bar||2 bar|
|56||2 bar||2 bar||2 bar|
|59||blank||1 bar||1 bar|
|60||1 bar||1 bar||1 bar|
|61||1 bar||1 bar||1 bar|
|62||1 bar||1 bar||1 bar|
Immediately after the random numbers are chosen they will get mapped to a stop on the machine via the Lookup Table, the outcome will be scored, and the player paid if he won anything. For example, if the random numbers chosen were 26, 8, and 43 the player would get Blue 7, Blank, Red 7.
Note how there are clusters of the same symbol in a row. For example, stops 60 to 62 on reel 1 all are mapped to a 1 bar symbol. These will all be directed to the same 1 bar symbol on the actual reel. There are exactly 22 groups of like symbols on each reel, which is the standard number of stops on an electro-mechanical three-reel slot machine, known as a "Stepper Slot."
Also note that only stop 45 on reel 1 is mapped to the red 7 symbol. However the blanks above and below it have five positions each. This causes the often seen near miss effect, where the reel stops directly above or below the highest paying symbol. Many people have written to me, claiming that this near miss effect is against the law. My slot machine Appendix 1 proves otherwise.
To calculate the return of the machine, add up the number of positions for each symbol on each reel, to get the total symbol weightings. The following table shows these totals. This table is what was indicated on the Red White & Blue machine in the Netherlands. The Lookup Table above, was reverse engineered to produce these total weights.
|Total Weights for Red White & Blue|
|Stop Number||Reel 1||Reel 2||Reel 3|
With the weighting of each symbol and reel known, it is just take simple math to calculate the return. The following table shows the win, number of combinations, probability, and contribution to the return for all possible events. For example, the table above shows the number of white 7's are 6, 1, and 7, for reels 1, 2, and 3 respectively. The total number of winning combinations for three white sevens is thus 6 × 1 × 7 = 42.
Return Table for Red White & Blue
|Red 7, white 7, blue 7||2400||1||0.000004||0.009155|
|Red 7, red 7, red 7||1199||3||0.000011||0.013721|
|White 7, white 7, white 7||200||42||0.000160||0.032043|
|Blue 7, blue 7, blue 7||150||42||0.000160||0.024033|
|Any 3 sevens||80||1199||0.004574||0.365906|
|1 bar, 2 bar, 3 bar||50||180||0.000687||0.034332|
|3 bar, 3 bar, 3 bar||40||210||0.000801||0.032043|
|2 bar, 2 bar, 2 bar||25||378||0.001442||0.036049|
|Any red, any white, any blue||20||113||0.000431||0.008621|
|1 bar, 1 bar, 1 bar||10||432||0.001648||0.016479|
|Any 3 bars||5||7977||0.030430||0.152149|
|Any 3 reds||2||335||0.001278||0.002556|
|Any 3 white||2||1036||0.003952||0.007904|
|Any 3 blues||2||756||0.002884||0.005768|
|Blank, blank, blank||1||32768||0.125000||0.125000|
The lower right cell shows a return of 86.58%. That means that for every dollar bet at the one coin level, the player will get back 86.58 cents, on average. Doing the same table for two coins results in a return of 86.58% as well, and three coins has a higher return of 87.47%, due to the disproportionately high win on the top two pays. The standard deviation is 9.03 for 1 or 2 coins, and 10.80 for 3 coins.
Other Information on Slots
- Slots main page
- Appendix 1 shows the details and analysis of almost 4000 actual spins on a Reno slot machine.
- Appendix 2 shows an example of the virtual reels behind a hypothetical slot machine and how the average return is calculated.
- Appendix 3A Las Vegas slot machine rankings.
- Appendix 3B Jean/Primm slot machine rankings.
- Appendix 3C Tunica slot machine rankings.
- Appendix 3D Henderson/Lake Mead slot machine rankings.
- Appendix 3E Quarter and dollar returns for Las Vegas slots
- Appendix 3F Miscellaneous slot machine rankings.
- Appendix 4 shows how the return is calculated for my Wizard's Fruit Slot Machine
- Appendix 5 analysis of the 21 Bell Slot Machine.
- Lock and Roll analysis of the skill-based slot machine found in North Carolina.
- Deconstructing Megabucks
- Baltimore Sun article in which I am quoted.
- For a simplified explanation of slots, please see my companion site Wizard of Vegas.
- German translation of this page is available at richtigspielen.com.
- Another decent overview of how slots work and some practical advice for playing them is How Slot Machines Work at VegasClick.com.
- PAR Sheets, probabilities, and slot machine play:Implications for problem and non-problem gambling by Kevin A. Harrigan and Mike Dixon, University of Waterloo, Waterloo, Ontario, Canada. This is an outstanding academic paper that details how some popular slot machines were designed.
- Blazing Sevens simulator.