Aces Guide to Gambling

Casino Slot Machine Strategy -

Odds on Slot Machines

About The Author

Michael Shackleford is known as "The Wizard of Odds", due to his mathematical analysis of many games of chance.

If you are willing to learn and want to maximize your odds, then visit his website at www.thewizardofodds.com

The Wizard of Odds

In my experience slot machines are the most misunderstood form of gambling in the casinos. The false statements on how the machines actually work in several books make the hair on the back of my neck stand up.

Most books on slot machines incorrectly state that you can figure out their average payback by taking the payoff table and frequency of each symbol on each reel and doing the math. For example one book states that if a three reel machine has 20 symbols on each reel and one gold seven on each one then the odds of hitting 3 gold 7s is (1/20)3 = 1/8,000.

This statement is based on the assumption that each reel can stop on any symbol with equal probability, which is simply not true.

For evidence, visit the IGT home page which indicates the progressive jackpots on a variety of slot machines. Typical slot machines, like the Triple Diamond, have three reels with 22 stops on each reel. Assuming each stop on each reel were equally likely and only one combination qualified for the jackpot then the odds of hitting the jackpot would be 1 in 223 or 1 in 10,648. Using the Quartermania machine as an example which had a jackpot of $1,421,399 on June 20, 1999 the expected return of the maximum 50 cent bet would be $1,421,399*(1/10,468) = $133.49, and that is without counting all the lower paying wins. If the books about slot machines were right then this machine would pay back at least 26,698%. Again it must be concluded that the odds of hitting the jackpot are much less than 1 in 10,648 and thus each combination of stops is not equally likely.

How Slot Machines Work

For IGT, Bally, and Anchor slot machines:

  • Every second the machine, whether being played or not, chooses numerous random integers between 1 to 4,294,967,295 (232-1).

  • When you put in a coin or spin the reels, the machine selects the next three of these random numbers.

  • Each of these random numbers is then divided by a specific number, 64 or greater with IGT slots and 32 for Ballys. If the divisor were 64 then the remainders would be uniformly distributed integers in the range of 0 to 63.

  • Each of these remainders is then associated or mapped to one of the usually 22 stops on the actual reel, one remainder for each reel. These mapping functions are known as "virtual reels" because they are like a 64 position reel but don't physically exist.

    There is not a one to one relationship between remainders and positions on the reel, many remainders are typically mapped to the blank positions directly above or below jackpot symbols and only one remainder will be mapped to the jackpot symbol itself. The manufacturer designs these mapping functions to achieve desired payback percentages requested by the casino.

    For machines with very large jackpots relative to the coinage the divisor is much greater, for example 256 or 512 for games like Quatermania and Megabucks, to achieve very long odds of hitting the jackpot. Assuming one number out of 256 were mapped to each jackpot symbol the odds of hitting the jackpot would be in 1 in 2563 or 1 in 16,777,216.

    IGT owns the patent on the process described above and has allowed Ballys a license stipulating that the divisor could not be greater than 32, thus not allowing them to create machines with huge jackpots with small coinages. IGT leases the use of their idea to many other makers of slot machines.

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