Slot Machines

Last update: September 14, 2007

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How They Work

A good place to begin a discussion about slot machines is to explain how they really work, in the United States at least. My credentials to speak to this topic are that I have seen hundreds of PARS (an acronym for Program and Reel Strips) sheets, which show exactly how they are designed, and I know many dozens of people in the slot machine manufacturing business. Contrary to popular myth, the outcome of each play is determined by random numbers, and each play is completely independent of past outcomes.

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.

After the player makes a bets 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.

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.

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.

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.

Variable State Slots

Some slot machines have a feature in which a bonus rises the more the player plays it. When the reels stop in a particular configuration the player wins the coins in the meter. These kinds of slots have variable states. In other words the higher the state the greater the expected payback. Examples of this kind of machine include Piggy Bank, Car Race, Temperature Rising, and Double Diamond Mine.

It is possible to have a positive expected value playing slots if you only play variable state slots in very high states. Sometimes casual players will walk away from a machine in a high state. However this secret is long since out and competition for these games can be severe, fistfights have been known to occur over them.

Myths

Below are some of the biggest myths about slot machines.

• Slot machines stop on any possible set of stops with equal probability

  As explained above this is not true of modern three-reel slot machines. Some stops are much more likely than others.

• Slot machines are programmed to go through a cycle of payoffs. Although the cycle can span thousands of spins once it reaches the end the outcomes will repeat themselves in exactly the same order as the last cycle.

  This is not true at all. Every trial is random and independent of all past trials.

• Slot machines are programmed to pay off a particular percentage of money bet. Thus after a jackpot is hit the machine will tighten up to get back in balance, and when a jackpot has not been hit for a long time it is overdue and more likely to hit.

  The only part of this that is true is that they are designed to pay off a particular percentage. However the laws of probability dictate that the longer the machine is played the closer it will come to its target payoff, even with every trial being completely random. A jackpot is equally as likely to be hit on every spin, regardless of past outcomes.

• Hot/cold coins are more likely to yield good returns.

  The temperature of the coin does not matter. It also does not matter how long it has been since the coin was last played.

• Machines pay more if a player card is not used.

  The mechanism that determines the outcome of each play does not consider whether a card is used or not. Not considering cash back and comps the odds are the same with or without a player card.

• If I use a slot card the casino will report my winnings to the IRS.

  The use of a slot card will not change your tax liability. If you get back $1200 or more in a single spin (including the original wager) then the casino will report the win whether a slot card is used or not. The casino does not add up the smaller wins and report them to the IRS. Aside from the big wins, the player is on the honor system to report a net win over the entire year.

Other Tips

Here are some other miscellaneous tips to help you cut down the house edge.

• Most machines reward you for playing the maximum coins. For example the jackpot may pay 2000 coins with 2 coins played, but 4000 with 3 coins played. Many other gambling writers advise the player to always play the maximum coins. However if the max coin incentive is small I believe it is better to play one coin at a higher coinage than max coins at a lower coinage. This is because casinos increase the return percentage as the coinage goes up.
• Don't forget to cash out and take your coins or ticket when you leave a machine. Vegas is full of vultures looking for machines people left with credits or a ticket hanging out.
• Look for certain banks of machines that are certified to a certain percentage. Some casinos will have banks of dollar machines that are certified at 97% payback or so. Be careful to believe claims such as "our slots return 97%." This likely refers to just certain machines, so look for those specifically under a sign indicating their payback percentage.
• Check the slot card reader from time to time. Sometimes contact will be lost for no apparent reason and you won't get credit for any play until you reinsert it.
• Tipping in slots, as well as all electronic games, is a matter of much debate. After discussing this with a number of experts in this area I think a good rule of thumb is to tip 0.5% to 1.0% on any jackpot requiring a hand pay. The smaller the jackpot the larger the percentage.

Beware of Scams

As with most casinos games there is no shortage of con men selling books or systems explaining how to beat slots. One possible way to beat slots over the long run is to look for variable state slots abandoned in a high state, which I explain above. That angle has been well known for years and in my opinion is not a practical use of time. Another is to play progressives at extremely high amounts. Other than that I claim there is no other way to gain an advantage over slots. There really are no secrets about slot machines. Anyone who claims they have some secret to beating them is trying to scam you.

Las Vegas Slot Machine Survey

In 2002 I did a survey of the loosest slots in Vegas. Here are my results, which were widely quoted by the winner. This survey is rather dated now so take it with a grain of salt.

For the entire list please visit my slot machine appendix 3.

Play for Free Slot Machine

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Other Slot Guides

Another decent overview of how slots work and some practical advice for playing them is How Slot Machines Work at VegasClick.com.

Appendices

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.
Baltimore Sun article, in which I am quoted.
Reno Gazette article (9/30/03), in which I am quoted.
Las Vegas Sun article, in which I am quoted about the "statistically overdue" Megabucks advertising.

Translation Links

A German translation of this page is available at richtigspielen.com.