Introduction to Roulette Wheels
After I explain to my audience casinos remotely adjust the odds of winning on individual slot machines every day, usually multiple times each day, I’m often asked by irate fans, “You’re saying the slot machines aren’t totally random??”
My reply is usually along the lines of, “Oh, slot machines are random. But their spinning reels aren’t like roulette wheels.”
While this comparison enlightens some slots enthusiasts, you deserve a better explanation.
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Roulette Wheel Randomness
A roulette wheel is a random number generator. A dealer spins the numbered wheel in one direction while flinging a small white ball in the opposite direction to ride along its edge.
Eventually, in a rather exciting fashion, both the wheel and ball slow down and stop moving. Just before they both stop moving, the ball ends up in a numbered recess on the wheel.
With a balanced and level wheel, and no abrupt breaking applied when turning, this a random process. Like flipping a coin, there is an equal chance for each possible outcome. In other words, the ball is as likely to end up in any one slot as any other slot.
This randomness, like flipping a coin or rolling dice, is what most people consider to be the only type of random behavior. Yet what if the rolling die is misshapen, the coin bent, or the roulette wheel not perfectly level? Are these still random processes?
Yes, they are random. However, what’s changed is that there is no longer an equal chance for each possible outcome. For example, a malformed six-sided die where every side has a different surface area is still random, but different surface areas correlate to the likeliness of an outcome.
For the misshapen die, there is still a chance for each possible outcome, but no longer an equal chance.
RNGs in Slot Machines
Let’s incorrectly consider the physical reels on a non-video slot machine turn freely like roulette wheels. Meaning, they come to a halt due to axle friction and air resistance. Other setup conditions for this example include:
- Three reels
- A single pay line for one possible reel combination outcome
- Twelve stops per reel, i.e., twelve symbols per reel
What are the odds of winning? First, there are 12 x 12 x 12 equals 1,728 possible reel combination outcomes. Next, let’s estimate there are 100 possible winning reel combinations.
The odds of winning, just like throwing a die, is possible winning outcomes divided by total possible outcomes. Using the above conditions, the odds of one outcome is 100/1,728 or just under 6%.
If there was an equal chance for every outcome, including the 1,628 non-winning outcomes, there’s a 6% chance of getting one of the 100 winning reel combinations.
Further, because all outcomes have an equal chance of 1/1,728 or 0.06%, the top jackpot reel combination is just as likely as any other identical symbols reel combinations, such as three 1-bar symbols worth far less than the top jackpot.
Since theoretical payout limits are often a legal minimum of 75% and return statistics usually near 90%, it’s obvious a 6% chance of winning in our model isn’t how slot machines work.
Slot machines aren’t random like roulette wheels. Instead of the type of randomness where there is an equal chance of winning like roulette wheel or perfect die, slot machines use the type of randomness from weighted averages.
Average Versus Weighted Average
If you roll a perfectly shaped die or spin a balanced roulette wheel, you have an equal chance at every possible outcome. Because that chance is so low, less than 6% to get a winning reel combination, slots machines would not be popular to play. At all.
Only 6% chance to win would mean slots machines would be a historic oddity few would remember. But instead, they are the mostly game in modern casinos. By far.
Game designers don’t determine the odds of winning. Instead, they create reel symbols, bonus games, and game rules to create the best possible player appeal. When they finish their design work, one of their obligations is to hand over a list of game outcomes.
This list a table of reel symbol combinations with how many credits won. As already explained for an old-style slot machine, most of these outcomes are a zero win.
The game designer’s employer takes this table and removes all outcomes which have the same win amount. Not only are all but one of the many zero returns removed, it removes all other duplicates. This leaves a much shorter list ranked in order from a zero win to the top jackpot.
At this point, this other team the game designers hand their work off to applies a weighted average to this list of outcomes. Let’s call them the Odds Team. Their work is like the misshapen die discussed previously.
For a slot machine, there might be 100 possible winning outcomes. Adding an outcome for zero, the Odds Team is essentially creating a misshapen die with 101 sides.
Each side of this misshapen 101-sided die would have a different surface area, with the zero-win result having the largest area. While large, this surface area for the zero side is much smaller than it would have been otherwise.
Dropping the die analogy, this Odds Team creates this list of weights to apply a weighted average to the output of the Random Number Generator (RNG). Historically, before central servers arrived in 2012, they did this six times. Yes, they generated six sets of weighted averages.
Before central servers, these weighted averages were loaded into slot machines for one set to be selected by the casino at any given time. But they weren’t programmed into the RNG, not exactly. This is what that old 2009 video with 8 million views trying to explain this gets wrong.
Before central servers, an army slot mechanics would regularly open a slot machine and manually enter a code associated with one of these sets of weighted average. They did this about once every seven to ten days.
Probability Distributions Matter
With central servers, casinos were able to reduce their army of slot machine mechanics to only enough employees to perform maintenance of their slot machines. Like cleaning fans, replacing broken buttons, or installing new slot machines after removing ones. Gone are the long days spent up updating the odds of winning on individual slot machines.
Casinos reduced their operational costs by reducing the number of slot machine mechanics needed. This was the second-greatest benefit to them for switching to a central computer server remotely updating the odds of individual slot machines.
The greatest advantage for casino was how fast the central server can remotely update the odds. Instead of seven to ten for slots mechanics, the server can update every slot machine daily, hourly, or more often.
But to this they need two things. They need sets of weighted averages, also known as probability distributions in the field of statistics, and a plan. Casinos need a business plan. And slot machine manufacturers, who also make central computer serves for casinos, are happy to provide them.
Casino Central Servers
Slot machine manufacturers don’t just fabricate slot machines and development game themes. These global businesses include other business segments for lottery, online gaming, and casino operating software and hardware solutions. They provide casino central servers along with the software algorithm which remotely controls all slot machines in that casino.
Prior to their arrival in 2012, casino operations were approaching the limit of what was possible. Beforehand, casino processes needed pen and paper, an army of slot machine mechanics, and a massive accounting department. Now, operational software has automated casinos to easily allow them to withstand large crowds.
With central servers, not only can casinos handle larger crowds. but those crowds are happier. Everything happens faster and with less errors leading to greater customer satisfaction not possible, for example, with overworked casino employees running a slot tournament with a clipboard manually entering results into a spreadsheet.
Besides enabling improved customer relations, central servers save casinos a lot of money in different ways. For instance, server systems help casinos comply with local gaming regulations.
Further, savings come from a significantly reduced workforce such as reducing an army of slot machine mechanics no longer needed to physically change the odds of winning on 1,000s of gaming machines as fast as possible.
Remote control by the central server both reduced this workforce while speeding up turnaround time from several days to instantaneous. This increased efficiency also allows casinos to reduce risk and more accurately meet their daily performance metrics, both huge money savers.
Summary of Roulette Wheels
There are few educational opportunities for learning how slot machines work in modern casino environments. The random behavior of slot machines is more complex than most players are aware. A place to start is improving a common misunderstanding involving the concept of randomness.